Noncommuting Electric Fields and Algebraic Consistency in Noncommutative Gauge theories
Banerjee, R
2003-01-01
We show that noncommuting electric fields occur naturally in noncommutative gauge theories. Using this noncommutativity, which is field dependent, and a hamiltonian generalisation of the Seiberg-Witten Map, the algebraic consistency in the lagrangian and hamiltonian formulations of these theories, is established. The stability of the Poisson algebra, under this generalised map, is studied.
Noncommuting electric fields and algebraic consistency in noncommutative gauge theories
Banerjee, Rabin
2003-05-01
We show that noncommuting electric fields occur naturally in θ-expanded noncommutative gauge theories. Using this noncommutativity, which is field dependent, and a Hamiltonian generalization of the Seiberg-Witten map, the algebraic consistency in the Lagrangian and Hamiltonian formulations of these theories is established. A comparison of results in different descriptions shows that this generalized map acts as a canonical transformation in the physical subspace only. Finally, we apply the Hamiltonian formulation to derive the gauge symmetries of the action.
Noncommutative Gauge Theories: Model for Hodge theory
Upadhyay, Sudhaker
2013-01-01
The nilpotent BRST, anti-BRST, dual-BRST and anti-dual-BRST symmetry transformations are constructed in the context of noncommutative (NC) 1-form as well as 2-form gauge theories. The corresponding Noether's charges for these symmetries on the Moyal plane are shown to satisfy the same algebra as by the de Rham cohomological operators of differential geometry. The Hodge decomposition theorem on compact manifold is also studied. We show that noncommutative gauge theories are field theoretic models for Hodge theory.
The Dyon Charge in Noncommutative Gauge Theories
Directory of Open Access Journals (Sweden)
L. Cieri
2008-01-01
Full Text Available We construct a dyon solution for the noncommutative version of the Yang-Mills-Higgs model with a ϑ-term. Extending the Noether method to the case of a noncommutative gauge theory, we analyze the effect of CP violation induced both by the ϑ-term and by noncommutativity proving that the Witten effect formula for the dyon charge remains the same as in ordinary space.
Holographic Entanglement in a Noncommutative Gauge Theory
Fischler, Willy; Kundu, Sandipan
2014-01-01
In this article we investigate aspects of entanglement entropy and mutual information in a large-N strongly coupled noncommutative gauge theory, both at zero and at finite temperature. Using the gauge-gravity duality and the Ryu-Takayanagi (RT) prescription, we adopt a scheme for defining spatial regions on such noncommutative geometries and subsequently compute the corresponding entanglement entropy. We observe that for regions which do not lie entirely in the noncommutative plane, the RT-prescription yields sensible results. In order to make sense of the divergence structure of the corresponding entanglement entropy, it is essential to introduce an additional cut-off in the theory. For regions which lie entirely in the noncommutative plane, the corresponding minimal area surfaces can only be defined at this cut-off and they have distinctly peculiar properties.
Holographic entanglement in a noncommutative gauge theory
Energy Technology Data Exchange (ETDEWEB)
Fischler, Willy [Theory Group, Department of Physics, University of Texas,Austin, TX 78712 (United States); Texas Cosmology Center, University of Texas,Austin, TX 78712 (United States); Kundu, Arnab [Theory Group, Department of Physics, University of Texas,Austin, TX 78712 (United States); Kundu, Sandipan [Theory Group, Department of Physics, University of Texas,Austin, TX 78712 (United States); Texas Cosmology Center, University of Texas,Austin, TX 78712 (United States)
2014-01-24
In this article we investigate aspects of entanglement entropy and mutual information in a large-N strongly coupled noncommutative gauge theory, both at zero and at finite temperature. Using the gauge-gravity duality and the Ryu-Takayanagi (RT) prescription, we adopt a scheme for defining spatial regions on such noncommutative geometries and subsequently compute the corresponding entanglement entropy. We observe that for regions which do not lie entirely in the noncommutative plane, the RT-prescription yields sensible results. In order to make sense of the divergence structure of the corresponding entanglement entropy, it is essential to introduce an additional cut-off in the theory. For regions which lie entirely in the noncommutative plane, the corresponding minimal area surfaces can only be defined at this cut-off and they have distinctly peculiar properties.
Noncommutative SO(2,3) gauge theory and noncommutative gravity
Dimitrijevic, Marija
2014-01-01
In this paper noncommutative gravity is constructed as a gauge theory of the noncommutative SO(2,3) group, while the noncommutativity is canonical (constant). The Seiberg-Witten map is used to express noncommutative fields in terms of the corresponding commutative fields. The commutative limit of the model is the Einstein-Hilbert action with the cosmological constant term and the topological Gauss-Bonnet term. We calculate the second order correction to this model and obtain terms that are of zeroth to fourth power in the curvature tensor and torsion. Trying to relate our results with $f(R)$ and $f(T)$ models, we analyze different limits of our model. In the limit of big cosmological constant and vanishing torsion we obtain a $x$-dependent correction to the cosmological constant, i.e. noncommutativity leads to a $x$-dependent cosmological constant. We also discuss the limit of small cosmological constant and vanishing torsion and the teleparallel limit.
Exact formulas in noncommutative gauge theories
Wallet, Jean-Christophe
2016-01-01
The noncommutative space $\\mathbb{R}^3_\\lambda$, a deformation of $\\mathbb{R}^3$, supports a $3$-parameter family of gauge theory models with gauge-invariant harmonic term, stable vacuum and which are perturbatively finite to all orders. Properties of this family are discussed. The partition function factorizes as an infinite product of reduced partition functions, each one corresponding to the reduced gauge theory on one of the fuzzy spheres entering the decomposition of $\\mathbb{R}^3_\\lambda$. For a particular sub-family of gauge theories, each reduced partition function is exactly expressible as a ratio of determinants. A relation with integrable 2-D Toda lattice hierarchy is indicated.
Noncommutative Geometric Gauge Theory from Superconnections
Lee, Chang-Yeong
1996-01-01
Noncommutative geometric gauge theory is reconstructed based on the superconnection concept. The bosonic action of the Connes-Lott model including the symmetry breaking Higgs sector is obtained by using a new generalized derivative, which consists of the usual 1-form exterior derivative plus an extra element called the matrix derivative, for the curvatures. We first derive the matrix derivative based on superconnections and then show how the matrix derivative can give rise to spontaneous symm...
A review of non-commutative gauge theories
Indian Academy of Sciences (India)
N G Deshpande
2003-02-01
Construction of quantum ﬁeld theory based on operators that are functions of non-commutative space-time operators is reviewed. Examples of 4 theory and QED are then discussed. Problems of extending the theories to () gauge theories and arbitrary charges in QED are considered. Construction of standard model on non-commutative space is then brieﬂy discussed. The phenomenological implications are then considered. Limits on non-commutativity from atomic physics as well as accelerator experiments are presented.
C, P, and T invariance of noncommutative gauge theories
Sheikh-Jabbari
2000-06-05
In this paper we study the invariance of the noncommutative gauge theories under C, P, and T transformations. For the noncommutative space (when only the spatial part of straight theta is nonzero) we show that noncommutative QED (NCQED) is parity invariant. In addition, we show that under charge conjugation the theory on noncommutative R(4)(straight theta) is transformed to the theory on R(4)(-straight theta), so NCQED is a CP violating theory. The theory remains invariant under time reversal if, together with proper changes in fields, we also change straight theta by -straight theta. Hence altogether NCQED is CPT invariant. Moreover, we show that the CPT invariance holds for general noncommutative space-time.
Compactified D=11 supermembranes and symplectic noncommutative gauge theories
Martín, I.; Ovalle, J.; Restuccia, A.
2001-08-01
It is shown that a double compactified D=11 supermembrane with nontrivial wrapping may be formulated as a symplectic noncommutative gauge theory on the world volume. The symplectic noncommutative structure is intrinsically obtained from the symplectic two-form on the world volume defined by the minimal configuration of its Hamiltonian. The gauge transformations on the symplectic fibration are generated by the area preserving diffeomorphisms on the world volume. Geometrically, this gauge theory corresponds to a symplectic fibration over a compact Riemann surface with a symplectic connection.
Compactified D=11 supermembranes and symplectic noncommutative gauge theories
Energy Technology Data Exchange (ETDEWEB)
Martin, I.; Ovalle, J.; Restuccia, A.
2001-08-15
It is shown that a double compactified D=11 supermembrane with nontrivial wrapping may be formulated as a symplectic noncommutative gauge theory on the world volume. The symplectic noncommutative structure is intrinsically obtained from the symplectic two-form on the world volume defined by the minimal configuration of its Hamiltonian. The gauge transformations on the symplectic fibration are generated by the area preserving diffeomorphisms on the world volume. Geometrically, this gauge theory corresponds to a symplectic fibration over a compact Riemann surface with a symplectic connection.
Yukawa couplings and seesaw neutrino masses in noncommutative gauge theory
Energy Technology Data Exchange (ETDEWEB)
Horvat, Raul [Physics Division, Rudjer Boskovic Institute, Bijenicka 54, Zagreb (Croatia); Ilakovac, Amon [Faculty of Science, University of Zagreb, Bijenicka 32, Zagreb (Croatia); Schupp, Peter [Center for Mathematics, Modeling and Computing, Jacobs University Bremen, Campus Ring 1, 28759 Bremen (Germany); Trampetic, Josip [Physics Division, Rudjer Boskovic Institute, Bijenicka 54, Zagreb (Croatia); Max-Planck-Institut fuer Physik, Werner-Heisenberg-Institut, Foehringer Ring 6, D-80805 Muenchen (Germany); You, Jiangyang, E-mail: Jiangyang.You@irb.hr [Physics Division, Rudjer Boskovic Institute, Bijenicka 54, Zagreb (Croatia)
2012-09-10
We consider Yukawa couplings in a {theta}-exact approach to noncommutative gauge field theory and show that both Dirac and singlet Majorana neutrino mass terms can be consistently accommodated. This shows that in fact the whole neutrino-mass extended standard model on noncommutative spacetime can be formulated in the new nonperturbative (in {theta}) approach which eliminates the previous restriction of Seiberg-Witten map based theories to low-energy phenomena. Spacetime noncommutativity induced couplings between neutrinos and photons as well as Z-bosons appear quite naturally in the model. We derive relevant Feynman rules for the type I seesaw mechanism.
Gauge Theories on Open Lie Algebra Noncommutative Spaces
Agarwal, A.; Akant, L.
It is shown that noncommutative spaces, which are quotients of associative algebras by ideals generated by highly nonlinear relations of a particular type, admit extremely simple formulae for deformed or star products. Explicit construction of these star products is carried out. Quantum gauge theories are formulated on these spaces, and the Seiberg-Witten map is worked out in detail.
Graviton Propagators in Supergravity and Noncommutative Gauge Theory
Kitazawa, Y; Kitazawa, Yoshihisa; Nagaoka, Satoshi
2007-01-01
We investigate the graviton propagator in the type IIB supergravity background which is dual to 4 dimensional noncommutative gauge theory. We assume that the boundary is located not at the infinity but at the noncommutative scale where the string frame metric exhibits the maximum. We argue that the Neumann boundary condition is the appropriate boundary condition to be adopted at the boundary. We find that the graviton propagator behaves just as that of the 4 dimensional massless graviton. On the other hand, the non-analytic behaviors of the other Kaluza-Klein modes are not significantly affected by the Neumann boundary condition.
D-branes, symplectomorphisms and noncommutative gauge theories
Energy Technology Data Exchange (ETDEWEB)
Martin, I.; Ovalle, J.; Restuccia, A
2001-09-01
It is shown that the dual of the double compactified D=11 Supermembrane and a suitable compactified D=10 Super 4D-brane with nontrivial wrapping on the target space may be formulated as non-commutative gauge theories. The Poisson bracket over the world-volume is intrinsically defined in terms of the minima of the hamiltonian of the theory, which may be expressed in terms of a non degenerate 2-form. A deformation of the Poisson bracket in terms of the Moyal brackets is then performed. A non-commutative gauge theory in terms of the Moyal star bracket is obtained. It is shown that all these theories may be described in terms of symplectic connections on symplectic fibrations, the world volume being its base manifold and the (sub)group of volume preserving diffeomorphisms, p = 2 (p > 2), generate the symplectomorphisms which preserve the (infinite dimensional) Poisson bracket of the fibration.
D-branes, symplectomorphisms and noncommutative gauge theories
Martín, I.; Ovalle, J.; Restuccia, A.
It is shown that the dual of the double compactified D=11 Supermembrane and a suitable compactified D=10 Super 4D-brane with nontrivial wrapping on the target space may be formulated as non-commutative gauge theories. The Poisson bracket over the world-volume is intrinsically defined in terms of the minima of the hamiltonian of the theory, which may be expressed in terms of a non degenerate 2-form. A deformation of the Poisson bracket in terms of the Moyal brackets is then performed. A non-commutative gauge theory in terms of the Moyal star bracket is obtained. It is shown that all these theories may be described in terms of symplectic connections on symplectic fibrations, the world volume being its base manifold and the (sub)group of volume preserving diffeomorphisms, p = 2 ( p > 2), generate the symplectomorphisms which preserve the (infinite dimensional) Poisson bracket of the fibration.
The Seiberg-Witten Map for Noncommutative Gauge Theories
Cerchiai, B L; Zumino, B
2002-01-01
The Seiberg-Witten map for noncommutative Yang-Mills theories is studied and methods for its explicit construction are discussed which are valid for any gauge group. In particular the use of the evolution equation is described in some detail and its relation to the cohomological approach is elucidated. Cohomological methods which are applicable to gauge theories requiring the Batalin-Vilkoviskii antifield formalism are briefly mentioned. Also, the analogy of the Weyl-Moyal star product with the star product of open bosonic string field theory and possible ramifications of this analogy are briefly mentioned.
Space-Time Diffeomorphisms in Noncommutative Gauge Theories
Directory of Open Access Journals (Sweden)
L. Román Juarez
2008-07-01
Full Text Available In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007, 10367–10382] we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the theory, the representation of space-time diffeomorphisms provides a very convenient scheme for analyzing the induced twisted deformation of these diffeomorphisms, as a result of the space-time noncommutativity. However, for gauge field theories (and of course also for canonical geometrodynamics where the Poisson brackets of the constraints explicitely depend on the embedding variables, this Poisson algebra cannot be connected directly with a representation of the complete Lie algebra of space-time diffeomorphisms, because not all the field variables turn out to have a dynamical character [Isham C.J., Kuchar K.V., Ann. Physics 164 (1985, 288–315, 316–333]. Nonetheless, such an homomorphic mapping can be recuperated by first modifying the original action and then adding additional constraints in the formalism in order to retrieve the original theory, as shown by Kuchar and Stone for the case of the parametrized Maxwell field in [Kuchar K.V., Stone S.L., Classical Quantum Gravity 4 (1987, 319–328]. Making use of a combination of all of these ideas, we are therefore able to apply our canonical reparametrization approach in order to derive the deformed Lie algebra of the noncommutative space-time diffeomorphisms as well as to consider how gauge transformations act on the twisted algebras of gauge and particle fields. Thus, hopefully, adding clarification on some outstanding issues in the literature concerning the symmetries for gauge theories in noncommutative space-times.
Derivations of the Moyal algebra and noncommutative gauge theories
Wallet, Jean-Christophe
2008-01-01
The differential calculus based on the derivations of an associative algebra underlies most of the noncommutative field theories considered so far. We review the essential properties of this framework and the main features of noncommutative connections in the case of non graded associative unital algebras with involution. We extend this framework to the case of ${\\mathbb{Z}}_2$-graded unital involutive algebras. We show, in the case of the Moyal algebra or some related ${\\mathbb{Z}}_2$-graded version of it, that the derivation based differential calculus is a suitable framework to construct Yang-Mills-Higgs type models on Moyal (or related) algebras, the covariant coordinates having in particular a natural interpretation as Higgs fields. We also exhibit, in one situation, a link between the renormalisable NC $\\varphi^4$-model with harmonic term and a gauge theory model. Some possible consequences of this are briefly discussed.
Derivations of the Moyal Algebra and Noncommutative Gauge Theories
Directory of Open Access Journals (Sweden)
Jean-Christophe Wallet
2009-01-01
Full Text Available The differential calculus based on the derivations of an associative algebra underlies most of the noncommutative field theories considered so far. We review the essential properties of this framework and the main features of noncommutative connections in the case of non graded associative unital algebras with involution. We extend this framework to the case of Z2-graded unital involutive algebras. We show, in the case of the Moyal algebra or some related Z2-graded version of it, that the derivation based differential calculus is a suitable framework to construct Yang-Mills-Higgs type models on Moyal (or related algebras, the covariant coordinates having in particular a natural interpretation as Higgs fields. We also exhibit, in one situation, a link between the renormalisable NC φ4-model with harmonic term and a gauge theory model. Some possible consequences of this are briefly discussed.
Derivations of the Moyal Algebra and Noncommutative Gauge Theories
Wallet, Jean-Christophe
2009-01-01
The differential calculus based on the derivations of an associative algebra underlies most of the noncommutative field theories considered so far. We review the essential properties of this framework and the main features of noncommutative connections in the case of non graded associative unital algebras with involution. We extend this framework to the case of Z2-graded unital involutive algebras. We show, in the case of the Moyal algebra or some related Z2-graded version of it, that the derivation based differential calculus is a suitable framework to construct Yang-Mills-Higgs type models on Moyal (or related) algebras, the covariant coordinates having in particular a natural interpretation as Higgs fields. We also exhibit, in one situation, a link between the renormalisable NC φ4-model with harmonic term and a gauge theory model. Some possible consequences of this are briefly discussed.
Non-commutative U(1) Gauge Theory on R**4 with Oscillator Term
Blaschke, Daniel N; Schweda, Manfred
2007-01-01
Inspired by the renormalizability of the non-commutative $\\Phi^4$ model with added oscillator term, we formulate a non-commutative gauge theory, where the oscillator enters as a gauge fixing term. All propagators turn out to be essentially given by the Mehler kernel and the bilinear part of the action is invariant under the Langmann-Szabo duality. The model is a promising candidate for a renormalizable non-commutative U(1) gauge theory.
Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 1. Perturbative Expansion
Ambjørn, Jan; Makeenko, Y
2004-01-01
We calculate quantum averages of Wilson loops (holonomies) in gauge theories on the Euclidean noncommutative plane, using a path-integral representation of the star-product. We show how the perturbative expansion emerges from a concise general formula and demonstrate its anomalous behavior at large parameter of noncommutativity for the simplest nonplanar diagram of genus 1. We discuss various UV/IR regularizations of the two-dimensional noncommutative gauge theory in the axial gauge and, using the noncommutative loop equation, construct a consistent regularization.
Noncommutative electromagnetism as a large N gauge theory
Energy Technology Data Exchange (ETDEWEB)
Yang, Hyun Seok [Humboldt Universitaet zu Berlin, Institut fuer Physik, Berlin (Germany); Korea Institute for Advanced Study, School of Physics, Seoul (Korea)
2009-12-15
We map noncommutative (NC) U(1) gauge theory on R{sub C} {sup d} x R{sub NC} {sup 2n} to U(N {yields}{infinity}) Yang-Mills theory on R{sub C} {sup d}, where R{sub C} {sup d} is a d-dimensional commutative spacetime while R{sub NC} {sup 2n} is a 2n-dimensional NC space. The resulting U(N) Yang-Mills theory on R{sub C} {sup d} is equivalent to that obtained by the dimensional reduction of (d+2n)-dimensional U(N) Yang-Mills theory onto R{sub C} {sup d}. We show that the gauge-Higgs system (A{sub {mu}}, {phi} {sup a}) in the U(N {yields}{infinity}) Yang-Mills theory on R{sub C} {sup d} leads to an emergent geometry in the (d+2n)-dimensional spacetime whose metric was determined by Ward a long time ago. In particular, the 10-dimensional gravity for d=4 and n=3 corresponds to the emergent geometry arising from the 4-dimensional N=4 vector multiplet in the AdS/CFT duality. We further elucidate the emergent gravity by showing that the gauge-Higgs system (A{sub {mu}}, {phi} {sup a}) in half-BPS configurations describes self-dual Einstein gravity. (orig.)
Matrix models, noncommutative gauge theory and emergent gravity
Energy Technology Data Exchange (ETDEWEB)
Steinacker, Harold [Fakultaet fuer Physik, Universitaet Wien (Austria)
2009-07-01
Matrix Models of Yang-Mills type are studied with focus on the effective geometry. It is shown that SU(n) gauge fields and matter on general 4-dimensional noncommutative branes couple to an effective metric, leading to emergent gravity. The effective metric is reminiscent of the open string metric, and depends on the dynamical Poisson structure. Covariant equations of motion are derived, which are protected from quantum corrections due to an underlying Noether theorem. The quantization is discussed qualitatively, which singles out the IKKT model as a candidate for a quantum theory of gravity coupled to matter. UV/IR mixing plays a central role. A mechanism for avoiding the cosmological constant problem is exhibited.
On the renormalizability of noncommutative U(1) Gauge Theory: an algebraic approach
Energy Technology Data Exchange (ETDEWEB)
Ventura, Ozemar Souto; Vilar, Luiz Claudio; Lemes, Vitor; Tedesco, D. [Instituto Federal de Educacao, Ciencia e Tecnologia do Espirito Santo (IFES), ES (Brazil)
2011-07-01
Full text: The year of 1999 witnessed two major developments in the noncommutative quantum field theory program. In the first one, Seiberg and Witten, inspired by the previously known result that the low energy limit of open strings could lead both to a gauge theory defined on a noncommutative space as well as to an usual commutative gauge theory, depending only on gauge choices, announced the existence of what became called the Seiberg-Witten map between noncommutative and commutative gauge theories.This achievement was then fully tested and confirmed by several authors both in the general structure of gauge transformations as in specific examples of gauge theories. It opened a window to an alternative approach to the quantum properties of the noncommutative theories. The second development just revealed the kind of difficulties one has to face when tackling the renormalization of field theories in the noncommutative space. An intrinsic mixing between high and low energy scales was associated to the noncommutativity of space-time, generating divergence which in the general case make these theories not renormalizable as they stand, the case of noncommutative gauge theories being no exception. Recently, it was finally understood that this infrared-ultraviolet (IR-UV) mix is still present even after a Seiberg- Witten map, showing that the commutative theories generated by their noncommutative counterparts suffer from the same non renormalizability. It took some time until the first proposal appeared in order to cure a noncommutative scalar theory from this IR divergence. The basic idea was to alter the free propagator of the theory through the introduction of an harmonic potential, then changing its low energy behavior. This in fact made the theory convergent in the infrared region, but at the cost of explicitly breaking translation invariance. In the reference Commun. Math. Phys. 287 : 275-290, (2009), this problem was circumvented now by the introduction of a
Martín, C. P.; Tamarit, C.
2008-01-01
We consider noncommutative gauge theory defined by means of Seiberg-Witten maps for an arbitrary semisimple gauge group. We compute the one-loop UV divergent matter contributions to the gauge field effective action to all orders in the noncommutative parameters θ. We do this for Dirac fermions and complex scalars carrying arbitrary representations of the gauge group. We use path-integral methods in the framework of dimensional regularisation and consider arbitrary invertible Seiberg-Witten maps that are linear in the matter fields. Surprisingly, it turns out that the UV divergent parts of the matter contributions are proportional to the noncommutative Yang-Mills action where traces are taken over the representation of the matter fields; this result supports the need to include such traces in the classical action of the gauge sector of the noncommutative theory.
Martín, C P
2008-01-01
We consider noncommutative gauge theory defined by means of Seiberg-Witten maps for an arbitrary semisimple gauge group. We compute the one-loop UV divergent matter contributions to the gauge field effective action to all orders in the noncommutative parameters $\\theta$. We do this for Dirac fermions and complex scalars carrying arbitrary representations of the gauge group. We use path-integral methods in the framework of dimensional regularisation and consider arbitrary invertible Seiberg-Witten maps that are linear in the matter fields. Surprisingly, it turns out that the UV divergent parts of the matter contributions are proportional to the noncommutative Yang-Mills action where traces are taken over the representation of the matter fields; this result supports the need to include such traces in the classical action of the gauge sector of the noncommutative theory.
Space-Time Diffeomorphisms in Noncommutative Gauge Theories
Rosenbaum, Marcos; Juarez, L Roman
2008-01-01
In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007), 10367-10382, hep-th/0611160] we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the theory, the representation of space-time diffeomorphisms provides a very convenient scheme for analyzing the induced twisted deformation of these diffeomorphisms, as a result of the space-time noncommutativity. However, for gauge field theories (and of course also for canonical geometrodynamics) where the Poisson brackets of the constraints explicitely depend on the embedding variables, this Poisson algebra cannot be connected directly with a representation of the complete Lie algebra of space-time diffeomorphisms, because not all the field variables turn out to have a dynamical character [Isham C.J., Kuchar K.V., Ann. Physics 164 (1985), 288-315, 316-333]. Nonetheless, such an homomorphic mapping can be recuperated by first modifying the original action and then adding addi...
Duality and gauge invariance of non-commutative spacetime Podolsky electromagnetic theory
Abreu, Everton M. C.; Fernandes, Rafael L.; Mendes, Albert C. R.; Neto, Jorge Ananias; Neves, Mario, Jr.
2017-01-01
The interest in higher derivative field theories has its origin mainly in their influence concerning the renormalization properties of physical models and to remove ultraviolet divergences. In this paper, we have introduced the non-commutative (NC) version of the Podolsky theory and we investigated the effect of the non-commutativity over its original gauge invariance property. We have demonstrated precisely that the non-commutativity spoiled the primary gauge invariance of the original action under this primary gauge transformation. After that we have used the Noether dualization technique to obtain a dual and gauge invariant action. We have demonstrated that through the introduction of a Stueckelberg field in this NC model, we can also recover the primary gauge invariance. In this way, we have accomplished a comparison between both methods.
Blaschke, D. N.; Grosse, H.; Schweda, M.
2007-09-01
Inspired by the renormalizability of the non-commutative Φ4 model with added oscillator term, we formulate a non-commutative gauge theory, where the oscillator enters as a gauge fixing term in a BRST invariant manner. All propagators turn out to be essentially given by the Mehler kernel and the bilinear part of the action is invariant under the Langmann-Szabo duality. The model is a promising candidate for a renormalizable non-commutative U(1) gauge theory.
Noncommutative o*(N) and usp*(2N) algebras and the corresponding gauge field theories
Bars, Itzhak; Vasilev, M
2001-01-01
The extension of the noncommutative u*(N) Lie algebra to noncommutative orthogonal and symplectic Lie algebras is studied. Using an anti-automorphism of the star-matrix algebra, we show that the u*(N) can consistently be restricted to o*(N) and usp*(N) algebras that have new mathematical structures. We give explicit fundamental matrix representations of these algebras, through which the formulation for the corresponding noncommutative gauge field theories are obtained. In addition, we present a D-brane configuration with an orientifold which realizes geometrically our algebraic construction, thus embedding the new noncommutative gauge theories in superstring theory in the presence of a constant background magnetic field. Some algebraic generalizations that may have applications in other areas of physics are also discussed.
Noncommutative o*(N) and usp*(2N) algebras and the corresponding gauge field theories
Bars, I.; Sheikh-Jabbari, M. M.; Vasiliev, M. A.
2001-10-01
The extension of the noncommutative u*(N) Lie algebra to noncommutative orthogonal and symplectic Lie algebras is studied. Using an antiautomorphism of the star-matrix algebra, we show that the u*(N) can consistently be restricted to o*(N) and usp*(N) algebras that have new mathematical structures. We give explicit fundamental matrix representations of these algebras, through which the formulation for the corresponding noncommutative gauge field theories are obtained. In addition, we present a D-brane configuration with an orientifold that realizes geometrically our algebraic construction, thus embedding the new noncommutative gauge theories in a superstring theory in the presence of a constant background magnetic field. Some algebraic generalizations that may have applications in other areas of physics are also discussed.
One-loop Noncommutative U(1) Gauge Theory from Bosonic Worldline Approach
Kiem, Y H; Ryou, C; Sato, H T; Kiem, Youngjai; Kim, Yeonjung; Ryou, Cheol; Sato, Haru-Tada
2002-01-01
We develop a method to compute the one-loop effective action of noncommutative U(1) gauge theory based on the bosonic worldline formalism, and derive compact expressions for N-point 1PI amplitudes. The method, resembling perturbative string computations, shows that open Wilson lines emerge as a gauge invariant completion of certain terms in the effective action. The terms involving open Wilson lines are of the form reminiscent of closed string exchanges between the states living on the two boundaries of a cylinder. They are also consistent with recent matrix theory analysis and the results from noncommutative scalar field theories with cubic interactions.
M-theory in the Omega-background and 5-dimensional non-commutative gauge theory
Costello, Kevin
2016-01-01
The $\\Omega$-background is defined for supergravity, and a very general class of such backgrounds is constructed for 11-dimensional supergravity. 11-dimensional supergravity in a certain $\\Omega$-background is shown to be equivalent to a 5-dimensional non-commutative gauge theory of Chern-Simons type. M2 and M5 branes are expressed as 1 and 2-dimensional extended objects in the 5-dimensional gauge theory. This 5-dimensional gauge theory is shown to admit a consistent quantization with two coupling constants, despite being formally non-renormalizable. A check of a twisted version of AdS/CFT is performed relating this 5-dimensional non-commutative gauge theory to the theory on N M5 branes, wrapping an $A_{k-1}$ singularity and placed in an $\\Omega$-background. The operators on the M5 branes, in the $\\Omega$-background, are described by a certain chiral algebra which in the large N limit becomes a $W_{k+\\infty}$ algebra. This chiral algebra is recovered from the 5-dimensional gauge theory. This argument also pro...
Domain walls in noncommutative gauge theories, folded D-branes, and communication with mirror world
Energy Technology Data Exchange (ETDEWEB)
Dubovsky, S.L.; Sibiryakov, S.M. E-mail: sibir@ms2.inr.ac.ru
2004-07-19
Noncommutative U(N) gauge theories at different N may be often thought of as different sectors of a single theory. For instance, U(1) theory possesses a sequence of vacua labeled by an integer parameter N, and the theory in the vicinity of the Nth vacuum coincides with the U(N) noncommutative gauge theory. We construct domain walls on noncommutative plane, which separate vacua with different gauge groups in gauge theory with adjoint scalar field. The scalar field has nonminimal coupling to the gauge field, such that the scale of noncommutativity is determined by the vacuum value of the scalar field. The domain walls are solutions of the BPS equations in the theory. It is natural to interprete the domain wall as a stack of D-branes plus a stack of folded D-branes. We support this interpretation by the analysis of small fluctuations around domain walls, and suggest that such configurations of branes emerge as solutions of the Matrix model in large class of pp-wave backgrounds with inhomogeneous field strength. We point out that the folded D-brane per se provides an explicit realization of the 'mirror world' idea, and speculate on some phenomenological consequences of this scenario.
On n-ary algebras, branes and poly-vector gauge theories in noncommutative Clifford spaces
Castro, Carlos
2010-09-01
In this paper, poly-vector-valued gauge field theories in noncommutative Clifford spaces are presented. They are based on noncommutative (but associative) star products that require the use of the Baker-Campbell-Hausdorff formula. Using these star products allows the construction of actions for noncommutative p-branes (branes moving in noncommutative spaces). Noncommutative Clifford-space gravity as a poly-vector-valued gauge theory of twisted diffeomorphisms in Clifford spaces would require quantum Hopf algebraic deformations of Clifford algebras. We proceed with the study of n-ary algebras and find an important relationship among the n-ary commutators of the noncommuting spacetime coordinates [X1, X2, ..., Xn] with the poly-vector-valued coordinates X123sdotsdotsdotn in noncommutative Clifford spaces given by [X1, X2, ..., Xn] = n!X123sdotsdotsdotn. The large N limit of n-ary commutators of n hyper-matrices {\\bf X}_{i_1 i_2 \\cdots i_n} leads to Eguchi-Schild p-brane actions for p + 1 = n. A noncomutative n-ary • product of n functions is constructed which is a generalization of the binary star product * of two functions and is associated with the deformation quantization of n-ary structures and deformations of the Nambu-Poisson brackets.
Gauge Theories with Fuzzy Extra Dimensions and Noncommutative Vortices and Fluxons
Energy Technology Data Exchange (ETDEWEB)
Kuerkcueoglu, Seckin, E-mail: kseckin@metu.edu.tr [Middle East Technical University, Department of Physics, Inoenue Boulevard, 06531, Ankara (Turkey)
2011-07-08
A U (2) Yang-Mills theory on the space M x S{sup 2}{sub F} is considered, where it is assumed that M is an arbitrary noncommutative space and S{sup 2}{sub F} is a fuzzy sphere spontaneously generated from a noncommutative U(N) Yang-Mills theory on M coupled to a triplet of scalars in the adjoint of U(N). SU(2)-equivariant reduction of this theory leads to a noncommutative U(1) gauge theory coupled adjointly to a set of scalar fields. The emergent model is studied on the Groenewald-Moyal plane R{sup 2}{sub {theta} }and it is found that, in certain limits, it admits noncommutative, non-BPS vortex as well as fluxon solutions.
Wilson Loops and Area-Preserving Diffeomorphisms in Twisted Noncommutative Gauge Theory
Riccardi, M; Riccardi, Mauro; Szabo, Richard J.
2007-01-01
We use twist deformation techniques to analyse the behaviour under area-preserving diffeomorphisms of quantum averages of Wilson loops in Yang-Mills theory on the noncommutative plane. We find that while the classical gauge theory is manifestly twist covariant, the holonomy operators break the quantum implementation of the twisted symmetry in the usual formal definition of the twisted quantum field theory. These results are deduced by analysing general criteria which guarantee twist invariance of noncommutative quantum field theories. From this a number of general results are also obtained, such as the twisted symplectic invariance of noncommutative scalar quantum field theories with polynomial interactions and the existence of a large class of holonomy operators with both twisted gauge covariance and twisted symplectic invariance.
Area-preserving diffeomorphisms in gauge theory on a non-commutative plane. A lattice study
Energy Technology Data Exchange (ETDEWEB)
Bietenholz, W. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Bigarini, A. [Univ. degli Studi di Perugia (Italy). Dipt. di Fisica]|[INFN, Sezione di Perugia (Italy)]|[Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Torrielli, A. [Massachusetts Institute of Technology, Cambridge, MA (United States). Center for Theoretical Physics, Lab. for Nuclear Sciences
2007-06-15
We consider Yang-Mills theory with the U(1) gauge group on a non-commutative plane. Perturbatively it was observed that the invariance of this theory under area-preserving diffeomorphisms (APDs) breaks down to a rigid subgroup SL(2,R). Here we present explicit results for the APD symmetry breaking at finite gauge coupling and finite non-commutativity. They are based on lattice simulations and measurements of Wilson loops with the same area but with a variety of different shapes. Our results confirm the expected loss of invariance under APDs. Moreover, they strongly suggest that non-perturbatively the SL(2,R) symmetry does not persist either. (orig.)
Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
van Tongeren, Stijn J
2016-01-01
We discuss the AdS/CFT interpretation of homogeneous Yang-Baxter deformations of the AdS_5 x S^5 superstring as noncommutative deformations of the dual gauge theory, going well beyond the canonical noncommutative case. These homogeneous Yang-Baxter deformations can be of so-called abelian or jordanian type. While abelian deformations have a clear interpretation in string theory and many already had well understood gauge theory duals, jordanian deformations appear novel on both counts. We discuss the symmetry structure of the deformed string from the uniformizing perspective of Drinfeld twists and show how it can be realized on the gauge theory side by considering various noncommutative spaces. We then conjecture that these give gauge theory duals of our strings, modulo subtleties involving time and singularities. We support this conjecture by a brane construction for two nontrivial examples, corresponding to noncommutative spaces with [x^-,x^i] ~ x^i (i=1,2). We also briefly discuss a deformation which may be...
Compactified D=11 Supermembranes and Symplectic Non-Commutative Gauge Theories
Martin, I; Restuccia, A
2001-01-01
It is shown that a double compactified D=11 supermembrane with non trivial wrapping may be formulated as a symplectic non-commutative gauge theory on the world volume. The symplectic non commutative structure is intrinsically obtained from the symplectic 2-form on the world volume defined by the minimal configuration of its hamiltonian. The gauge transformations on the symplectic fibration are generated by the area preserving diffeomorphisms on the world volume. Geometrically, this gauge theory corresponds to a symplectic fibration over a compact Riemman surface with a symplectic connection.
A non-perturbative study of non-commutative U(1) gauge theory
Energy Technology Data Exchange (ETDEWEB)
Nishimura, J. [High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki (Japan)]|[Graduate Univ. for Advanced Studies (SOKENDAI), Tsukuba (Japan). Dept. of Particle and Nuclear Physics; Bietenholz, W. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Susaki, Y. [High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki (Japan)]|[Tsukuba Univ. (Japan). Graduate School of Pure and Applied Science; Volkholz, J. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2007-06-15
We study U(1) gauge theory on a 4d non-commutative torus, where two directions are non-commutative. Monte Carlo simulations are performed after mapping the regularized theory onto a U(N) lattice gauge theory in d=2. At intermediate coupling strength, we find a phase in which open Wilson lines acquire non-zero vacuum expectation values, which implies the spontaneous breakdown of translational invariance. In this phase, various physical quantities obey clear scaling behaviors in the continuum limit with a fixed non- commutativity parameter {theta}, which provides evidence for a possible continuum theory. In the weak coupling symmetric phase, the dispersion relation involves a negative IR-singular term, which is responsible for the observed phase transition. (orig.)
Matrix models from localization of five-dimensional supersymmetric noncommutative U(1) gauge theory
Lee, Bum-Hoon; Yang, Hyun Seok
2016-01-01
We study localization of five-dimensional supersymmetric $U(1)$ gauge theory on $\\mathbb{S}^3 \\times \\mathbb{R}_{\\theta}^{2}$ where $\\mathbb{R}_{\\theta}^{2}$ is a noncommutative (NC) plane. The theory can be isomorphically mapped to three-dimensional supersymmetric $U(N \\to \\infty)$ gauge theory on $\\mathbb{S}^3$ using the matrix representation on a separable Hilbert space on which NC fields linearly act. Therefore the NC space $\\mathbb{R}_{\\theta}^{2}$ allows for a flexible path to derive matrix models via localization from a higher-dimensional supersymmetric NC $U(1)$ gauge theory. The result shows a rich duality between NC $U(1)$ gauge theories and large $N$ matrix models in various dimensions.
Simulations results for U(1) gauge theory on non-commutative spaces
Energy Technology Data Exchange (ETDEWEB)
Bietenholz, W. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Bigarini, A. [Univ. degli Studi di Perugia (Italy). Dipt. di Fisica; Nishimura, J. [High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki (Japan)]|[Graduate Univ. for Advanced Studies Tsukuba (Japan). Dept. of Particle and Nuclear Physics; Susaki, Y. [High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki (Japan)]|[Tsukuba Univ. (Japan). Graduate School of Pure and Applied Science; Torrielli, A. [Massachusetts Institute of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics, Lab. for Nuclear Sciences and Dept. of Physics; Volkholz, J. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2007-11-15
We present numerical results for U(1) gauge theory in 2d and 4d spaces involving a noncommutative plane. Simulations are feasible thanks to a mapping of the non-commutative plane onto a twisted matrix model. In d=2 it was a long-standing issue if Wilson loops are (partially) invariant under area-preserving diffeomorphisms. We show that non-perturbatively this invariance breaks, including the subgroup SL(2,R). In both cases, d=2 and d=4, we extrapolate our results to the continuum and infinite volume by means of a Double Scaling Limit. In d=4 this limit leads to a phase with broken translation symmetry, which is not affected by the perturbatively known IR instability. Therefore the photon may survive in a non-commutative world. (orig.)
Simulation Results for U(1) Gauge Theory on Non-Commutative Spaces
Bietenholz, W; Nishimura, J; Susaki, Y; Torrielli, A; Volkholz, J
2007-01-01
We present numerical results for U(1) gauge theory in 2d and 4d spaces involving a non-commutative plane. Simulations are feasible thanks to a mapping of the non-commutative plane onto a twisted matrix model. In d=2 it was a long-standing issue if Wilson loops are (partially) invariant under area-preserving diffeomorphisms. We show that non-perturbatively this invariance breaks, including the subgroup SL(2,R). In both cases, d=2 and d=4, we extrapolate our results to the continuum and infinite volume by means of a Double Scaling Limit. In d=4 this limit leads to a phase with broken translation symmetry, which is not affected by the perturbatively known IR instability. Therefore the photon may survive in a non-commutative world.
On supermatrix models, Poisson geometry, and noncommutative supersymmetric gauge theories
Energy Technology Data Exchange (ETDEWEB)
Klimčík, Ctirad [Aix Marseille Université, CNRS, Centrale Marseille I2M, UMR 7373, 13453 Marseille (France)
2015-12-15
We construct a new supermatrix model which represents a manifestly supersymmetric noncommutative regularisation of the UOSp(2|1) supersymmetric Schwinger model on the supersphere. Our construction is much simpler than those already existing in the literature and it was found by using Poisson geometry in a substantial way.
Non-commutative Differential Calculus and the Axial Anomaly in Abelian Lattice Gauge Theories
Fujiwara, T; Wu, K; Fujiwara, Takanori; Suzuki, Hiroshi; Wu, Ke
2000-01-01
The axial anomaly in lattice gauge theories has topological nature when the Dirac operator satisfies the Ginsparg-Wilson relation. We study the axial anomaly in Abelian gauge theories on an infinite hypercubic lattice by utilizing cohomological techniques. The crucial tool in our approach is the non-commutative differential calculus (NCDC) which validates the Leibniz rule of exterior derivatives on the lattice. The topological nature of the ``Chern character'' on the lattice becomes manifest with NCDC. Our result provides an algebraic proof of Lüscher's theorem for a four-dimensional lattice and its generalization to arbitrary dimensions.
Geometry of the gauge algebra in noncommutative Yang-Mills theory
Lizzi, Fedele; Zampini, Alessandro; Szabo, Richard J.
2001-08-01
A detailed description of the infinite-dimensional Lie algebra of star-gauge transformations in non-commutative Yang-Mills theory is presented. Various descriptions of this algebra are given in terms of inner automorphisms of the underlying deformed algebra of functions on spacetime, of deformed symplectic diffeomorphisms, of the infinite unitary Lie algebra u(∞), and of the C*-algebra of compact operators on a quantum mechanical Hilbert space. The spacetime and string interpretations are also elucidated.
Geometry of the Gauge Algebra in Noncommutative Yang-Mills Theory
Lizzi, F; Zampini, A
2001-01-01
A detailed description of the infinite-dimensional Lie algebra of star-gauge transformations in noncommutative Yang-Mills theory is presented. Various descriptions of this algebra are given in terms of inner automorphisms of the underlying deformed algebra of functions on spacetime, of deformed symplectic diffeomorphisms, of the infinite unitary Lie algebra, and of the algebra of compact operators on a quantum mechanical Hilbert space. The spacetime and string interpretations are also elucidated.
Softer Hard Scattering and Noncommutative Gauge-String Duality
Rey, S J; Rey, Soo-Jong; Yee, Jung-Tay
2003-01-01
We study exclusive scattering of `hadrons' at high energy and fixed angle in (nonconformal) noncommutative gauge theories. Via gauge-string duality, we show that the noncommutativity renders the scattering soft, leading to exponential suppression. The result fits with the picture that, in noncommutative gauge theory, fundamental parton contents constitute wee-partons only and `hadrons' are made out of open Wilson lines.
Noncommutative gauge theories on {R}_{\\uplambda}^3 : perturbatively finite models
Géré, Antoine; Jurić, Tajron; Wallet, Jean-Christophe
2015-12-01
We show that natural noncommutative gauge theory models on {R}_{\\uplambda}^3 can accommodate gauge invariant harmonic terms, thanks to the existence of a relationship between the center of {R}_{\\uplambda}^3 and the components of the gauge invariant 1-form canonical connection. This latter object shows up naturally within the present noncommutative differential calculus. Restricting ourselves to positive actions with covariant coordinates as field variables, a suitable gauge-fixing leads to a family of matrix models with quartic interactions and kinetic operators with compact resolvent. Their perturbative behavior is then studied. We first compute the 2-point and 4-point functions at the one-loop order within a subfamily of these matrix models for which the interactions have a symmetric form. We find that the corresponding contributions are finite. We then extend this result to arbitrary order. We find that the amplitudes of the ribbon diagrams for the models of this subfamily are finite to all orders in perturbation. This result extends finally to any of the models of the whole family of matrix models obtained from the above gauge-fixing. The origin of this result is discussed. Finally, the existence of a particular model related to integrable hierarchies is indicated, for which the partition function is expressible as a product of ratios of determinants.
Noncommutative gauge theories on ℝ{sub λ}{sup 3}: perturbatively finite models
Energy Technology Data Exchange (ETDEWEB)
Géré, Antoine [Dipartimento di Matematica, Università di Genova,Via Dodecaneso, 35, I-16146 Genova (Italy); Jurić, Tajron [Ruđer Bošković Institute, Theoretical Physics Division,Bijenička c.54, HR-10002 Zagreb (Croatia); Wallet, Jean-Christophe [Laboratoire de Physique Théorique, CNRS, University Paris-Sud, University Paris-Saclay,Bât. 210, 91405 Orsay (France)
2015-12-09
We show that natural noncommutative gauge theory models on ℝ{sub λ}{sup 3} can accommodate gauge invariant harmonic terms, thanks to the existence of a relationship between the center of ℝ{sub λ}{sup 3} and the components of the gauge invariant 1-form canonical connection. This latter object shows up naturally within the present noncommutative differential calculus. Restricting ourselves to positive actions with covariant coordinates as field variables, a suitable gauge-fixing leads to a family of matrix models with quartic interactions and kinetic operators with compact resolvent. Their perturbative behavior is then studied. We first compute the 2-point and 4-point functions at the one-loop order within a subfamily of these matrix models for which the interactions have a symmetric form. We find that the corresponding contributions are finite. We then extend this result to arbitrary order. We find that the amplitudes of the ribbon diagrams for the models of this subfamily are finite to all orders in perturbation. This result extends finally to any of the models of the whole family of matrix models obtained from the above gauge-fixing. The origin of this result is discussed. Finally, the existence of a particular model related to integrable hierarchies is indicated, for which the partition function is expressible as a product of ratios of determinants.
Noncommutative gauge theories on $\\mathbb{R}^3_\\lambda$: Perturbatively finite models
Géré, Antoine; Wallet, Jean-Christophe
2015-01-01
We show that natural noncommutative gauge theory models on $\\mathbb{R}^3_\\lambda$ can accommodate gauge invariant harmonic terms, thanks to the existence of a relationship between the center of $\\mathbb{R}^3_\\lambda$ and the components of the gauge invariant 1-form canonical connection. This latter object shows up naturally within the present noncommutative differential calculus. Restricting ourselves to positive actions with covariant coordinates as field variables, a suitable gauge-fixing leads to a family of matrix models with quartic interactions and kinetic operators with compact resolvent. Their perturbative behavior is then studied. We first compute the 2-point and 4-point functions at the one-loop order within a subfamily of these matrix models for which the interactions have a symmetric form. We find that the corresponding contributions are finite. We then extend this result to arbitrary order. We find that the amplitudes of the ribbon diagrams for the models of this subfamily are finite to all order...
Noncommutative 6D Gauge Higgs Unification Models
Lopez-Dominguez, J C; Ramírez, C
2005-01-01
The influence of higher dimensions in noncommutative field theories is considered. For this purpose, we analize the bosonic sector of a recently proposed 6 dimensional SU(3) orbifold model for the electroweak interactions. The corresponding noncommutative theory is constructed by means of the Seiberg-Witten map in 6D. We find, in the corresponding 4D theory, couplings between the gauge and Higgs fields with interesting phenomenological implications and which are new with respect to other known 4D noncommutative formulations under the Seiberg-Witten map.
Quantum Field Theory on Noncommutative Spaces
Szabó, R J
2003-01-01
A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative Yang-Mills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an in-depth study of the gauge group of noncommutative Yang-Mills theory. Some of the more mathematical ideas and techniques of noncommutative geometry are also briefly explained.
Wilson Loops in 2D Noncommutative Euclidean Gauge Theory: 2. 1/\\theta Expansion
Ambjørn, Jan; Makeenko, Y; Ambjorn, Jan; Dubin, Andrei; Makeenko, Yuri
2007-01-01
We analyze the $1/\\theta$ and 1/N expansions of the Wilson loop averages $_{U_\\theta (N)}$ in the two-dimensional noncommutative $U_\\theta (N)$ gauge theory with the parameter of noncommutativity $\\theta$. For a generic rectangular contour $C$, a concise integral representation is derived (non-perturbatively both in the coupling constant $g^{2}$ and in $\\theta$) for the next-to-leading term of the $1/\\theta$ expansion. In turn, in the limit when ${\\theta}$ is much larger than the area $A(C)$ of the surface bounded by $C$, the large $\\theta$ asymptote of this representation is argued to yield the next-to-leading term of the $1/\\theta$ series. For both of the expansions, the next-to-leading contribution exhibits only a power-like decay for areas $A(C)>>\\sigma^{-1}$ (but $A(C)<<{\\theta}$) much larger than the inverse of the string tension $\\sigma$ defining the range of the exponential decay of the leading term. Consequently, for large $\\theta$, it hinders a direct stringy interpretation of the subleading t...
Emergent Abelian Gauge Fields from Noncommutative Gravity
Directory of Open Access Journals (Sweden)
Allen Stern
2010-02-01
Full Text Available We construct exact solutions to noncommutative gravity following the formulation of Chamseddine and show that they are in general accompanied by Abelian gauge fields which are first order in the noncommutative scale. This provides a mechanism for generating cosmological electromagnetic fields in an expanding space-time background, and also leads to multipole-like fields surrounding black holes. Exact solutions to noncommutative Einstein-Maxwell theory can give rise to first order corrections to the metric tensor, as well as to the electromagnetic fields. This leads to first order shifts in the horizons of charged black holes.
Phenomenology of Noncommutative Field Theories
Carone, C D
2006-01-01
Experimental limits on the violation of four-dimensional Lorentz invariance imply that noncommutativity among ordinary spacetime dimensions must be small. In this talk, I review the most stringent bounds on noncommutative field theories and suggest a possible means of evading them: noncommutativity may be restricted to extra, compactified spatial dimensions. Such theories have a number of interesting features, including Abelian gauge fields whose Kaluza-Klein excitations have self couplings. We consider six-dimensional QED in a noncommutative bulk, and discuss the collider signatures of the model.
Non-commutative U(1) gauge theory on R{sub {theta}}{sup 4} with oscillator term and BRST symmetry
Energy Technology Data Exchange (ETDEWEB)
Blaschke, D.N.; Schweda, M. [Vienna Univ. of Technology, Institute for Theoretical Physics (Austria); Grosse, H. [Vienna Univ., Faculty of Physics(Austria)
2007-09-15
Inspired by the renormalizability of the non-commutative {phi}{sup 4} model with added oscillator term, we formulate a non-commutative gauge theory, where the oscillator enters as a gauge fixing term in a BRST (Becchi-Rouet-Stora-Tyutin) invariant manner. All propagators turn out to be essentially given by the Mehler kernel and the bilinear part of the action is invariant under the Langmann-Szabo duality. The model is a promising candidate for a renormalizable non-commutative U(1) gauge theory. (authors)
Wilson Line Correlators in N=4 Non-commutative Gauge Theory on S^2 x S^2
Kitazawa, Y; Tomino, D
2004-01-01
We investigate the Wilson line correlators dual to supergravity multiplets in N=4 non-commutative gauge theory on S^2 x S^2. We find additional non-analytic contributions to the correlators due to UV/IR mixing in comparison to ordinary gauge theory. Although they are no longer BPS off shell, their renormalization effects are finite as long as they carry finite momenta. We propose a renormalization procedure to obtain local operators with no anomalous dimensions in perturbation theory. We reflect on our results from dual supergravity point of view. We show that supergravity can account for both IR and UV/IR contributions.
Anomalies and noncommutative index theory
Perrot, D
2006-01-01
These are the notes of a lecture given during the summer school "Geometric and Topological Methods for Quantum Field Theory", Villa de Leyva, Colombia, july 11 - 29, 2005. We review basic facts concerning gauge anomalies and discuss the link with the Connes-Moscovici index formula in noncommutative geometry.
The Yang-Mills gauge theory in DFR noncommutative space-time
Abreu, Everton M C
2015-01-01
The Doplicher-Fredenhagen-Roberts (DFR) framework for noncommutative (NC) space-times is considered as an alternative approach to describe the physics of quantum gravity, for instance. In this formalism, the NC parameter, {\\it i.e.} $\\theta^{\\mu\
Renormalization and Induced Gauge Action on a Noncommutative Space
Grosse, Harald
2007-01-01
Field theories on deformed spaces suffer from the IR/UV mxing and renormalization is generically spoiled. In work with R. Wulkenhaar, one of us realized a way to cure this desease by adding one more marginal operator. We review these ideas, show the application to $\\phi^3$ models and use heat kernel expansion methods for a scalar field theory coupled to an external gauge field on a $\\theta$-deformed space and derive noncommutative gauge actions.
Noncommutative Topological Theories of Gravity
García-Compéan, H; Ramírez, C; Sabido, M
2003-01-01
The possibility of noncommutative gravity arising in the same manner as Yang-Mills theory is explored. Using the Seiberg-Witten map we give a noncommutative version of topological gravity, from which the Euler characteristic and the signature are obtained, in both cases up to third order in the noncommutativity parameter. Finally, we discuss possible ways towards obtaining noncommutative gravitational instantons and to detect local and global gravitational anomalies within this context.
Quantum principal bundles and corresponding gauge theories
Durdevic, M
1995-01-01
A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge transformations, are introduced and investigated. A natural differential calculus on quantum gauge bundles is constructed and analyzed. Kinematical and dynamical properties of corresponding gauge theories are discussed.
Strings, Conformal Field Theory And Noncommutative Geometry
Matsubara, K
2004-01-01
This thesis describes some aspects of noncommutative geometry and conformal field theory. The motivation for the investigations made comes to a large extent from string theory. This theory is today considered to be the most promising way to find a solution to the problem of unifying the four fundamental interactions in one single theory. The thesis gives a short background presentation of string theory and points out how noncommutative geometry and conformal field theory are of relevance within the string theoretical framework. There is also given some further information on noncommutative geometry and conformal field theory. The results from the three papers on which the thesis is based are presented in the text. It is shown in Paper 1 that, for a gauge theory in a flat noncommutative background only the gauge groups U(N) can be used in a straightforward way. These theories can arise as low energy limits of string theory. Paper 2 concerns boundary conformal field theory, which can be used to describe open s...
Left-right symmetric gauge theory in non-commutative geometry on M{sub 4} x Z{sub N}
Energy Technology Data Exchange (ETDEWEB)
Okumura, Yoshitaka [Chubu Univ., Kasugai, Aichi (Japan)
1995-10-01
The left-right symmetric gauge model (LRSM) is reconstructed using the previously proposed formalism based on the non-commutative differential geometry extended on the discrete space M{sub 4} x Z{sub N}. This formalism is so flexible and applicable that not only the standard model but also the SU(5) grand unified model have already been reformulated in this formalism, which presents many attractive points such as the unified picture of the gauge field and Higgs field as the generalized connection in non-commutative geometry. LRSM is still alive as a model with the intermediate symmetry of the spontaneously broken SO(10) grand unified theory (GUT). Six sheets are prepared for LRSM (N=6), one is for SU(3){sub c} color symmetry and the rest of five are for SU(2){sub L} x SU(2){sub R} x U(1) symmetry. We can achieve the reformulation of LRSM with the quite different configurations of Higgs particles from the ordinary one. Namely, the left-right symmetric gauge groups are broken owing to two (2, 1) and two (1, 2) doublet Higgs fields with hypercharge 1, one (2, 2{sup *}) Higgs field, and one (1, 3) Higgs field with hypercharge -2. The fermion sectors are nicely incorporated so that the seesaw mechanism works well to make the right-handed neutrino super heavy and the left-handed neutrino super light. (author).
Gravity and nonabelian gauge fields in noncommutative space-time
Nguyen, Viet Ai
2015-01-01
Noncommutative geometric constructions of gravity in the spacetime extended by an extra dimension of two points can be viewed as a discretized version of a Kaluza-Klein theory \\cite{LVW,VW1,VW2}. In this paper, we show that it is possible to generalize the framework to incorporate the nonabelian gauge fields. However, the generalized Hilbert-Einstein action is gauge invariant only in two cases. In the first case, the gauge group must be abelian on one sheet of spacetime and nonabelian on the other one. In the second case, the gauge group must be the same on two sheets of spacetime. Accidentally, the theories of electroweak and strong interactions are exactly these two cases.
Noncommutative Gravity and Quantum Field Theory on Noncommutative Curved Spacetimes
Schenkel, Alexander
2012-01-01
The focus of this PhD thesis is on applications, new developments and extensions of the noncommutative gravity theory proposed by Julius Wess and his group. In part one we propose an extension of the usual symmetry reduction procedure to noncommutative gravity. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models. In part two we develop a new formalism for quantum field theory on noncommutative curved spacetimes by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. We also study explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories. The convergent deformation of simple toy models is investigated and it is found that ...
Embedding Commutative and Noncommutative Theories in the Symplectic Framework
Neves, C; Rodrigues, D C; Wotzasek, C; Neves, Clifford; Oliveira, Wilson; Rodrigues, Davi C.; Wotzasek, Clovis
2004-01-01
This paper is devoted to study gauge embedding of either commutative and noncommutative theories in the framework of the symplectic formalism. We illustrate our ideas in the Proca model, the irrotational fluid model and the noncommutative self-dual model. In the process of this new path of embedding, the infinitesimal gauge generators of the gauge embedded theory are easily and directly chosen. Among other advantages, this enables a greater control over the final Lagrangian and puts some light on the so called ''arbitrariness problem".
Gauge-invariant extensions of the Proca model in a noncommutative space-time
Abreu, Everton M C; Fernandes, Rafael L; Mendes, Albert C R
2016-01-01
The gauge invariance analysis of theories described in noncommutative (NC) space-times can lead us to interesting results since noncommutativity is one of the possible paths to investigate quantum effects in classical theories such as general relativity, for example. This theoretical possibility has motivated us to analyze the gauge invariance of the NC version of the Proca model, which is a second-class system, in Dirac's classification, since its classical formulation (commutative space-time) has its gauge invariance broken thanks to the mass term. To obtain such gauge invariant model, we have used the gauge unfixing method to construct a first-class NC version of the Proca model. We have also questioned if the gauge symmetries of NC theories, are affected necessarily or not by the NC parameter. In this way, we have calculated its respective symmetries in a standard way via Poisson brackets.
Gauge-invariant extensions of the Proca model in a noncommutative space-time
Abreu, Everton M. C.; Neto, Jorge Ananias; Fernandes, Rafael L.; Mendes, Albert C. R.
2016-09-01
The gauge invariance analysis of theories described in noncommutative (NC) space-times can lead us to interesting results since noncommutativity is one of the possible paths to investigate quantum effects in classical theories such as general relativity, for example. This theoretical possibility has motivated us to analyze the gauge invariance of the NC version of the Proca model, which is a second-class system, in Dirac’s classification, since its classical formulation (commutative space-time) has its gauge invariance broken thanks to the mass term. To obtain such gauge invariant model, we have used the gauge unfixing method to construct a first-class NC version of the Proca model. We have also questioned if the gauge symmetries of NC theories are affected necessarily or not by the NC parameter. In this way, we have calculated its respective symmetries in a standard way via Poisson brackets.
Noncommutative field theory and Lorentz violation.
Carroll, S M; Harvey, J A; Kostelecký, V A; Lane, C D; Okamoto, T
2001-10-01
The role of Lorentz symmetry in noncommutative field theory is considered. Any realistic noncommutative theory is found to be physically equivalent to a subset of a general Lorentz-violating standard-model extension involving ordinary fields. Some theoretical consequences are discussed. Existing experiments bound the scale of the noncommutativity parameter to (10 TeV)(-2).
Instantons, Fluxons and Open Gauge String Theory
Griguolo, L; Szabó, R J; Griguolo, Luca; Seminara, Domenico; Szabo, Richard J.
2004-01-01
We use the exact instanton expansion to illustrate various string characteristics of noncommutative gauge theory in two dimensions. We analyse the spectrum of the model and present some evidence in favour of Hagedorn and fractal behaviours. The decompactification limit of noncommutative torus instantons is shown to map in a very precise way, at both the classical and quantum level, onto fluxon solutions on the noncommutative plane. The weak-coupling singularities of the usual Gross-Taylor string partition function for QCD on the torus are studied in the instanton representation and its double scaling limit, appropriate for the mapping onto noncommutative gauge theory, is shown to be a generating function for the volumes of the principal moduli spaces of holomorphic differentials. The noncommutative deformation of this moduli space geometry is described and appropriate open string interpretations are proposed in terms of the fluxon expansion.
Instantons, quivers and noncommutative Donaldson-Thomas theory
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Cirafici, Michele, E-mail: cirafici@math.ist.utl.pt [Centro de Analise Matematica, Geometria e Sistemas Dinamicos, Departamento de Matematica, Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisboa (Portugal); Sinkovics, Annamaria, E-mail: A.Sinkovics@damtp.cam.ac.uk [Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Szabo, Richard J., E-mail: R.J.Szabo@ma.hw.ac.uk [Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS (United Kingdom); Maxwell Institute for Mathematical Sciences, Edinburgh (United Kingdom)
2011-12-11
We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analyzing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes according to the orbifold group. We construct a moduli space for these gauge field configurations which allows us to compute its virtual numbers via the counting of representations of a quiver with relations. The quiver encodes the instanton dynamics of the noncommutative gauge theory, and is associated to the geometry of the singularity via the generalized McKay correspondence. The index of BPS states which compute the noncommutative Donaldson-Thomas invariants is realized via topological quantum mechanics based on the quiver data. We illustrate these constructions with several explicit examples, involving also higher rank Coulomb branch invariants and geometries with compact divisors, and connect our approach with other ones in the literature.
Chern-Simons in the Seiberg-Witten map for non-commutative Abelian gauge theories in 4D
Picariello, M; Sorella, S P; Picariello, Marco; Quadri, Andrea; Sorella, Silvio P.
2002-01-01
A cohomological BRST characterization of the Seiberg-Witten (SW) map is given. We prove that the coefficients of the SW map can be identified with elements of the cohomology of the BRST operator modulo a total derivative. As an example, it will be illustrated how the first coefficients of the SW map can be written in terms of the Chern-Simons three form. This suggests a deep topological and geometrical origin of the SW map. The existence of the map for both Abelian and non-Abelian case is discussed. By using a recursive argument and the associativity of the $\\star$-product, we shall be able to prove that the Wess-Zumino consistency condition for non-commutative BRST transformations is fulfilled. The recipe of obtaining an explicit solution by use of the homotopy operator is briefly reviewed in the Abelian case.
Worldline Formalism and Noncommutative Theories
Franchino-Viñas, Sebastián A
2015-01-01
The objective of this Ph.D. thesis is the implementation of the Worldline Formalism in the frame of Noncommutative Quantum Field Theories. The result is a master formula for the 1-loop effective action that is applied to a number of scalar models -- among them the Grosse-Wulkenhaar model. As a byproduct we find an expression for the small propertime expansion of general nonlocal operators' Heat Kernel. As an introduction, basic notions of spectral functions, Quantum Field Theories --path integrals and renormalization by means of spectral functions-- and the Worldline Formalism for commutative theories are given.
Field Theory on Curved Noncommutative Spacetimes
Directory of Open Access Journals (Sweden)
Alexander Schenkel
2010-08-01
Full Text Available We study classical scalar field theories on noncommutative curved spacetimes. Following the approach of Wess et al. [Classical Quantum Gravity 22 (2005, 3511 and Classical Quantum Gravity 23 (2006, 1883], we describe noncommutative spacetimes by using (Abelian Drinfel'd twists and the associated *-products and *-differential geometry. In particular, we allow for position dependent noncommutativity and do not restrict ourselves to the Moyal-Weyl deformation. We construct action functionals for real scalar fields on noncommutative curved spacetimes, and derive the corresponding deformed wave equations. We provide explicit examples of deformed Klein-Gordon operators for noncommutative Minkowski, de Sitter, Schwarzschild and Randall-Sundrum spacetimes, which solve the noncommutative Einstein equations. We study the construction of deformed Green's functions and provide a diagrammatic approach for their perturbative calculation. The leading noncommutative corrections to the Green's functions for our examples are derived.
Noncommutative Time in Quantum Field Theory
Salminen, Tapio
2011-01-01
We analyze, starting from first principles, the quantization of field theories, in order to find out to which problems a noncommutative time would possibly lead. We examine the problem in the interaction picture (Tomonaga-Schwinger equation), the Heisenberg picture (Yang-Feldman-K\\"all\\'{e}n equation) and the path integral approach. They all indicate inconsistency when time is taken as a noncommutative coordinate. The causality issue appears as the key aspect, while the unitarity problem is subsidiary. These results are consistent with string theory, which does not admit a time-space noncommutative quantum field theory as its low-energy limit, with the exception of light-like noncommutativity.
Gauge field theories: various mathematical approaches
Jordan, François; Thierry, Masson
2014-01-01
This paper presents relevant modern mathematical formulations for (classical) gauge field theories, namely, ordinary differential geometry, noncommutative geometry, and transitive Lie algebroids. They provide rigorous frameworks to describe Yang-Mills-Higgs theories or gravitation theories, and each of them improves the paradigm of gauge field theories. A brief comparison between them is carried out, essentially due to the various notions of connection. However they reveal a compelling common mathematical pattern on which the paper concludes.
Nonperturbative studies of quantum field theories on noncommutative spaces
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Volkholz, J.
2007-11-16
This work deals with three quantum field theories on spaces with noncommuting position operators. Noncommutative models occur in the study of string theories and quantum gravity. They usually elude treatment beyond the perturbative level. Due to the technique of dimensional reduction, however, we are able to investigate these theories nonperturbatively. This entails translating the action functionals into a matrix language, which is suitable for numerical simulations. First we explore the {lambda}{phi}{sup 4} model on a noncommutative plane. We investigate the continuum limit at fixed noncommutativity, which is known as the double scaling limit. Here we focus especially on the fate of the striped phase, a phase peculiar to the noncommutative version of the regularized {lambda}{phi}{sup 4} model. We find no evidence for its existence in the double scaling limit. Next we examine the U(1) gauge theory on a four-dimensional spacetime, where two spatial directions are noncommutative. We examine the phase structure and find a new phase with a spontaneously broken translation symmetry. In addition we demonstrate the existence of a finite double scaling limit which confirms the renormalizability of the theory. Furthermore we investigate the dispersion relation of the photon. In the weak coupling phase our results are consistent with an infrared instability predicted by perturbation theory. If the translational symmetry is broken, however, we find a dispersion relation corresponding to a massless particle. Finally, we investigate a supersymmetric theory on the fuzzy sphere, which features scalar neutral bosons and Majorana fermions. The supersymmetry is exact in the limit of infinitely large matrices. We investigate the phase structure of the model and find three distinct phases. Summarizing, we study noncommutative field theories beyond perturbation theory. Moreover, we simulate a supersymmetric theory on the fuzzy sphere, which might provide an alternative to attempted
Space-Time Noncommutative Field Theories And Unitarity
Gomis, Jaume; Mehen, Thomas
2000-01-01
We study the perturbative unitarity of noncommutative scalar field theories. Field theories with space-time noncommutativity do not have a unitary S-matrix. Field theories with only space noncommutativity are perturbatively unitary. This can be understood from string theory, since space noncommutative field theories describe a low energy limit of string theory in a background magnetic field. On the other hand, there is no regime in which space-time noncommutative field theory is an appropriat...
Noncommutative Geometry in M-Theory and Conformal Field Theory
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Morariu, Bogdan [Univ. of California, Berkeley, CA (United States)
1999-05-01
In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U_{q}(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun_{q} (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.
Magnetic Backgrounds and Noncommutative Field Theory
Szabo, Richard J.
2004-01-01
This paper is a rudimentary introduction, geared at non-specialists, to how noncommutative field theories arise in physics and their applications to string theory, particle physics and condensed matter systems.
Noncommutative quantum field theory
Energy Technology Data Exchange (ETDEWEB)
Grosse, H. [Fakultaet fuer Physik, Universitaet Wien, Boltzmanngasse 5, 1090 Wien (Austria); Wulkenhaar, R. [Mathematisches Institut der Westfaelischen Wilhelms-Universitaet, Einsteinstrasse 62, 48149 Muenster (Germany)
2014-09-11
We summarize our recent construction of the φ{sup 4}-model on four-dimensional Moyal space. This is achieved by solving the quartic matrix model for a general external matrix in terms of the solution of a non-linear equation for the 2-point function and the eigenvalues of that matrix. The β-function vanishes identically. For the Moyal model, the theory of Carleman type singular integral equations reduces the construction to a fixed point problem. The resulting Schwinger functions in position space are symmetric and invariant under the full Euclidean group. The Schwinger 2-point function is reflection positive iff the diagonal matrix 2-point function is a Stieltjes function. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Gauge theory and little gauge theory
Koizumi, Kozo
2016-01-01
The gauge theory is the most important type of the field theory, in which the interactions of the elementary particles are described by the exchange of the gauge bosons.In this article, the gauge theory is reexamined as geometry of the vector space, and a new concept of "little gauge theory" is introduced. A key peculiarity of the little gauge theory is that the theory is able to give a restriction for form of the connection field. Based on the little gauge theory, Cartan geometry, a charged boson and the Dirac fermion field theory are investigated. In particular, the Dirac fermion field theory leads to an extension of Sogami's covariant derivative. And it is interpreted that Higgs bosons are included in new fields introduced in this article.
Noncommutative Field Theory on Homogeneous Gravitational Waves
Halliday, S; Halliday, Sam; Szabo, Richard J.
2006-01-01
We describe an algebraic approach to the time-dependent noncommutative geometry of a six-dimensional Cahen-Wallach pp-wave string background supported by a constant Neveu-Schwarz flux, and develop a general formalism to construct and analyse quantum field theories defined thereon. Various star-products are derived in closed explicit form and the Hopf algebra of twisted isometries of the plane wave is constructed. Scalar field theories are defined using explicit forms of derivative operators, traces and noncommutative frame fields for the geometry, and various physical features are described. Noncommutative worldvolume field theories of D-branes in the pp-wave background are also constructed.
Aspects of perturbative quantum field theory on non-commutative spaces
Blaschke, Daniel N
2016-01-01
In this contribution to the proceedings of the Corfu Summer Institute 2015, I give an overview over quantum field theories on non-commutative Moyal space and renormalization. In particular, I review the new features and challenges one faces when constructing various scalar, fermionic and gauge field theories on Moyal space, and especially how the UV/IR mixing problem was solved for certain models. Finally, I outline more recent progress in constructing a renormalizable gauge field model on non-commutative space, and how one might attempt to prove renormalizability of such a model using a generalized renormalization scheme adapted to the non-commutative (and hence non-local) setting.
Topological Charge of Lattice Abelian Gauge Theory
Fujiwara, T; Wu, K
2001-01-01
Configuration space of abelian gauge theory on a periodic lattice becomes topologically disconnected by excising exceptional gauge field configurations. It is possible to define a U(1) bundle from the nonexceptional link variables by a smooth interpolation of the transition functions. The lattice analogue of Chern character obtained by a cohomological technique based on the noncommutative differential calculus is shown to give a topological charge related to the topological winding number of the U(1) bundle.
Noncommutative Dipole Field Theories And Unitarity
Chiou, D W; Chiou, Dah-Wei; Ganor, Ori J.
2004-01-01
We extend the argument of Gomis and Mehen for violation of unitarity in field theories with space-time noncommutativity to dipole field theories. In dipole field theories with a timelike dipole vector, we present 1-loop amplitudes that violate the optical theorem. A quantum mechanical system with nonlocal potential of finite extent in time also shows violation of unitarity.
de Wild Propitius, M.D.F.; Bais, F.A.
1999-01-01
In these lectures, we present a self-contained treatment of planar gauge theories broken down to some finite residual gauge group $H$ via the Higgs mechanism. The main focus is on the discrete $H$ gauge theory describing the long distance physics of such a model. The spectrum features global $H$ cha
Quantum Fields on Noncommutative Spacetimes: Theory and Phenomenology
Directory of Open Access Journals (Sweden)
Aiyalam P. Balachandran
2010-06-01
Full Text Available In the present work we review the twisted field construction of quantum field theory on noncommutative spacetimes based on twisted Poincaré invariance. We present the latest development in the field, in particular the notion of equivalence of such quantum field theories on a noncommutative spacetime, in this regard we work out explicitly the inequivalence between twisted quantum field theories on Moyal and Wick-Voros planes; the duality between deformations of the multiplication map on the algebra of functions on spacetime F(R^4 and coproduct deformations of the Poincaré-Hopf algebra HP acting on F(R^4; the appearance of a nonassociative product on F(R^4 when gauge fields are also included in the picture. The last part of the manuscript is dedicated to the phenomenology of noncommutative quantum field theories in the particular approach adopted in this review. CPT violating processes, modification of two-point temperature correlation function in CMB spectrum analysis and Pauli-forbidden transition in Be^4 are all effects which show up in such a noncommutative setting. We review how they appear and in particular the constraint we can infer from comparison between theoretical computations and experimental bounds on such effects. The best bound we can get, coming from Borexino experiment, is >10^{24} TeV for the energy scale of noncommutativity, which corresponds to a length scale <10^{-43} m. This bound comes from a different model of spacetime deformation more adapted to applications in atomic physics. It is thus model dependent even though similar bounds are expected for the Moyal spacetime as well as argued elsewhere.
Natural discretization in noncommutative field theory
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Acatrinei, Ciprian Sorin, E-mail: acatrine@theory.nipne.ro [Department of Theoretical Physics, Horia Hulubei National Institute for Nuclear Physics, Bucharest (Romania)
2015-12-07
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
Natural discretization in noncommutative field theory
Acatrinei, Ciprian Sorin
2015-12-01
A discretization scheme for field theory is developed, in which the space time coordinates are assumed to be operators forming a noncommutative algebra. Generic waves without rotational symmetry are studied in (2+1) - dimensional scalar field theory with Heisenberg-type noncommutativity. In the representation chosen, the radial coordinate is naturally rendered discrete. Nonlocality along this coordinate, induced by noncommutativity, accounts for the angular dependence of the fields. A complete solution and the interpretation of its nonlocal features are given. The exact form of standing and propagating waves on such a discrete space is found in terms of finite series. A precise correspondence is established between the degree of nonlocality and the angular momentum of a field configuration. At small distance no classical singularities appear, even at the location of the sources. At large radius one recovers the usual commutative/continuum behaviour.
López-Permouth, Sergio
1990-01-01
The papers of this volume share as a common goal the structure and classi- fication of noncommutative rings and their modules, and deal with topics of current research including: localization, serial rings, perfect endomorphism rings, quantum groups, Morita contexts, generalizations of injectivitiy, and Cartan matrices.
Combinatorial Hopf Algebras in (Noncommutative) Quantum Field Theory
Tanasa, Adrian
2010-01-01
We briefly review the r\\^ole played by algebraic structures like combinatorial Hopf algebras in the renormalizability of (noncommutative) quantum field theory. After sketching the commutative case, we analyze the noncommutative Grosse-Wulkenhaar model.
Prime divisors and noncommutative valuation theory
Marubayashi, Hidetoshi
2012-01-01
Classical valuation theory has applications in number theory and class field theory as well as in algebraic geometry, e.g. in a divisor theory for curves. But the noncommutative equivalent is mainly applied to finite dimensional skewfields. Recently however, new types of algebras have become popular in modern algebra; Weyl algebras, deformed and quantized algebras, quantum groups and Hopf algebras, etc. The advantage of valuation theory in the commutative case is that it allows effective calculations, bringing the arithmetical properties of the ground field into the picture. This arithmetical nature is also present in the theory of maximal orders in central simple algebras. Firstly, we aim at uniting maximal orders, valuation rings, Dubrovin valuations, etc. in a common theory, the theory of primes of algebras. Secondly, we establish possible applications of the noncommutative arithmetics to interesting classes of algebras, including the extension of central valuations to nice classes of quantized a...
Lie algebraic Noncommutative Gravity
Banerjee, R; Samanta, S; Banerjee, Rabin; Mukherjee, Pradip; Samanta, Saurav
2007-01-01
The minimal (unimodular) formulation of noncommutative general relativity, based on gauging the Poincare group, is extended to a general Lie algebra valued noncommutative structure. We exploit the Seiberg -- Witten map technique to formulate the theory as a perturbative Lagrangian theory. Detailed expressions of the Seiberg -- Witten maps for the gauge parameters, gauge potentials and the field strengths have been worked out. Our results demonstrate that notwithstanding the introduction of more general noncommutative structure there is no first order correction, exactly as happens for a canonical (i.e. constant) noncommutativity.
Generalized Higher Gauge Theory
Ritter, Patricia; Schmidt, Lennart
2015-01-01
We study a generalization of higher gauge theory which makes use of generalized geometry and seems to be closely related to double field theory. The local kinematical data of this theory is captured by morphisms of graded manifolds between the canonical exact Courant Lie 2-algebroid $TM\\oplus T^*M$ over some manifold $M$ and a semistrict gauge Lie 2-algebra. We discuss generalized curvatures and their infinitesimal gauge transformations. Finite gauge transformation as well as global kinematical data are then obtained from principal 2-bundles over 2-spaces. As dynamical principle, we consider first the canonical Chern-Simons action for such a gauge theory. We then show that a previously proposed 3-Lie algebra model for the six-dimensional (2,0) theory is very naturally interpreted as a generalized higher gauge theory.
Supergravity from Gauge Theory
Berkowitz, Evan
2016-01-01
Gauge/gravity duality is the conjecture that string theories have dual descriptions as gauge theories. Weakly-coupled gravity is dual to strongly-coupled gauge theories, ideal for lattice calculations. I will show precision lattice calculations that confirm large-N continuum D0-brane quantum mechanics correctly reproduces the leading-order supergravity prediction for a black hole's internal energy---the first leading-order test of the duality---and constrains stringy corrections.
W∞ Algebras from Noncommutative Chern Simons Theory
Pinzul, A.; Stern, A.
We examine Chern Simons theory written on a noncommutative plane with a "hole", and show that the algebra of observables is a nonlinear deformation of the w∞ algebra. The deformation depends on the level (the coefficient in the Chern Simons action), and the noncommutativity parameter, which were identified, respectively, with the inverse filling fraction (minus one) and the inverse density in a recent description of the fractional quantum Hall effect. We remark on the quantization of our algebra. The results are sensitive to the choice of ordering in the Gauss law.
Measure Theory in Noncommutative Spaces
Directory of Open Access Journals (Sweden)
Steven Lord
2010-09-01
Full Text Available The integral in noncommutative geometry (NCG involves a non-standard trace called a Dixmier trace. The geometric origins of this integral are well known. From a measure-theoretic view, however, the formulation contains several difficulties. We review results concerning the technical features of the integral in NCG and some outstanding problems in this area. The review is aimed for the general user of NCG.
Monopoles in Space-Time Noncommutative Born-Infeld theory
Aschieri, Paolo
2001-01-01
We transform static solutions of space-noncommutative Dirac-Born-Infeld theory (DBI) into static solutions of space-time noncommutative DBI. Via Seiberg-Witten map we match this symmetry transformation with a corresponding symmetry of commutative DBI. This allows to: 1) study new BPS type magnetic monopoles, with constant electric and magnetic background and describe them both in the commutative and in the noncommutative setting; 2) relate by S-duality space-noncommutative magnetic monopoles ...
Lie algebraic noncommutative gravity
Banerjee, Rabin; Mukherjee, Pradip; Samanta, Saurav
2007-06-01
We exploit the Seiberg-Witten map technique to formulate the theory of gravity defined on a Lie algebraic noncommutative space-time. Detailed expressions of the Seiberg-Witten maps for the gauge parameters, gauge potentials, and the field strengths have been worked out. Our results demonstrate that notwithstanding the introduction of more general noncommutative structure there is no first order correction, exactly as happens for a canonical (i.e. constant) noncommutativity.
Higher order theories and their relationship with noncommutativity
Energy Technology Data Exchange (ETDEWEB)
Sánchez-Santos, Oscar, E-mail: oscarsanbuzz@yahoo.com.mx [Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, C.P. 09340, México D.F., México (Mexico); Vergara, José David, E-mail: vergara@nucleares.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, C.P. 04510, México D.F., México (Mexico)
2014-06-13
We present a relationship between noncommutativity and higher order time derivative theories using a perturbation method. We make a generalization of the Chern–Simons quantum mechanics for higher order time derivatives. This model presents noncommutativity in a natural way when we project to low-energy physical states without the necessity of taking the strong field limit. We quantize the theory using a Bopp's shift of the noncommutative variables and we obtain a spectrum without negative energies, under the perturbation limits. In addition, we extent the model to high order time derivatives and noncommutativity with variable dependent parameter. - Highlights: • We show a relationship between high order derivative theories and noncommutativity. • The noncommutativity appears when we project to low-energy physical states. • We extend the model to high order time derivatives. • We include cases with variable dependent noncommutative parameter.
Chung, Daniel J H
2016-01-01
We reformulate gauge theories in analogy with the vierbein formalism of general relativity. More specifically, we reformulate gauge theories such that their gauge dynamical degrees of freedom are local fields that transform linearly under the dual representation of the charged matter field. These local fields, which naively have the interpretation of non-local operators similar to Wilson lines, satisfy constraint equations. A set of basis tensor fields are used to solve these constraint equations, and their field theory is constructed. A new local symmetry in terms of the basis tensor fields is used to make this field theory local and maintain a Hamiltonian that is bounded from below. The field theory of the basis tensor fields is what we call the basis tensor gauge theory.
Healey, Richard
Those looking for holism in contemporary physics have focused their attention primarily on quantum entanglement. But some gauge theories arguably also manifest the related phenomenon of nonseparability. While the argument is strong for the classical gauge theory describing electromagnetic interactions with quantum "particles", it fails in the case of general relativity even though that theory may also be formulated in terms of a connection on a principal fiber bundle. Anandan has highlighted the key difference in his analysis of a supposed gravitational analog to the Aharonov-Bohm effect. By contrast with electromagnetism in the original Aharonov-Bohm effect, gravitation is separable and exhibits no novel holism in this case. Whether the nonseparability of classical gauge theories of nongravitational interactions is associated with holism depends on what counts as the relevant part-whole relation. Loop representations of quantized gauge theories of nongravitational interactions suggest that these conclusions about holism and nonseparability may extend also to quantum theories of the associated fields.
Geometry of time-spaces non-commutative algebraic geometry, applied to quantum theory
Landau, Olav Arnfinn
2011-01-01
This is a monograph about non-commutative algebraic geometry, and its application to physics. The main mathematical inputs are the non-commutative deformation theory, moduli theory of representations of associative algebras, a new non-commutative theory o
O (θ ) Feynman rules for quadrilinear gauge boson couplings in the noncommutative standard model
Sajadi, Seyed Shams; Boroun, G. R.
2017-02-01
We examine the electroweak gauge sector of the noncommutative standard model and, in particular, obtain the O (θ ) Feynman rules for all quadrilinear gauge boson couplings. Surprisingly, an electroweak-chromodynamics mixing appears in the gauge sector of the noncommutative standard model, where the photon as well as the neutral weak boson is coupled directly to three gluons. The phenomenological perspectives of the model in W-W+→Z Z scattering are studied and it is shown that there is a characteristic oscillatory behavior in azimuthal distribution of scattering cross sections that can be interpreted as a direct signal of the noncommutative standard model. Assuming the integrated luminosity 100 fb-1, the number of W-W+→Z Z subprocesses are estimated for some values of noncommutative scale ΛNC at different center of mass energies and the results are compared with predictions of the standard model.
Sasai, Yuya; Sasakura, Naoki
2009-12-01
We have investigated the unitarity of three dimensional noncommutative scalar field theory in Lie algebraic noncommutative spacetime [x̂i, x̂j] = 2iκɛijkx̂k, (i, j, k = 0, 1, 2). This noncommutative field theory possesses an SL(2, R)/Z2 group momentum space, which leads to a Hopf algebraic translational symmetry. We have checked the Cutkosky rule of the one-loop self-energy diagrams in the noncommutative φ3 theory when we include a braiding, which is necessary for the noncommutative field theory to possess the Hopf algebraic translational symmetry at quantum level. Then, we have found that the Cutkosky rule is satisfied if the mass of the scalar field is less than 1/√2κ , which however leads to be violations of the Cutkosky rule for smaller masses in more complicated diagrams.
Sasai, Yuya
2009-01-01
We investigate the unitarity of three dimensional noncommutative scalar field theory in the Lie algebraic noncommutative spacetime [x^i,x^j]=2i kappa epsilon^{ijk}x_k. This noncommutative field theory possesses a SL(2,R)/Z_2 group momentum space, which leads to a Hopf algebraic translational symmetry. We check the Cutkosky rule of the one-loop self-energy diagrams in the noncommutative phi^3 theory when we include a braiding, which is necessary for the noncommutative field theory to possess the Hopf algebraic translational symmetry at quantum level. Then, we find that the Cutkosky rule is satisfied if the mass is less than 1/(2^(1/2)kappa).
Maas, Axel
2012-01-01
QCD can be formulated using any gauge group. One particular interesting choice is to replace SU(3) by the exceptional group G2. Conceptually, this group is the simplest group with a trivial center. It thus permits to study the conjectured relevance of center degrees of freedom for QCD. Practically, since all its representation are real, it is possible to perform lattice simulations for this theory also at finite baryon densities. It is thus an excellent environment to test methods and to investigate general properties of gauge theories at finite densities. We review the status of our understanding of gauge theories with the gauge group G2, including Yang-Mills theory, Yang-Mills-Higgs theory, and QCD both in the vacuum and in the phase diagram.
Carlson, C E; Lebed, R F; Carlson, Carl E.; Carone, Christopher D.; Lebed, Richard F.
2001-01-01
Jurco, Moller, Schraml, Schupp, and Wess have shown how to construct noncommutative SU(N) gauge theories from a consistency relation. Within this framework, we present the Feynman rules for noncommutative QCD and compute explicitly the most dangerous Lorentz-violating operator generated through radiative corrections. We find that interesting effects appear at the one-loop level, in contrast to conventional noncommutative U(N) gauge theories, leading to a stringent bound. Our results are consistent with others appearing recently in the literature that suggest collider limits are not competitive with low-energy tests of Lorentz violation for bounding the scale of spacetime noncommutativity.
Non-commutative field theory and the parameters of Lorentz violation in QED
Directory of Open Access Journals (Sweden)
S Aghababaei
2011-09-01
Full Text Available Non-commutative field theory as a theory including the Lorentz violation can be constructed in two different ways. In the first method, the non-commutative fields are the same as the ordinary ones while the gauge group is restricted to U(n. For example, the symmetry group of standard model in non-commutative space is U(3×(2×U(1 which can be reduced to SU(3×SU(2×U(1 by two appropriate spontaneous symmetry breaking. In contrast, in the second method, the non-commutative gauge theory can be constructed for SU(n gauge group via Seiberg- Witten map. In this work, we want to find the relation between the NC-parameter and the Lorentz violation parameters for the first method and compare our results with what is already found in the second one. At the end, we obtain new limits on non-commutative parameter by using the existing bounds on the Lorentz Violation parameters.
Henneaux, Marc; Vasiliev, Mikhail A
2017-01-01
Symmetries play a fundamental role in physics. Non-Abelian gauge symmetries are the symmetries behind theories for massless spin-1 particles, while the reparametrization symmetry is behind Einstein's gravity theory for massless spin-2 particles. In supersymmetric theories these particles can be connected also to massless fermionic particles. Does Nature stop at spin-2 or can there also be massless higher spin theories. In the past strong indications have been given that such theories do not exist. However, in recent times ways to evade those constraints have been found and higher spin gauge theories have been constructed. With the advent of the AdS/CFT duality correspondence even stronger indications have been given that higher spin gauge theories play an important role in fundamental physics. All these issues were discussed at an international workshop in Singapore in November 2015 where the leading scientists in the field participated. This volume presents an up-to-date, detailed overview of the theories i...
Viscous conformal gauge theories
DEFF Research Database (Denmark)
Toniato, Arianna; Sannino, Francesco; Rischke, Dirk H.
2017-01-01
We present the conformal behavior of the shear viscosity-to-entropy density ratio and the fermion-number diffusion coefficient within the perturbative regime of the conformal window for gauge-fermion theories.......We present the conformal behavior of the shear viscosity-to-entropy density ratio and the fermion-number diffusion coefficient within the perturbative regime of the conformal window for gauge-fermion theories....
Exact partition functions for gauge theories on Rλ3
Directory of Open Access Journals (Sweden)
Jean-Christophe Wallet
2016-11-01
Full Text Available The noncommutative space Rλ3, a deformation of R3, supports a 3-parameter family of gauge theory models with gauge-invariant harmonic term, stable vacuum and which are perturbatively finite to all orders. Properties of this family are discussed. The partition function factorizes as an infinite product of reduced partition functions, each one corresponding to the reduced gauge theory on one of the fuzzy spheres entering the decomposition of Rλ3. For a particular sub-family of gauge theories, each reduced partition function is exactly expressible as a ratio of determinants. A relation with integrable 2-D Toda lattice hierarchy is indicated.
Exact partition functions for gauge theories on Rλ3
Wallet, Jean-Christophe
2016-11-01
The noncommutative space R,SUB>λ3, a deformation of R3, supports a 3-parameter family of gauge theory models with gauge-invariant harmonic term, stable vacuum and which are perturbatively finite to all orders. Properties of this family are discussed. The partition function factorizes as an infinite product of reduced partition functions, each one corresponding to the reduced gauge theory on one of the fuzzy spheres entering the decomposition of R&x03bb;3. For a particular sub-family of gauge theories, each reduced partition function is exactly expressible as a ratio of determinants. A relation with integrable 2-D Toda lattice hierarchy is indicated.
Gauge theory on twisted kappa-Minkowski: old problems and possible solutions
Dimitrijevic, Marija; Pachol, Anna
2014-01-01
We review the application of twist deformation formalism and the construction of noncommutative gauge theory on kappa-Minkowski space-time. We compare two different types of twists: the Abelian and the Jordanian one. In each case we provide the twisted differential calculus and consider U(1) gauge theory. Different methods of obtaining a gauge invariant action and related problems are thoroughly discussed.
Gauge Theory on Twisted kappa-Minkowski: Old Problems and Possible Solutions
Dimitrijević, Marija; Jonke, Larisa; Pachoł, Anna
2014-06-01
We review the application of twist deformation formalism and the construction of noncommutative gauge theory on κ-Minkowski space-time. We compare two different types of twists: the Abelian and the Jordanian one. In each case we provide the twisted differential calculus and consider {U}(1) gauge theory. Different methods of obtaining a gauge invariant action and related problems are thoroughly discussed.
Digital lattice gauge theories
Zohar, Erez; Reznik, Benni; Cirac, J Ignacio
2016-01-01
We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with $2+1$ dimensions and higher, are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through pertubative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a $\\mathbb{Z}_{3}$ lattice gauge theory with dynamical fermionic matter in $2+1$ dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms...
Noncommutative gravity and quantum field theory on noncummutative curved spacetimes
Energy Technology Data Exchange (ETDEWEB)
Schenkel, Alexander
2011-10-24
The purpose of the first part of this thesis is to understand symmetry reduction in noncommutative gravity, which then allows us to find exact solutions of the noncommutative Einstein equations. We propose an extension of the usual symmetry reduction procedure, which is frequently applied to the construction of exact solutions of Einstein's field equations, to noncommutative gravity and show that this leads to preferred choices of noncommutative deformations of a given symmetric system. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models, for which the noncommutative metric field coincides with the classical one. In the second part we focus on quantum field theory on noncommutative curved spacetimes. We develop a new formalism by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. The result is an algebra of observables for scalar quantum field theories on a large class of noncommutative curved spacetimes. A precise relation to the algebra of observables of the corresponding undeformed quantum field theory is established. We focus on explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories, which is not the case in the simplest example of the Moyal-Weyl deformed Minkowski spacetime. The convergent deformation of simple toy-models is investigated and it is shown that these quantum field theories have many new features compared to formal deformation quantization. In addition to the expected nonlocality, we obtain that the relation between the deformed and the undeformed quantum field theory is affected in a nontrivial way, leading to an improved behavior of the
Blagojević, Milutin
2012-01-01
During the last five decades, gravity, as one of the fundamental forces of nature, has been formulated as a gauge field theory of the Weyl-Cartan-Yang-Mills type. The resulting theory, the Poincar\\'e gauge theory of gravity, encompasses Einstein's gravitational theory as well as the teleparallel theory of gravity as subcases. In general, the spacetime structure is enriched by Cartan's torsion and the new theory can accommodate fermionic matter and its spin in a perfectly natural way. The present reprint volume contains articles from the most prominent proponents of the theory and is supplemented by detailed commentaries of the editors. This guided tour starts from special relativity and leads, in its first part, to general relativity and its gauge type extensions a la Weyl and Cartan. Subsequent stopping points are the theories of Yang-Mills and Utiyama and, as a particular vantage point, the theory of Sciama and Kibble. Later, the Poincar\\'e gauge theory and its generalizations are explored and specific topi...
Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theory
Energy Technology Data Exchange (ETDEWEB)
Cirafici, Michele [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands)], E-mail: m.cirafici@uu.nl; Sinkovics, Annamaria [Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)], E-mail: a.sinkovics@damtp.cam.ac.uk; Szabo, Richard J. [Department of Mathematics, Heriot-Watt University and Maxwell Institute for Mathematical Sciences, Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS (United Kingdom)], E-mail: r.j.szabo@ma.hw.ac.uk
2009-03-11
We study the relation between Donaldson-Thomas theory of Calabi-Yau threefolds and a six-dimensional topological Yang-Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its partition function we use equivariant localization techniques on its noncommutative deformation. As a result the gauge theory localizes on noncommutative instantons which can be classified in terms of N-coloured three-dimensional Young diagrams. We give to these noncommutative instantons a geometrical description in terms of certain stable framed coherent sheaves on projective space by using a higher-dimensional generalization of the ADHM formalism. From this formalism we construct a topological matrix quantum mechanics which computes an index of BPS states and provides an alternative approach to the six-dimensional gauge theory.
Frampton, Paul H
2008-01-01
This third edition on the classic Gauge Field Theories is an ideal reference for researchers starting work with the Large Hadron Collider and the future International Linear Collider. This latest title continues to offer an up to date reference containing revised chapters on electroweak interactions and model building including a completely new chapter on conformality. Within this essential reference logical organization of the material on gauge invariance, quantization, and renormalization is also discussed providing necessary reading for Cosmologists and Particle Astrophysicists
Bassetto, A.; Nardelli, G.; Torrielli, A.
2002-10-01
Commutative Yang-Mills theories in 1+1 dimensions exhibit an interesting interplay between geometrical properties and U(N) gauge structures: in the exact expression of a Wilson loop with n windings a nontrivial scaling intertwines n and N. In the noncommutative case the interplay becomes tighter owing to the merging of space-time and ``internal'' symmetries in a larger gauge group U(∞). We perform an explicit perturbative calculation of such a loop up to O(g6) rather surprisingly, we find that in the contribution from the crossed graphs (the genuine noncommutative terms) the scaling we mentioned occurs for large n and N in the limit of maximal noncommutativity θ=∞. We present arguments in favor of the persistence of such a scaling at any perturbative order and succeed in summing the related perturbative series.
Gaussian processes in non-commutative probability theory
Guţǎ, M.I.
2002-01-01
The generalisation of the notion of Gaussian processes from probability theory is investigated in the context of non-commutative probability theory. A non-commutative Gaussian process is viewed as a linear map from an infinite dimensional (real) Hilbert space into an algebra with involution and a po
Causality in non-commutative quantum field theories
Energy Technology Data Exchange (ETDEWEB)
Haque, Asrarul; Joglekar, Satish D [Department of Physics, I.I.T. Kanpur, Kanpur 208 016 (India)], E-mail: ahaque@iitk.ac.in, E-mail: sdj@iitk.ac.in
2008-05-30
We study causality in noncommutative quantum field theory with a space-space noncommutativity. We employ the S operator approach of Bogoliubov-Shirkov (BS). We generalize the BS criterion of causality to the noncommutative theory. The criterion to test causality leads to a nonzero difference between the T* product and the T product as a condition of causality violation for a spacelike separation. We discuss two examples; one in a scalar theory and another in the Yukawa theory. In particular, in the context of a noncommutative Yukawa theory, with the interaction Lagrangian {psi}-bar(x)*{psi}(x)*{phi}(x), is observed to be causality violating even in the case of space-space noncommutativity for which {theta}{sup 0i} = 0.
Modesto, Leonardo; Piva, Marco; Rachwał, Lesław
2016-07-01
We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular, Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is unitary (ghost-free) and perturbatively super-renormalizable. Moreover, in the action we can always choose the potential (consisting of one "killer operator") to make zero the beta function of the running gauge coupling constant. The outcome is a UV finite theory for any gauge interaction. Our calculations are done in D =4 , but the results can be generalized to even or odd spacetime dimensions. We compute the contribution to the beta function from two different killer operators by using two independent techniques, namely, the Feynman diagrams and the Barvinsky-Vilkovisky traces. By making the theories finite, we are able to solve also the Landau pole problems, in particular, in QED. Without any potential, the beta function of the one-loop super-renormalizable theory shows a universal Landau pole in the running coupling constant in the ultraviolet regime (UV), regardless of the specific higher-derivative structure. However, the dressed propagator shows neither the Landau pole in the UV nor the singularities in the infrared regime (IR).
High-Energy Scattering in Non-Commutative Field Theory
Kumar, J; Kumar, Jason; Rajaraman, Arvind
2005-01-01
We analyze high energy scattering for non-commutative field theories using the dual gravity description. We find that the Froissart-Martin bound still holds, but that cross-sections stretch in the non-commutative directions in a way dependent on the infrared cutoff. This puzzling behavior suggests new aspects of UV/IR mixing.
DEFF Research Database (Denmark)
Mojaza, Matin; Pica, Claudio; Sannino, Francesco
2010-01-01
We compute the nonzero temperature free energy up to the order g^6 \\ln(1/g) in the coupling constant for vector like SU(N) gauge theories featuring matter transforming according to different representations of the underlying gauge group. The number of matter fields, i.e. flavors, is arranged in s.......e. they are independent on the specific matter representation.......We compute the nonzero temperature free energy up to the order g^6 \\ln(1/g) in the coupling constant for vector like SU(N) gauge theories featuring matter transforming according to different representations of the underlying gauge group. The number of matter fields, i.e. flavors, is arranged...... in such a way that the theory develops a perturbative stable infrared fixed point at zero temperature. Due to large distance conformality we trade the coupling constant with its fixed point value and define a reduced free energy which depends only on the number of flavors, colors and matter representation. We...
Digital lattice gauge theories
Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J. Ignacio
2017-02-01
We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with 2 +1 dimensions and higher are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through perturbative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a Z3 lattice gauge theory with dynamical fermionic matter in 2 +1 dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge, and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms with a proper sequence of steps, we show how we can obtain the desired evolution in a clean, controlled way.
Weisz, Peter; Majumdar, Pushan
2012-03-01
Lattice gauge theory is a formulation of quantum field theory with gauge symmetries on a space-time lattice. This formulation is particularly suitable for describing hadronic phenomena. In this article we review the present status of lattice QCD. We outline some of the computational methods, discuss some phenomenological applications and a variety of non-perturbative topics. The list of references is severely incomplete, the ones we have included are text books or reviews and a few subjectively selected papers. Kronfeld and Quigg (2010) supply a reasonably comprehensive set of QCD references. We apologize for the fact that have not covered many important topics such as QCD at finite density and heavy quark effective theory adequately, and mention some of them only in the last section "In Brief". These topics should be considered in further Scholarpedia articles.
Noncommutative spectral geometry and the deformed Hopf algebra structure of quantum field theory
Sakellariadou, Mairi; Stabile, Antonio; Vitiello, Giuseppe
2013-06-01
We report the results obtained in the study of Alain Connes noncommutative spectral geometry construction focusing on its essential ingredient of the algebra doubling. We show that such a two-sheeted structure is related with the gauge structure of the theory, its dissipative character and carries in itself the seeds of quantization. From the algebraic point of view, the algebra doubling process has the same structure of the deformed Hops algebra structure which characterizes quantum field theory.
Noncommutative spectral geometry and the deformed Hopf algebra structure of quantum field theory
Sakellariadou, Mairi; Vitiello, Giuseppe
2013-01-01
We report the results obtained in the study of Alain Connes noncommutative spectral geometry construction focusing on its essential ingredient of the algebra doubling. We show that such a two-sheeted structure is related with the gauge structure of the theory, its dissipative character and carries in itself the seeds of quantization. From the algebraic point of view, the algebra doubling process has the same structure of the deformed Hops algebra structure which characterizes quantum field theory.
Noncommutative analysis, operator theory and applications
Cipriani, Fabio; Colombo, Fabrizio; Guido, Daniele; Sabadini, Irene; Sauvageot, Jean-Luc
2016-01-01
This book illustrates several aspects of the current research activity in operator theory, operator algebras and applications in various areas of mathematics and mathematical physics. It is addressed to specialists but also to graduate students in several fields including global analysis, Schur analysis, complex analysis, C*-algebras, noncommutative geometry, operator algebras, operator theory and their applications. Contributors: F. Arici, S. Bernstein, V. Bolotnikov, J. Bourgain, P. Cerejeiras, F. Cipriani, F. Colombo, F. D'Andrea, G. Dell'Antonio, M. Elin, U. Franz, D. Guido, T. Isola, A. Kula, L.E. Labuschagne, G. Landi, W.A. Majewski, I. Sabadini, J.-L. Sauvageot, D. Shoikhet, A. Skalski, H. de Snoo, D. C. Struppa, N. Vieira, D.V. Voiculescu, and H. Woracek.
Quantum field theory on a discrete space and noncommutative geometry
Haeussling, R.
2001-01-01
We analyse in detail the quantization of a simple noncommutative model of spontaneous symmetry breaking in zero dimensions taking into account the noncommutative setting seriously. The connection to the counting argument of Feyman diagrams of the corresponding theory in four dimensions is worked out explicitly. Special emphasis is put on the motivation as well as the presentation of some well-known basic notions of quantum field theory which in the zero-dimensional theory can be studied witho...
Noncommutative Topological Half-flat Gravity
García-Compéan, H; Ramírez, C
2004-01-01
We formulate a noncommutative description of topological half-flat gravity in four dimensions. BRST symmetry of this topological gravity is deformed through a twisting of the usual BRST quantization of noncommutative gauge theories. Finally it is argued that resulting moduli space of instantons is characterized by the solutions of a noncommutative version of the Plebanski's heavenly equation.
Enveloping algebra Noncommutative SM: Renormalisability and High Energy Physics Phenomenology
Trampetic, Josip
2009-01-01
In this talk we discuss enveloping algebra based noncommutative gauge field theory, constructed at the first order in noncommutative parameter theta, as an effective, anomaly free theory, with one-loop renormalizable gauge sector. Limits on the scale of noncommutativity parameter Lambda_NC, via related phenomenology and associated experiments, are analyzed and a firm bound to the scale of the noncommutativity is set around few TeV's.
Comments on Noncommutative Superspace
Terashima, S; Terashima, Seiji; Yee, Jung-Tay
2003-01-01
We study the N=1/2 supersymmetric theory on noncommutative superspace found by Seiberg which is a deformation of usual superspace. We consider deformed Wess-Zumino model as an example and shows vanishing of vacuum energy, renormalization of superpotential and nonvanishing of tadpole. We find that the perturbative effective action has terms which are not written in the star deformation. Also we consider gauge theory on noncommutative superspace and observe that gauge group is restricted. We generalize the star deformation to include noncommutativity between bosonic coordinates and fermionic coordinates.
Gauge Theory On The Fuzzy Torus
Bigatti, D
2001-01-01
In this paper a formulation of U(1) gauge theory on a fuzzy torus is discussed. The theory is regulated in both the infrared and ultraviolet. It can be thought of as a non-commutative version of lattice gauge theory on a periodic lattice. The construction of Wilson loops is particularly transparent in this formulation. Following Ishibashi, Iso, Kawai and Kitazawa, we show that certain Fourier modes of open Wilson lines are gauge invariant. We also introduce charged matter fields which can be thought of as fundamentals of the gauge group. These particles behave like charges in a strong magnetic field and are frozen into the lowest Landau levels. The resulting system is a simple matrix quantum mechanics which should reflect much of the physics of charged particles in strong magnetic fields. The present results were first presented as a talk at the Institute for Mathematical Science, Chennai, India; the author wishes to thank Prof. T. R. Govindarajan and the IMS for hospitality and financial support, and the aud...
Noncommutative string theory, the R-matrix, and Hopf algebras
Watts, P.
2000-02-01
Motivated by the form of the noncommutative /*-product in a system of open strings and Dp-branes with constant nonzero Neveu-Schwarz 2-form, we define a deformed multiplication operation on a quasitriangular Hopf algebra in terms of its R-matrix, and comment on some of its properties. We show that the noncommutative string theory /*-product is a particular example of this multiplication, and comment on other possible Hopf algebraic properties which may underlie the theory.
U(1) Gauge Field in 6D Space-Time With Compact Noncommutative Dimensions: A Coherent State Approach
Nasseri, M; Souri, M
2012-01-01
We consider the U(1) gauge field defined over a six dimensional space-time with extra dimensions compactified on a noncommutative toroidal orbifold, within the context of coherent state approach to the noncommutative spaces. We demonstrate that the fuzzines of extra dimensions can lead to the canceling of the part of electrostatic interaction mediated by the massive KK modes.
On the renormalization of non-commutative field theories
Blaschke, Daniel N.; Garschall, Thomas; Gieres, François; Heindl, Franz; Schweda, Manfred; Wohlgenannt, Michael
2013-01-01
This paper addresses three topics concerning the quantization of non-commutative field theories (as defined in terms of the Moyal star product involving a constant tensor describing the non-commutativity of coordinates in Euclidean space). To start with, we discuss the Quantum Action Principle and provide evidence for its validity for non-commutative quantum field theories by showing that the equation of motion considered as insertion in the generating functional Z c [ j] of connected Green functions makes sense (at least at one-loop level). Second, we consider the generalization of the BPHZ renormalization scheme to non-commutative field theories and apply it to the case of a self-interacting real scalar field: Explicit computations are performed at one-loop order and the generalization to higher loops is commented upon. Finally, we discuss the renormalizability of various models for a self-interacting complex scalar field by using the approach of algebraic renormalization.
The universality question for noncommutative quantum field theory
Schlesinger, K G
2006-01-01
Present day physics rests on two main pillars: General relativity and quantum field theory. We discuss the deep and at the same time problematic interplay between these two theories. Based on an argument by Doplicher, Fredenhagen, and Roberts, we propose a possible universality property for noncommutative quantum field theory in the sense that any theory of quantum gravity should involve quantum field theories on noncommutative space-times as a special limit. We propose a mathematical framework to investigate such a universality property and start the discussion of its mathematical properties. The question of its connection to string theory could be a starting point for a new perspective on string theory.
Algebraic aspects of gauge theories
Zharinov, V. V.
2014-08-01
Gauge theories are primary tools in modern elementary particle physics. The generally recognized mathematical foundations of these theories are in differential geometry, namely, in the theory of connections in a principal fiber bundle. We propose another approach to the mathematical description of gauge theories based on a combination of algebraic and geometric methods.
Mojaza, Matin; Sannino, Francesco
2010-01-01
We compute the nonzero temperature free energy up to the order g^6 \\ln(1/g) in the coupling constant for vector like SU(N) gauge theories featuring matter transforming according to different representations of the underlying gauge group. The number of matter fields, i.e. flavors, is arranged in such a way that the theory develops a perturbative stable infrared fixed point at zero temperature. Due to large distance conformality we trade the coupling constant with its fixed point value and define a reduced free energy which depends only on the number of flavors, colors and matter representation. We show that the reduced free energy changes sign, at the second, fifth and sixth order in the coupling, when decreasing the number of flavors from the upper end of the conformal window. If the change in sign is interpreted as signal of an instability of the system then we infer a critical number of flavors. Surprisingly this number, if computed to the order g^2, agrees with previous predictions for the lower boundary o...
Quantum field theory on locally noncommutative spacetimes
Energy Technology Data Exchange (ETDEWEB)
Lechner, Gandalf [Univ. Leipzig (Germany). Inst. fuer Theoretische Physik; Waldmann, Stefan [Leuven Univ. (Belgium)
2012-07-01
A class of spacetimes which are noncommutative only in a prescribed region is presented. These spacetimes are obtained by a generalization of Rieffel's deformation procedure to deformations of locally convex algebras and modules by smooth polynomially bounded R{sup n}-actions with compact support. Extending previous results of Bahns and Waldmann, it is shown how to perform such deformations in a strict sense. Some results on quantum fields propagating on locally noncommutative spacetimes are also given.
AdS-inspired noncommutative gravity on the Moyal plane
Radovanovic, Marija Dimitrijevic Voja
2012-01-01
We consider noncommutative gravity on a space with canonical noncommutativity that is based on the commutative AdS gravity. Gravity is treated as gauge theory of the noncommutative $SO(1,3)_\\star$ group and the Seiberg-Witten (SW) map is used to express noncommutative fields in terms of the corresponding commutative fields. In the commutative limit the noncommutative action reduces to the Einstein-Hilbert action plus the cosmological term and the topological Gauss-Bonnet term. After the SW expansion in the noncommutative parameter the first order correction to the action, as expected, vanishes. We calculate the second order correction and write it in a manifestly gauge covariant way.
Quantum field theory on a discrete space and noncommutative geometry
Häussling, R
2001-01-01
We analyse in detail the quantization of a simple noncommutative model of spontaneous symmetry breaking in zero dimensions taking into account the noncommutative setting seriously. The connection to the counting argument of Feyman diagrams of the corresponding theory in four dimensions is worked out explicitly. Special emphasis is put on the motivation as well as the presentation of some well-known basic notions of quantum field theory which in the zero-dimensional theory can be studied without being spoiled by technical complications due to the absence of divergencies.
Modular Theory, Non-Commutative Geometry and Quantum Gravity
Directory of Open Access Journals (Sweden)
Wicharn Lewkeeratiyutkul
2010-08-01
Full Text Available This paper contains the first written exposition of some ideas (announced in a previous survey on an approach to quantum gravity based on Tomita-Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of spectral geometries from an operational formalism of states and categories of observables in a covariant theory. Care has been taken to provide a coverage of the relevant background on modular theory, its applications in non-commutative geometry and physics and to the detailed discussion of the main foundational issues raised by the proposal.
Lorentz covariant field theory on noncommutative spacetime based on DFR algebra
Okumura, Y
2003-01-01
Lorentz covariance is the fundamental principle of every relativistic field theory which insures consistent physical descriptions. Even if the space-time is noncommutative, field theories on it should keep Lorentz covariance. In this letter, it is shown that the field theory on noncommutative spacetime is Lorentz covariant if the noncommutativity emerges from the algebra of spacetime operators described by Doplicher, Fredenhagen and Roberts.
Field Theories on Canonical and Lie-Algebra Noncommutative Spacetimes
Amelino-Camelia, G; Doplicher, L; Amelino-Camelia, Giovanni; Arzano, Michele; Doplicher, Luisa
2002-01-01
Field theories on canonical noncommutative spacetimes, which are being studied also in connection with string theory, and on $\\kappa$-Minkowski spacetime, which is a popular example of Lie-algebra noncommutative spacetime, can be naturally constructed by introducing a suitable generating functional for Green functions in energy-momentum space. Direct reference to a star product is not necessary. It is sufficient to make use of the simple properties that the Fourier transform preserves in these spacetimes and establish the rules for products of wave exponentials that are dictated by the non-commutativity of the coordinates. The approach also provides an elementary description of "planar" and "non-planar" Feynman diagrams. We also comment on the rich phenomenology emerging from the analysis of these theories.
Field Theories on Canonical and Lie-Algebra Noncommutative Spacetimes
Amelino-Camelia, G.; Arzano, M.; Doplicher, L.
2003-01-01
Field theories on canonical noncommutative spacetimes, which are being studied also in connection with string theory, and on k-Minkowski spacetime, which is a popular example of Lie-algebra noncommutative spacetime, can be naturally constructed by introducing a suitable generating functional for Green functions in energy-momentum space. Direct reference to a star product is not necessary. It is sufficient to make use of the simple properties that the Fourier transform preserves in these spacetimes and establish the rules for products of wave exponentials that are dictated by the non-commutativity of the coordinates. The approach also provides an elementary description of "planar" and "non-planar" Feynman diagrams. We also comment on the rich phenomenology emerging from the analysis of these theories.
Euclidean Quantum Field Theory on Commutative and Noncommutative Spaces
Wulkenhaar, R.
I give an introduction to Euclidean quantum field theory from the point of view of statistical physics, with emphasis both on Feynman graphs and on the Wilson-Polchinski approach to renormalisation. In the second part I discuss attempts to renormalise quantum field theories on noncommutative spaces.
Existence of Asymptotic Expansions in Noncommutative Quantum Field Theories
Linhares, C A; Roditi, I
2007-01-01
Starting from the complete Mellin representation of Feynman amplitudes for noncommutative vulcanized scalar quantum field theory, introduced in a previous publication, we generalize to this theory the study of asymptotic behaviours under scaling of arbitrary subsets of external invariants of any Feynman amplitude. This is accomplished for both convergent and renormalized amplitudes.
Gauge theories from D7-branes over vanishing 4-cycles
Energy Technology Data Exchange (ETDEWEB)
Franco, Sebastian; /Santa Barbara, KITP; Torroba, Gonzalo; /SLAC /Stanford U., Phys. Dept.
2010-12-16
We study quiver gauge theories on D7-branes wrapped over vanishing holomorphic 4-cycles. We investigate how to incorporate O7-planes and/or flavor D7-branes, which are necessary to cancel anomalies. These theories are chiral, preserve four supercharges and exhibit very rich infrared dynamics. Geometric transitions and duality in the presence of O-planes are analyzed. We study the Higgs branch of these quiver theories, showing the emergence of fuzzy internal dimensions. This branch is related to noncommutative instantons on the divisor wrapped by the seven-branes. Our results have a natural application to the recently introduced F(uzz) limit of F-theory.
Bi-local Fields in Noncommutative Field Theory
Iso, S; Kitazawa, Y; Iso, Satoshi; Kawai, Hikaru; Kitazawa, Yoshihisa
2000-01-01
We propose a bi-local representation in noncommutative field theory. It provides a simple description for high momentum degrees of freedom. It also shows that the low momentum modes can be well approximated by ordinary local fields. Long range interactions are generated in the effective action for the lower momentum modes after integrating out the high momentum bi-local fields. The low momentum modes can be represented by diagonal blocks in the matrix model picture and the high momentum bi-local fields correspond to off-diagonal blocks. This block-block interaction picture simply reproduces the infrared singular behaviors of nonplanar diagrams in noncommutative field theory.
Gauge bundles and Born-Infeld on the noncommutative torus
Hofman, C.; Verlinde, E.
1998-01-01
In this paper, we describe non-abelian gauge bundles with magnetic and electric uxes on higher dimensional noncomm utative tori. We give an explicit construction of a large class of bundles with nonzero magnetic 't Hooft uxes. W e discuss Morita equiv alence between these bundles. The action of
Non-topological non-commutativity in string theory
Guttenberg, Sebastian; Kreuzer, Maximilian; Rashkov, Radoslav
2007-01-01
Quantization of coordinates leads to the non-commutative product of deformation quantization, but is also at the roots of string theory, for which space-time coordinates become the dynamical fields of a two-dimensional conformal quantum field theory. Appositely, open string diagrams provided the inspiration for Kontsevich's solution of the long-standing problem of quantization of Poisson geometry by virtue of his formality theorem. In the context of D-brane physics non-commutativity is not limited, however, to the topolocial sector. We show that non-commutative effective actions still make sense when associativity is lost and establish a generalized Connes-Flato-Sternheimer condition through second order in a derivative expansion. The measure in general curved backgrounds is naturally provided by the Born--Infeld action and reduces to the symplectic measure in the topological limit, but remains non-singular even for degenerate Poisson structures. Analogous superspace deformations by RR--fields are also discus...
Formulae for topological charge in noncommutative U(1) theory in four dimensions
Energy Technology Data Exchange (ETDEWEB)
Ali Khan, Arifa; Al-Haydari, Ahmed; Hassan, Galal Saad [University of Taiz (Yemen); Markum, Harald [Vienna University of Technology (Austria)
2011-07-01
We discuss U(1) gauge theory with noncommutative space-time coordinates in two and four dimensions on a lattice with N sites. The mapping to a U(N) plaquette model in the sense of Eguchi and Kawai makes both analytical calculations and computer simulations feasible. The topological charge q can be transcribed to the plaquette and hypercube formulation in the matrix theory in 4D. There exist formulations of the classical equation of motion within the matrix model. From them we try to derive general formulae for q in four dimensions. The aim is to analyze an action-charge diagram as in 2D.
Introduction to Supersymmetric Gauge Theories
Piguet, O
1997-01-01
In these lectures I present a basic introduction to supersymmetry, especially to N=1 supersymmetric gauge theories and their renormalization, in the Wess-Zumino gauge. I also discuss the various ways supersymmetry may be broken in order to account for the lack of exact supersymmetry in the actual world of elementary particles.
Frobenius-Chern-Simons gauge theory
Bonezzi, Roberto; Boulanger, Nicolas; Sezgin, Ergin; Sundell, Per
2017-02-01
Given a set of differential forms on an odd-dimensional noncommutative manifold valued in an internal associative algebra H , we show that the most general cubic covariant Hamiltonian action, without mass terms, is controlled by an {{{Z}}2} -graded associative algebra F with a graded symmetric nondegenerate bilinear form. The resulting class of models provide a natural generalization of the Frobenius-Chern-Simons model (FCS) that was proposed in (arXiv:1505.04957) as an off-shell formulation of the minimal bosonic four-dimensional higher spin gravity theory. If F is unital and the {{{Z}}2} -grading is induced from a Klein operator that is outer to a proper Frobenius subalgebra, then the action can be written on a form akin to topological open string field theory in terms of a superconnection valued in H\\otimes F . We give a new model of this type based on a twisting of {C}≤ft[{{{Z}}2}× {{{Z}}4}\\right] , which leads to self-dual complexified gauge fields on AdS 4. If F is 3-graded, the FCS model can be truncated consistently as to contain no zero-form constraints on-shell. Two examples thereof are a twisting of {C}[{{({{{Z}}2})}3}] that yields the original model, and the Clifford algebra C{{\\ell}2n} which provides an FCS formulation of the bosonic Konstein-Vasiliev model with gauge algebra hu≤ft({{4}n-1},0\\right) .
Yang-Baxter σ -models, conformal twists, and noncommutative Yang-Mills theory
Araujo, T.; Bakhmatov, I.; Colgáin, E. Ó.; Sakamoto, J.; Sheikh-Jabbari, M. M.; Yoshida, K.
2017-05-01
The Yang-Baxter σ -model is a systematic way to generate integrable deformations of AdS5×S5 . We recast the deformations as seen by open strings, where the metric is undeformed AdS5×S5 with constant string coupling, and all information about the deformation is encoded in the noncommutative (NC) parameter Θ . We identify the deformations of AdS5 as twists of the conformal algebra, thus explaining the noncommutativity. We show that the unimodularity condition on r -matrices for supergravity solutions translates into Θ being divergence-free. Integrability of the σ -model for unimodular r -matrices implies the existence and planar integrability of the dual NC gauge theory.
A course on noncommutative geometry in string theory
Energy Technology Data Exchange (ETDEWEB)
Blumenhagen, R. [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany)
2014-09-11
In this pedagogical mini course the basics of the derivation of the noncommutative structures appearing in string theory are reviewed. First we discuss the well established appearance of the noncommutative Moyal-Weyl star-product in the correlation functions of open string vertex operators on a magnetized D-brane. Second, we will review the most recent attempts to generalize these concepts to the closed string moving in a nongeometric flux background. (Copyright copyright 2014 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Toward semistrict higher gauge theory
Zucchini, Roberto
2011-01-01
We work out a formulation of higher gauge theory, whose symmetry is encoded in a semistrict Lie 2-algebra v and which we call semistrict. We view v as a 2-term L-infinity algebra, a special case of strong homotopy Lie algebra generalizing an ordinary Lie algebra by allowing the Lie bracket to have a non trivial Jacobiator. Fields are v-valued and gauge transformations are special Aut(v)-valued maps organized as an ordinary group and acting on them. The global behaviour of fields is controlled by appropriate gauge transformation 1-cocycles. Using the BV quantization method in the AKSZ geometrical version, we write down a 3-dimensional semistrict higher BF gauge theory generalizing ordinary BF theory, carry out its gauge fixing and obtain as end result a semistrict higher topological gauge field theory of the Witten type. We also introduce a related 4-dimensional semistrict higher Chern--Simons gauge theory. We discuss merits and weaknesses of our formulation in relations to other approaches.
W-Infinity Algebras from Noncommutative Chern-Simons Theory
Pinzul, A N
2003-01-01
We examine Chern-Simons theory written on a noncommutative plane with a `hole', and show that the algebra of observables is a nonlinear deformation of the $w_\\infty$ algebra. The deformation depends on the level (the coefficient in the Chern-Simons action), which was identified recently with the inverse filling fraction in the fractional quantum Hall effect.
Gauge Mediation in String Theory
Kawano, Teruhiko; Ooguri, Hirosi; Ookouchi, Yutaka
2007-01-01
We show that a large class of phenomenologically viable models for gauge mediation of supersymmetry breaking based on meta-stable vacua can be realized in local Calabi–Yau compactifications of string theory.
Torrielli, Alessandro
2003-01-01
The results of our research on noncommutative perturbative quantum field theory and its relation to string theory are exposed with details. 1) We give an introduction to noncommutative quantum field theory and its derivation from open string theory in an antisymmetric background. 2) We perform a perturbative Wilson loop calculation for 2D NCYM. We compare the LCG results for the WML and the PV prescription. With WML the loop is well-defined and regular in the commutative limit. With PV the result is singular. This is intriguing: in the commutative theory their difference is related to topological excitations, moreover PV provides a point-like potential. 3) Commutative 2D YM exhibits an interplay between geometrical and U(N) gauge properties: in the exact expression of a Wilson loop with n windings a scaling intertwines n and N. In the NC case the interplay becomes tighter due to the merging of space-time and ``internal'' symmetries. Surprisingly, in our up to O(g^6) (and beyond) crossed graphs calculations the scaling we mentioned occurs for large n, N and theta. 4) We discuss the breakdown of perturbative unitarity of noncommutative electric-type QFT in the light of strings. We consider the analytic structure of string loop two-point functions suitably continuing them off-shell, and then study the Seiberg-Witten limit. In this way we pick up how the unphysical tachyonic branch cut appears in the NC field theory.
Gauge Theories of Vector Particles
Glashow, S. L.; Gell-Mann, M.
1961-04-24
The possibility of generalizing the Yang-Mills trick is examined. Thus we seek theories of vector bosons invariant under continuous groups of coordinate-dependent linear transformations. All such theories may be expressed as superpositions of certain "simple" theories; we show that each "simple theory is associated with a simple Lie algebra. We may introduce mass terms for the vector bosons at the price of destroying the gauge-invariance for coordinate-dependent gauge functions. The theories corresponding to three particular simple Lie algebras - those which admit precisely two commuting quantum numbers - are examined in some detail as examples. One of them might play a role in the physics of the strong interactions if there is an underlying super-symmetry, transcending charge independence, that is badly broken. The intermediate vector boson theory of weak interactions is discussed also. The so-called "schizon" model cannot be made to conform to the requirements of partial gauge-invariance.
Puffed Noncommutative Nonabelian Vortices
Bouatta, N; MacCaferri, C; Bouatta, Nazim; Evslin, Jarah; Maccaferri, Carlo
2007-01-01
We present new solutions of noncommutative gauge theories in which coincident unstable vortices expand into unstable circular shells. As the theories are noncommutative, the naive definition of the locations of the vortices and shells is gauge-dependent, and so we define and calculate the profiles of these solutions using the gauge-invariant noncommutative Wilson lines introduced by Gross and Nekrasov. We find that charge 2 vortex solutions are characterized by two positions and a single nonnegative real number, which we demonstrate is the radius of the shell. We find that the radius is identically zero in all 2-dimensional solutions. If one considers solutions that depend on an additional commutative direction, then there are time-dependent solutions in which the radius oscillates, resembling a braneworld description of a cyclic universe. There are also smooth BIon-like space-dependent solutions in which the shell expands to infinity, describing a vortex ending on a domain wall.
Three-dimensional noncommutative Yukawa theory: Induced effective action and propagating modes
Bufalo, R
2016-01-01
In this paper, we establish the analysis of noncommutative Yukawa theory, encompassing neutral and charged scalar fields. We approach the analysis by considering carefully the derivation of the respective effective actions. Hence, based on the obtained results, we compute the one-loop contributions to the neutral and charged scalar field self-energy, as well as to the Chern-Simons polarization tensor. In order to properly define the behaviour of the quantum fields, the known UV/IR mixing due to radiative corrections is analysed in the one-loop physical dispersion relation of the scalar and gauge fields.
Bassetto, A; Torrielli, A
2002-01-01
Commutative Yang-Mills theories in 1+1 dimensions exhibit an interesting interplay between geometrical properties and U(N) gauge structures: in the exact expression of a Wilson loop with $n$ windings a non trivial scaling intertwines $n$ and $N$. In the non-commutative case the interplay becomes tighter owing to the merging of space-time and ``internal'' symmetries in a larger group $U(\\infty)$. We perform an explicit perturbative calculation of such a loop up to ${\\cal O}(g^6)$; rather surprisingly, we find that in the contribution from the crossed graphs (the genuine non-commutative terms) the scaling we mentioned occurs for large $n$ and $N$ in the limit of maximal non-commutativity $\\theta=\\infty$. We present arguments in favour of the persistence of such a scaling at any perturbative order and succeed in summing the related perturbative series.
Gauge theory loop operators and Liouville theory
Energy Technology Data Exchange (ETDEWEB)
Drukker, Nadav [Humboldt Univ. Berlin (Germany). Inst. fuer Physik; Gomis, Jaume; Okuda, Takuda [Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); Teschner, Joerg [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2009-10-15
We propose a correspondence between loop operators in a family of four dimensional N=2 gauge theories on S{sup 4} - including Wilson, 't Hooft and dyonic operators - and Liouville theory loop operators on a Riemann surface. This extends the beautiful relation between the partition function of these N=2 gauge theories and Liouville correlators found by Alday, Gaiotto and Tachikawa. We show that the computation of these Liouville correlators with the insertion of a Liouville loop operator reproduces Pestun's formula capturing the expectation value of a Wilson loop operator in the corresponding gauge theory. We prove that our definition of Liouville loop operators is invariant under modular transformations, which given our correspondence, implies the conjectured action of S-duality on the gauge theory loop operators. Our computations in Liouville theory make an explicit prediction for the exact expectation value of 't Hooft and dyonic loop operators in these N=2 gauge theories. The Liouville loop operators are also found to admit a simple geometric interpretation within quantum Teichmueller theory as the quantum operators representing the length of geodesics. We study the algebra of Liouville loop operators and show that it gives evidence for our proposal as well as providing definite predictions for the operator product expansion of loop operators in gauge theory. (orig.)
Semiclassical Analysis of String/Gauge Duality on Non-commutative Space
Rashkov, R C; Yang, Y; Yang, Yi
2004-01-01
We use semiclassical method to study closed strings in the modified AdS_5*S^5 background with constant B-fields. The point-like closed strings and the streched closed strings rotating around the big circle of S^5 are considered. Quantization of these closed string leads to a time-dependent string spectrum, which we argue to correspond to the RG-flow of the dual noncommutative Yang Mills theory.
Instantons and vortices on noncommutative toric varieties
Cirio, Lucio S.; Landi, Giovanni; Szabo, Richard J.
2014-09-01
We elaborate on the quantization of toric varieties by combining techniques from toric geometry, isospectral deformations and noncommutative geometry in braided monoidal categories, and the construction of instantons thereon by combining methods from noncommutative algebraic geometry and a quantized twistor theory. We classify the real structures on a toric noncommutative deformation of the Klein quadric and use this to derive a new noncommutative four-sphere which is the unique deformation compatible with the noncommutative twistor correspondence. We extend the computation of equivariant instanton partition functions to noncommutative gauge theories with both adjoint and fundamental matter fields, finding agreement with the classical results in all instances. We construct moduli spaces of noncommutative vortices from the moduli of invariant instantons, and derive corresponding equivariant partition functions which also agree with those of the classical limit.
Gravity: a gauge theory perspective
Nester, James M
2016-01-01
The evolution of a generally covariant theory is under-determined. One hundred years ago such dynamics had never before been considered; its ramifications were perplexing, its future important role for all the fundamental interactions under the name gauge principle could not be foreseen. We recount some history regarding Einstein, Hilbert, Klein and Noether and the novel features of gravitational energy that led to Noether's two theorems. Under-determined evolution is best revealed in the Hamiltonian formulation. We developed a covariant Hamiltonian formulation. The Hamiltonian boundary term gives covariant expressions for the quasi-local energy, momentum and angular momentum. Gravity can be considered as a gauge theory of the local Poincar\\'e group. The dynamical potentials of the Poincar\\'e gauge theory of gravity are the frame and the connection. The spacetime geometry has in general both curvature and torsion. Torsion naturally couples to spin; it could have a significant magnitude and yet not be noticed,...
Frobenius-Chern-Simons gauge theory
Bonezzi, Roberto; Sezgin, Ergin; Sundell, Per
2016-01-01
Given a set of differential forms on an odd-dimensional noncommutative manifold valued in an internal associative algebra H, we show that the most general cubic covariant Hamiltonian action, without mass terms, is controlled by an Z_2-graded associative algebra F with a graded symmetric nondegenerate bilinear form. The resulting class of models provide a natural generalization of the Frobenius-Chern-Simons model (FCS) that was proposed in arXiv:1505.04957 as an off-shell formulation of the minimal bosonic four-dimensional higher spin gravity theory. If F is unital and the Z_2-grading is induced from a Klein operator that is outer to a proper Frobenius subalgebra, then the action can be written on a form akin to topological open string field theory in terms of a superconnection valued in the direct product of H and F. We give a new model of this type based on a twisting of C[Z_2 x Z_4], which leads to self-dual complexified gauge fields on AdS_4. If F is 3-graded, the FCS model can be truncated consistently as...
Gauge Theories, Tessellations & Riemann Surfaces
He, Yang-Hui
2014-01-01
We study and classify regular and semi-regular tessellations of Riemann surfaces of various genera and investigate their corresponding supersymmetric gauge theories. These tessellations are generalizations of brane tilings, or bipartite graphs on the torus as well as the Platonic and Archimedean solids on the sphere. On higher genus they give rise to intricate patterns. Special attention will be paid to the master space and the moduli space of vacua of the gauge theory and to how their geometry is determined by the tessellations.
Gauge theories, tessellations & Riemann surfaces
Energy Technology Data Exchange (ETDEWEB)
He, Yang-Hui [Department of Mathematics, City University,London, EC1V 0HB (United Kingdom); School of Physics, NanKai University,Tianjin, 300071 (China); Merton College, University of Oxford,Oxford, OX1 4JD (United Kingdom); Loon, Mark van [Merton College, University of Oxford,Oxford, OX1 4JD (United Kingdom)
2014-06-10
We study and classify regular and semi-regular tessellations of Riemann surfaces of various genera and investigate their corresponding supersymmetric gauge theories. These tessellations are generalizations of brane tilings, or bipartite graphs on the torus as well as the Platonic and Archimedean solids on the sphere. On higher genus they give rise to intricate patterns. Special attention will be paid to the master space and the moduli space of vacua of the gauge theory and to how their geometry is determined by the tessellations.
Institute of Scientific and Technical Information of China (English)
WANG Pei
2002-01-01
In this paper we study the spinor constructions of gauge fluxes and Ramond Ramond fields on noncommu-tative tori Td up to d＝6. In which the spinor and conjugate spinor are distinguished and dual bases are also introduced.So that we can express the Chern Simons Lagrangian in toroidal compactification as a product of spinors.
Operator Algebras and Noncommutative Geometric Aspects in Conformal Field Theory
Longo, Roberto
2010-03-01
The Operator Algebraic approach to Conformal Field Theory has been particularly fruitful in recent years (leading for example to the classification of all local conformal nets on the circle with central charge c < 1, jointly with Y. Kawahigashi). On the other hand the Operator Algebraic viewpoint offers a natural perspective for a Noncommutative Geometric context within Conformal Field Theory. One basic point here is to uncover the relevant structures. In this talk I will explain some of the basic steps in this "Noncommutative Geometrization program" up to the recent construction of a spectral triple associated with certain Ramond representations of the Supersymmetric Virasoro net. So Alain Connes framework enters into play. This is a joint work with S. Carpi, Y. Kawahigashi, and R. Hillier.
The inaction approach to gauge theories
Pivovarov, Grigorii
2012-01-01
The inaction approach introduced previously for phi^4 is generalized to gauge theories. It combines the advantages of the effective field theory and causal approaches to quantum fields. Also, it suggests ways to generalizing gauge theories.
Quantum Mechanics: Harbinger of a Non-Commutative Probability Theory?
Hiley, Basil J.
2014-01-01
In this paper we discuss the relevance of the algebraic approach to quantum phenomena first introduced by von Neumann before he confessed to Birkoff that he no longer believed in Hilbert space. This approach is more general and allows us to see the structure of quantum processes in terms of non-commutative probability theory, a non-Boolean structure of the implicate order which contains Boolean sub-structures which accommodates the explicate classical world. We move away from mechanical `wave...
Geometric Formulation of Gauge Theory of Gravity
Institute of Scientific and Technical Information of China (English)
WUNing; ZHANGDa-Hua; RUANTu-Nan
2003-01-01
DitTerential geometric formulation of quantum gauge theory of gravity is studied in this paper. The quantum gauge theory of gravity is formulated completely in the framework of traditional quantum field theory. In order to study the relationship between quantum gauge theory of gravity and traditional quantum gravity which is formulated in curved space, it is important to set up the geometry picture of quantum gauge theory of gravity. The correspondence between quantum gauge theory of gravity and differential geometry is discussed and the geometry picture of quantum gauge theory of gravity is studied.
Lectures on Matrix Field Theory
Ydri, Badis
The subject of matrix field theory involves matrix models, noncommutative geometry, fuzzy physics and noncommutative field theory and their interplay. In these lectures, a lot of emphasis is placed on the matrix formulation of noncommutative and fuzzy spaces, and on the non-perturbative treatment of the corresponding field theories. In particular, the phase structure of noncommutative $\\phi^4$ theory is treated in great detail, and an introduction to noncommutative gauge theory is given.
Non-commutative Field Theory on S^4
Nakayama, R; Nakayama, Ryuichi; Shimono, Yusuke
2004-01-01
In the previous paper (hep-th/0402010) we proposed a matrix configuration for a non-commutative S^4 (NC4S) and constructed a non-commutative (star) product for field theories on NC4S. This star product and the functions on NC4S turned out to be singular (ambiguous) on a circle on S^4. In the present paper we will show that any matrix can be expanded in terms of the matrix configuration representing NC4S just like any matrix can be expanded into symmetrized products of the matrix configuration for non-commutative S^2. Then we will show that the singularities of the functions on S^4 and the star product can be removed by covering the (commutative) manifold by coordinate neighborhoods and performing appropriate coordinate transformations. Finally a scalar field theory on NC4S is constructed. Our matrix configuration describes two S^4's joined at the circle and the Matrix theory action contains a projection matrix inside the trace to restrict the space of matrices to that for one S^4.
Entwinement in discretely gauged theories
Balasubramanian, V.; Bernamonti, A.; Craps, B.; De Jonckheere, T.; Galli, F.
2016-12-01
We develop the notion of "entwinement" to characterize the amount of quantum entanglement between internal, discretely gauged degrees of freedom in a quantum field theory. This concept originated in the program of reconstructing spacetime from entanglement in holographic duality. We define entwinement formally in terms of a novel replica method which uses twist operators charged in a representation of the discrete gauge group. In terms of these twist operators we define a non-local, gauge-invariant object whose expectation value computes entwinement in a standard replica limit. We apply our method to the computation of entwinement in symmetric orbifold conformal field theories in 1+1 dimensions, which have an S N gauging. Such a theory appears in the weak coupling limit of the D1-D5 string theory which is dual to AdS3 at strong coupling. In this context, we show how certain kinds of entwinement measure the lengths, in units of the AdS scale, of non-minimal geodesics present in certain excited states of the system which are gravitationally described as conical defects and the M = 0 BTZ black hole. The possible types of entwinement that can be computed define a very large new class of quantities characterizing the fine structure of quantum wavefunctions.
Entwinement in discretely gauged theories
Balasubramanian, V; Craps, B; De Jonckheere, T; Galli, F
2016-01-01
We develop the notion of entwinement to characterize the amount of quantum entanglement between internal, discretely gauged degrees of freedom in a quantum field theory. This concept originated in the program of reconstructing spacetime from entanglement in holographic duality. We define entwinement formally in terms of a novel replica method which uses twist operators charged in a representation of the discrete gauge group. In terms of these twist operators we define a non-local, gauge-invariant object whose expectation value computes entwinement in a standard replica limit. We apply our method to the computation of entwinement in symmetric orbifold conformal field theories in 1+1 dimensions, which have an $S_N$ gauging. Such a theory appears in the weak coupling limit of the D1-D5 string theory which is dual to AdS$_3$ at strong coupling. In this context, we show how certain kinds of entwinement measure the lengths, in units of the AdS scale, of non-minimal geodesics present in certain excited states of the...
Noncommutative magnetic moment of charged particles
Adorno, T C; Shabad, A E; Vassilevich, D V
2011-01-01
It has been argued, that in noncommutative field theories sizes of physical objects cannot be taken smaller than an elementary length related to noncommutativity parameters. By gauge-covariantly extending field equations of noncommutative U(1)_*-theory to the presence of external sources, we find electric and magnetic fields produces by an extended charge. We find that such a charge, apart from being an ordinary electric monopole, is also a magnetic dipole. By writing off the existing experimental clearance in the value of the lepton magnetic moments for the present effect, we get the bound on noncommutativity at the level of 10^4 TeV.
Differential renormalization of gauge theories
Energy Technology Data Exchange (ETDEWEB)
Aguila, F. del; Perez-Victoria, M. [Dept. de Fisica Teorica y del Cosmos, Universidad de Granada, Granada (Spain)
1998-10-01
The scope of constrained differential renormalization is to provide renormalized expressions for Feynman graphs, preserving at the same time the Ward identities of the theory. It has been shown recently that this can be done consistently at least to one loop for Abelian and non-Abelian gauge theories. We briefly review these results, evaluate as an example the gluon self energy in both coordinate and momentum space, and comment on anomalies. (author) 9 refs, 1 fig., 1 tab
Non-topological non-commutativity in string theory
Energy Technology Data Exchange (ETDEWEB)
Guttenberg, S. [NCSR Demokritos, INP, Patriarchou Gregoriou and Neapoleos Str., 15310 Agia Paraskevi Attikis (Greece); Herbst, M. [CERN, 1211 Geneva 23 (Switzerland); Kreuzer, M. [Institute for Theoretical Physics, TU Wien, Wiedner Hauptstr. 8-10, 1040 Vienna (Austria); Rashkov, R. [Erwin Schroedinger Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Vienna (Austria)
2008-04-15
Quantization of coordinates leads to the non-commutative product of deformation quantization, but is also at the roots of string theory, for which space-time coordinates become the dynamical fields of a two-dimensional conformal quantum field theory. Appositely, open string diagrams provided the inspiration for Kontsevich's solution of the long-standing problem of quantization of Poisson geometry by virtue of his formality theorem. In the context of D-brane physics non-commutativity is not limited, however, to the topological sector. We show that non-commutative effective actions still make sense when associativity is lost and establish a generalized Connes-Flato-Sternheimer condition through second order in a derivative expansion. The measure in general curved backgrounds is naturally provided by the Born-Infeld action and reduces to the symplectic measure in the topological limit, but remains non-singular even for degenerate Poisson structures. Analogous superspace deformations by RR-fields are also discussed. (Abstract Copyright [2008], Wiley Periodicals, Inc.)
An introduction to gauge theories
Cabibbo, Nicola; Benhar, Omar
2017-01-01
Written by three of the world's leading experts on particle physics and the standard model, including an award-winning former director general of CERN, this book provides a completely up-to-date account of gauge theories. Starting from Feynman’s path integrals, Feynman rules are derived, gauge fixing and Faddeev-Popov ghosts are discussed, and renormalization group equations are derived. Several important applications to quantum electrodynamics and quantum chromodynamics (QCD) are discussed, including the one-loop derivation of asymptotic freedom for QCD.
Gauge theory and variational principles
Bleecker, David
2005-01-01
This text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. A detailed and self-contained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. This well-organized treatment supplements its rigor with intuitive ideas.Starting with an examination of principal fiber bundles and connections, the text explores curvature; particle fields, Lagrangians, and gauge invariance; Lagrange's equation for particle fields; and the inhomogeneous field
Dark Solitons, D-branes and Noncommutative Tachyon Field Theory
Giaccari, Stefano
2016-01-01
In this paper we discuss the boson/vortex duality by mapping the Gross-Pitaevskii theory into an effective string theory, both with and without boundaries. Through the effective string theory, we find the Seiberg-Witten map between the commutative and the noncommutative tachyon field theories, and consequently identify their soliton solutions with the D-branes in the effective string theory. We perform various checks of the duality map and the identification of classical solutions. This new insight of the duality between the Gross-Pitaevskii theory and the effective string theory allows us to test many results of string theory in Bose-Einstein condensates, and at the same time help us understand the quantum behavior of superfluids and cold atom systems.
Introduction to lattice gauge theory
Gupta, R.
The lattice formulation of Quantum Field Theory (QFT) can be exploited in many ways. We can derive the lattice Feynman rules and carry out weak coupling perturbation expansions. The lattice then serves as a manifestly gauge invariant regularization scheme, albeit one that is more complicated than standard continuum schemes. Strong coupling expansions: these give us useful qualitative information, but unfortunately no hard numbers. The lattice theory is amenable to numerical simulations by which one calculates the long distance properties of a strongly interacting theory from first principles. The observables are measured as a function of the bare coupling g and a gauge invariant cut-off approx. = 1/alpha, where alpha is the lattice spacing. The continuum (physical) behavior is recovered in the limit alpha yields 0, at which point the lattice artifacts go to zero. This is the more powerful use of lattice formulation, so in these lectures the author focuses on setting up the theory for the purpose of numerical simulations to get hard numbers. The numerical techniques used in Lattice Gauge Theories have their roots in statistical mechanics, so it is important to develop an intuition for the interconnection between quantum mechanics and statistical mechanics.
N = 2 gauge theories, instanton moduli spaces and geometric representation theory
Szabo, Richard J.
2016-11-01
We survey some of the AGT relations between N = 2 gauge theories in four dimensions and geometric representations of symmetry algebras of two-dimensional conformal field theory on the equivariant cohomology of their instanton moduli spaces. We treat the cases of gauge theories on both flat space and ALE spaces in some detail, and with emphasis on the implications arising from embedding them into supersymmetric theories in six dimensions. Along the way we construct new toric noncommutative ALE spaces using the general theory of complex algebraic deformations of toric varieties, and indicate how to generalize the construction of instanton moduli spaces. We also compute the equivariant partition functions of topologically twisted six-dimensional Yang-Mills theory with maximal supersymmetry in a general Ω-background, and use the construction to obtain novel reductions to theories in four dimensions.
Gauge-fixing approach to lattice chiral gauge theories
Bock, W; Shamir, Y; Bock, Wolfgang; Golterman, Maarten F.L.; Shamir, Yigal
1998-01-01
We review the status of our recent work on the gauge-fixing approach to lattice chiral gauge theories. New numerical results in the reduced version of a model with a U(1) gauge symmetry are presented which strongly indicate that the factorization of the correlation functions of the left-handed neutral and right-handed charged fermion fields, which we established before in perturbation theory, holds also nonperturbatively.
Low energy gauge unification theory
Li Tian Jun
2002-01-01
Because of the problems arising from the fermion unification in the traditional Grand Unified Theory and the mass hierarchy between the 4-dimensional Planck scale and weak scale, we suggest the low energy gauge unification theory with low high-dimensional Planck scale. We discuss the non-supersymmetric SU(5) model on M sup 4 xS sup 1 /Z sub 2 xS sup 1 /Z sub 2 and the supersymmetric SU(5) model on M sup 4 xS sup 1 /(Z sub 2 xZ sub 2 ')xS sup 1 /(Z sub 2 xZ sub 2 ')xS sup 1 /(Z sub 2 xZ sub 2 '). The SU(5) gauge symmetry is broken by the orbifold projection for the zero modes, and the gauge unification is accelerated due to the SU(5) asymmetric light KK states. In our models, we forbid the proton decay, still keep the charge quantization, and automatically solve the fermion mass problem. We also comment on the anomaly cancellation and other possible scenarios for low energy gauge unification.
Noncommutative field theory and violation of translation invariance
Bertolami, O
2003-01-01
Noncommutative field theories with commutator of the coordinates of the form $[x^{mu},x^{nu}]=i Lambda_{quad omega}^{mu nu}x^{omega}$ are studied. Explicit Lorentz invariance is mantained considering $Lambda $ a Lorentz tensor. It is shown that a free quantum field theory is not affected. Since invariance under translations is broken, the conservation of energy-momentum is violated, obeying a new law which is expressed by a Poincar'e-invariant equation. The resulting new kinematics is studied and applied to simple examples and to astrophysical puzzles, such as the observed violation of the GZK cutoff. The $lambda
Asymptotically Free Gauge Theories. I
Wilczek, Frank; Gross, David J.
1973-07-01
Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization group techniques and their application to scaling phenomena. The renormalization group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large space-like momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3)xSU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of non-color singlet physical states. The deep inelastic structure functions, as well as the electron position total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive lightcone or parton model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.
Renormalisation group flows for gauge theories in axial gauges
Litim, Daniel F; Litim, Daniel F.; Pawlowski, Jan M.
2002-01-01
Gauge theories in axial gauges are studied using Exact Renormalisation Group flows. We introduce a background field in the infrared regulator, but not in the gauge fixing, in contrast to the usual background field gauge. It is shown how heat-kernel methods can be used to obtain approximate solutions to the flow and the corresponding Ward identities. Expansion schemes are discussed, which are not applicable in covariant gauges. As an application, we derive the one-loop effective action for covariantly constant field strength, and the one-loop beta-function for arbitrary regulator.
Scattering amplitudes in gauge theories
Henn, Johannes M
2014-01-01
At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum ...
Weak interactions and gauge theories
Energy Technology Data Exchange (ETDEWEB)
Gaillard, M.K.
1979-12-01
The status of the electroweak gauge theory, also known as quantum asthenodynamics (QAD), is examined. The major result is that the standard WS-GIM model describes the data well, although one should still look for signs of further complexity and better tests of its gauge theory aspect. A second important result is that the measured values of the three basic coupling constants of present-energy physics, g/sub s/, g, and ..sqrt..(5/3)g' of SU(3)/sub c/ x SU(2)/sub 2/ x U(1), are compatible with the idea that these interactions are unified at high energies. Much of the paper deals with open questions, and it takes up the following topics: the status of QAD, the scalar meson spectrum, the fermion spectrum, CP violation, and decay dynamics. 118 references, 20 figures. (RWR)
Narayanan, Rajamani
2008-01-01
Wilson loops in large N gauge theory exhibit a weak to strong coupling transition as the loop is dilated. A multiplicative matrix model captures the universal behavior associated with this transition. A universal scaling function is obtained in a double scaling limit. Numerical studies show that both large N QCD in three dimensions and the SU(N) principal chiral model in two dimensions are in the same universality class.
The numerical approach to quantum field theory in a non-commutative space
Panero, Marco
2016-01-01
Numerical simulation is an important non-perturbative tool to study quantum field theories defined in non-commutative spaces. In this contribution, a selection of results from Monte Carlo calculations for non-commutative models is presented, and their implications are reviewed. In addition, we also discuss how related numerical techniques have been recently applied in computer simulations of dimensionally reduced supersymmetric theories.
On magnetohydrodynamic gauge field theory
Webb, G. M.; Anco, S. C.
2017-06-01
Clebsch potential gauge field theory for magnetohydrodynamics is developed based in part on the theory of Calkin (1963 Can. J. Phys. 41 2241-51). It is shown how the polarization vector {P} in Calkin’s approach naturally arises from the Lagrange multiplier constraint equation for Faraday’s equation for the magnetic induction {B} , or alternatively from the magnetic vector potential form of Faraday’s equation. Gauss’s equation, (divergence of {B} is zero) is incorporated in the variational principle by means of a Lagrange multiplier constraint. Noether’s theorem coupled with the gauge symmetries is used to derive the conservation laws for (a) magnetic helicity, (b) cross helicity, (c) fluid helicity for non-magnetized fluids, and (d) a class of conservation laws associated with curl and divergence equations which applies to Faraday’s equation and Gauss’s equation. The magnetic helicity conservation law is due to a gauge symmetry in MHD and not due to a fluid relabelling symmetry. The analysis is carried out for the general case of a non-barotropic gas in which the gas pressure and internal energy density depend on both the entropy S and the gas density ρ. The cross helicity and fluid helicity conservation laws in the non-barotropic case are nonlocal conservation laws that reduce to local conservation laws for the case of a barotropic gas. The connections between gauge symmetries, Clebsch potentials and Casimirs are developed. It is shown that the gauge symmetry functionals in the work of Henyey (1982 Phys. Rev. A 26 480-3) satisfy the Casimir determining equations.
Gravity: A gauge theory perspective
Nester, James M.; Chen, Chiang-Mei
2016-07-01
The evolution of a generally covariant theory is under-determined. One hundred years ago such dynamics had never before been considered; its ramifications were perplexing, its future important role for all the fundamental interactions under the name gauge principle could not be foreseen. We recount some history regarding Einstein, Hilbert, Klein and Noether and the novel features of gravitational energy that led to Noether’s two theorems. Under-determined evolution is best revealed in the Hamiltonian formulation. We developed a covariant Hamiltonian formulation. The Hamiltonian boundary term gives covariant expressions for the quasi-local energy, momentum and angular momentum. Gravity can be considered as a gauge theory of the local Poincaré group. The dynamical potentials of the Poincaré gauge theory of gravity are the frame and the connection. The spacetime geometry has in general both curvature and torsion. Torsion naturally couples to spin; it could have a significant magnitude and yet not be noticed, except on a cosmological scale where it could have significant effects.
SO(2,3 noncommutative gravity model
Directory of Open Access Journals (Sweden)
Dimitrijević Marija
2014-01-01
Full Text Available In this paper the noncommutative gravity is treated as a gauge theory of the noncommutative SO(2,3* group, while the noncommutativity is canonical. The Seiberg-Witten (SW map is used to express noncommutative fields in terms of the corresponding commutative fields. The commutative limit of the model is the Einstein-Hilbert action plus the cosmological term and the topological Gauss-Bonnet term. We calculate the second order correction to this model and obtain terms that are zeroth, first, . . . and fourth power of the curvature tensor. Finally, we discuss physical consequences of those correction terms in the limit of big cosmological constant.
SO(2, 3) noncommutative gravity model
Dimitrijević, M.; Radovanović, V.
2014-12-01
In this paper the noncommutative gravity is treated as a gauge theory of the non-commutative SO(2, 3)★ group, while the noncommutativity is canonical. The Seiberg-Witten (SW) map is used to express noncommutative fields in terms of the corresponding commutative fields. The commutative limit of the model is the Einstein-Hilbert action plus the cosmological term and the topological Gauss-Bonnet term. We calculate the second order correction to this model and obtain terms that are zeroth, first, ... and fourth power of the curvature tensor. Finally, we discuss physical consequences of those correction terms in the limit of big cosmological constant.
Theorems for Asymptotic Safety of Gauge Theories
Bond, Andrew D
2016-01-01
We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasized. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated.
Renormalizable Quantum Gauge Theory of Gravity
Institute of Scientific and Technical Information of China (English)
WU Ning
2002-01-01
The quantum gravity is formulated based on the principle of local gauge invariance. The model discussedin this paper has local gravitational gauge symmetry, and gravitational field is represented by gauge field. In the leading-order approximation, it gives out classical Newton's theory of gravity. In the first-order approximation and for vacuum,it gives out Einstein's general theory of relativity. This quantum gauge theory of gravity is a renormalizable quantumtheory.
Theorems for asymptotic safety of gauge theories
Energy Technology Data Exchange (ETDEWEB)
Bond, Andrew D.; Litim, Daniel F. [University of Sussex, Department of Physics and Astronomy, Brighton (United Kingdom)
2017-06-15
We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasised. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated. (orig.)
Torrielli, A
2003-01-01
The results of our research on noncommutative perturbative quantum field theory and its relation to string theory are exposed with details. 1) We give an introduction to noncommutative quantum field theory and its derivation from open string theory in an antisymmetric background. 2) We perform a perturbative Wilson loop calculation for 2D NCYM. We compare the LCG results for the WML and the PV prescription. With WML the loop is well-defined and regular in the commutative limit. With PV the result is singular. This is intriguing: in the commutative theory their difference is related to topological excitations, moreover PV provides a point-like potential. 3) Commutative 2D YM exhibits an interplay between geometrical and U(N) gauge properties: in the exact expression of a Wilson loop with n windings a scaling intertwines n and N. In the NC case the interplay becomes tighter due to the merging of space-time and ``internal'' symmetries. Surprisingly, in our up to O(g^6) (and beyond) crossed graphs calculations th...
Local gauge coupling running in supersymmetric gauge theories on orbifolds
Energy Technology Data Exchange (ETDEWEB)
Hillenbach, M.
2007-11-21
By extending Feynman's path integral calculus to fields which respect orbifold boundary conditions we provide a straightforward and convenient framework for loop calculations on orbifolds. We take advantage of this general method to investigate supersymmetric Abelian and non-Abelian gauge theories in five, six and ten dimensions where the extra dimensions are compactified on an orbifold. We consider hyper and gauge multiplets in the bulk and calculate the renormalization of the gauge kinetic term which in particular allows us to determine the gauge coupling running. The renormalization of the higher dimensional theories in orbifold spacetimes exhibits a rich structure with three principal effects: Besides the ordinary renormalization of the bulk gauge kinetic term the loop effects may require the introduction of both localized gauge kinetic terms at the fixed points/planes of the orbifold and higher dimensional operators. (orig.)
Scattering amplitudes in gauge theories
Energy Technology Data Exchange (ETDEWEB)
Henn, Johannes M. [Institute for Advanced Study, Princeton, NJ (United States). School of Natural Sciences; Plefka, Jan C. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
2014-03-01
First monographical text on this fundamental topic. Course-tested, pedagogical and self-contained exposition. Includes exercises and solutions. At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum field theory. Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, these concise yet self-contained and course-tested lecture notes are well-suited for a one-semester graduate level course or as a self-study guide for anyone interested in fundamental aspects of quantum field theory and its applications. The numerous exercises and solutions included will help readers to embrace and apply the material presented in the main text.
Noncommutative Field Theory With General Translation Invariant Star Products
Rivera, Manolo
2015-01-01
We compute the two-point and four-point Green's function of the noncommutative $\\phi^{4}$ field theory; first with the s-ordered star products and then with a general translation invariant star product. We derive the differential expression for any translation invariant star product, and with the help of this expression we show that any of these products can be written in terms of a twist. Finally, using the notion of the twisted action of the infinitesimal Poincar\\'e transformations, we show that the commutator between the coordinate functions is invariant under Poincar\\'e transformations at a deformed level.
Technicolor and Lattice Gauge Theory
Chivukula, R Sekhar
2010-01-01
Technicolor and other theories of dynamical electroweak symmetry breaking invoke chiral symmetry breaking triggered by strong gauge-dynamics, analogous to that found in QCD, to explain the observed W, Z, and fermion masses. In this talk we describe why a realistic theory of dynamical electroweak symmetry breaking must, relative to QCD, produce an enhanced fermion condensate. We quantify the degree to which the technicolor condensate must be enhanced in order to yield the observed quark masses, and still be consistent with phenomenological constraints on flavor-changing neutral-currents. Lattice studies of technicolor and related theories provide the only way to demonstrate that such enhancements are possible and, hopefully, to discover viable candidate models. We comment briefly on the current status of non-perturbative investigations of dynamical electroweak symmetry breaking, and provide a "wish-list" of phenomenologically-relevant properties that are important to calculate in these theories
A nilpotent symmetry of quantum gauge theories
Lahiri, Amitabha
2001-09-01
For the Becchi-Rouet-Stora-Tyutin invariant extended action for any gauge theory, there exists another off-shell nilpotent symmetry. For linear gauges, it can be elevated to a symmetry of the quantum theory and used in the construction of the quantum effective action. Generalizations for nonlinear gauges and actions with higher-order ghost terms are also possible.
BRST symmetry in the general gauge theories
Hyuk-Jae, Lee; Jae, Hyung, Yee
1994-01-01
By using the residual gauge symmetry interpretation of BRST invariance we have constructed a new BRST formulation for general gauge theories including those with open algebras. For theories with open gauge algebra the formulation leads to a BRST invariant effective action which does not contain any higher order terms in the ghost fields.
Invariance, symmetry and periodicity in gauge theories
Energy Technology Data Exchange (ETDEWEB)
Jackiw, R
1980-02-01
The interplay between gauge transformations and coordinate transformations is discussed; the theory will aid in understanding the mixing of space-time and internal degrees of freedom. The subject is presented under the following headings: coordinate transformation laws for arbitrary fields, coordinate transformation laws for gauge fields, properties of symmetric gauge fields, construction of symmetric gauge fields, physical significance of gauge transformations, and magnetic monopole topology without Higgs fields. The paper ends with conclusions and suggestions for further research. (RWR)
Structural aspects of quantum field theory and noncommutative geometry
Grensing, Gerhard
2013-01-01
This book is devoted to the subject of quantum field theory. It is divided into two volumes. The first can serve as a textbook on the main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation. The first volume is directed at graduate students who want to learn the basic facts about quantum field theory. It begins with a gentle introduction to classical field theory, including the standard model of particle physics, general relativity, and also supergravity. The transition to quantized fields is performed with path integral techniques, by means of which the one-loop renormalization of a self-interacting scalar quantum field, of quantum electrodynamics, and the asymptotic freedom of quantum chromodynamics is treated. In the last part of the first volume, the application of path integral methods to systems of quantum statistical mechanics is covered. The book ends with a r...
Generalized Gauge Theories and Weinberg-Salam Model with Dirac-Kähler Fermions
Kawamoto, N; Umetsu, H; Kawamoto, Noboru; Tsukioka, Takuya; Umetsu, Hiroshi
2001-01-01
We extend previously proposed generalized gauge theory formulation of Chern-Simons type and topological Yang-Mills type actions into Yang-Mills type actions. We formulate gauge fields and Dirac-K\\"ahler matter fermions by all degrees of differential forms. The simplest version of the model which includes only zero and one form gauge fields accommodated with the graded Lie algebra of $SU(2|1)$ supergroup leads Weinberg-Salam model. Thus the Weinberg-Salam model formulated by noncommutative geometry is a particular example of the present formulation.
Photon defects in noncommutative standard model candidates
Energy Technology Data Exchange (ETDEWEB)
Abel, S.A.; Khoze, V.V. [Durham Univ. (United Kingdom). Center for Particle Theory; Jaeckel, J.; Ringwald, A. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2006-06-15
Restrictions imposed by gauge invariance in noncommutative spaces together with the effects of ultraviolet/infrared mixing lead to strong constraints on possible candidates for a noncommutative extension of the Standard Model. We study a general class of noncommutative models consistent with these restrictions. Specifically we consider models based upon a gauge theory with the gauge group U(N{sub 1}) x U(N{sub 2}) x.. x U(N{sub m}) coupled to matter fields transforming in the (anti)-fundamental, bi-fundamental and adjoint representations. We pay particular attention to overall trace-U(1) factors of the gauge group which are affected by the ultraviolet/infrared mixing. Typically, these trace-U(1) gauge fields do not decouple sufficiently fast in the infrared, and lead to sizable Lorentz symmetry violating effects in the low-energy effective theory. In a 4-dimensional theory on a continuous space-time making these effects unobservable would require making the effects of noncommutativity tiny, M{sub NC} >> M{sub P}. This severely limits the phenomenological prospects of such models. However, adding additional universal extra dimensions the trace-U(1) factors decouple with a power law and the constraint on the noncommutativity scale is weakened considerably. Finally, we briefly mention some interesting properties of the photon that could arise if the noncommutative theory is modified at a high energy scale. (Orig.)
Transport properties of cascading gauge theories
Buchel, A
2005-01-01
Cascading gauge theories of Klebanov et.al. provide a model within a framework of gauge theory/string theory duality for a four dimensional non-conformal gauge theory with a spontaneously generated mass scale. Using the dual supergravity description we study sound wave propagation in strongly coupled cascading gauge theory plasma. We analytically compute the speed of sound and the bulk viscosity of cascading gauge theory plasma at a temperature much larger than the strong coupling scale of the theory. The sound wave dispersion relation is obtained from the hydrodynamic pole in the stress-energy tensor two-point correlation function. The speed of sound extracted from the pole of the correlation function agrees with its value computed in [hep-th/0506002] using the equation of state. We find that the bulk viscosity of the hot cascading gauge theory plasma is non-zero at the leading order in the deviation from conformality.
Geometric Formulation of Gauge Theory of Gravity
Institute of Scientific and Technical Information of China (English)
WU Ning; ZHANG Da-Hua; RUAN Tu-Nan
2003-01-01
Differential geometric formulation of quantum gauge theory of gravity is studied in this paper. The quantumgauge theory of gravity is formulated completely in the framework of traditional quantum field theory. In order to studythe relationship between quantum gauge theory of gravity and traditional quantum gravity which is formulated in curvedspace, it is important to set up the geometry picture of quantum gauge theory of gravity. The correspondence betweenquantum gauge theory of gravity and differential geometry is discussed and the geometry picture of quantum gaugetheory of gravity is studied.
Noncommutative Solitons and the W_{1+\\infty} Algebras in Quantum Hall Theory
Chan, C T; Chan, Chuan-Tsung; Lee, Jen-Chi
2001-01-01
We show that U(\\infty) symmetry transformations of the noncommutative field theory in the Moyal space are generated by a combination of two W_{1+\\infty} algebras in the Landau problem. Geometrical meaning of this infinite symmetry is illustrated by examining the transformations of an invariant subgroup on the noncommutative solitons, which generate deformations and boosts of solitons.
Zeeman Effect In The Framework of Moyal Noncommutativity and String Theory
Boukili, A E; Sedra, M B
2006-01-01
Stimulated by the importance of noncommutative geometry in recent developments in string theory, the discovery of D-branes and integrable systems, one intends in this work to present a new insight towards adapting the famous idea of Zeeman effect to noncommutativity \\`a la Moyal and develop an analysis leading to connect our results to the Bigatti-Suskind (BS) formulation.
Superpotentials for Quiver Gauge Theories
Energy Technology Data Exchange (ETDEWEB)
Aspinwall, Paul S.; /Stanford U., Phys. Dept. /SLAC /Duke U., CGTP; Fidkowski, Lukasz M.; /Stanford U., Phys. Dept.
2005-06-10
We compute superpotentials for quiver gauge theories arising from marginal D-Brane decay on collapsed del Pezzo cycles S in a Calabi-Yau X. This is done using the machinery of A{sub {infinity}} products in the derived category of coherent sheaves of X, which in turn is related to the derived category of S and quiver path algebras. We confirm that the superpotential is what one might have guessed from analyzing the moduli space, i.e., it is linear in the fields corresponding to the Exts of the quiver and that each such Ext multiplies a polynomial in Exts equal to precisely the relation represented by the Ext.
2+1 Abelian `Gauge Theory' Inspired by Ideal Hydrodynamics
Krishnaswami, G S
2005-01-01
We study a theory of abelian gauge fields on a two-manifold M with volume form mu. The phase space coincides with that of incompressible hydrodynamics: a coadjoint orbit of the volume-preserving diffeomorphism group of M. Gauge fields satisfy a Poisson algebra different from the Heisenberg algebra of electrodynamics, but reminiscent of Yang-Mills theory on a null surface. Enstrophy invariants are Casimirs. Some symplectic leaves are identified. The magnetic energy depends on a metric unrelated to mu. The magnetic field evolves by a quadratically non-linear `Euler' equation, which may also be regarded as describing geodesic flow on SDiff(M,mu). Some static solutions are found. For uniform mu, we find infinitely many conserved charges in involution, suggesting integrability. This is a toy-model for ordinary Yang-Mills theory and matrix field theories, whose gauge-invariant phase space is conjectured to be a coadjoint orbit of a diffeomorphism group of a non-commutative space.
Gauge theories in local causal perturbation theory
Boas, F M
1999-01-01
In this thesis quantum gauge theories are considered in the framework of local, causal perturbation theory. Gauge invariance is described in terms of the BRS formalism. Local interacting field operators are constructed perturbatively and field equations are established. A nilpotent BRS transformation is defined on the local algebra of fields. It allows the definition of the algebra of local observables as an operator cohomology. This algebra of local observables can be represented in a Hilbert space. The interacting field operators are defined in terms of time ordered products of free field operators. For the results above to hold the time ordered products must satisfy certain normalization conditions. To formulate these conditions also for field operators that contain a spacetime derivative a suitable mathematical description of time ordered products is developed. Among the normalization conditions are Ward identities for the ghost current and the BRS current. The latter are generalizations of a normalizatio...
Testing gauge-invariant perturbation theory
Törek, Pascal
2016-01-01
Gauge-invariant perturbation theory for theories with a Brout-Englert-Higgs effect, as developed by Fr\\"ohlich, Morchio and Strocchi, starts out from physical, exactly gauge-invariant quantities as initial and final states. These are composite operators, and can thus be considered as bound states. In case of the standard model, this reduces almost entirely to conventional perturbation theory. This explains the success of conventional perturbation theory for the standard model. However, this is due to the special structure of the standard model, and it is not guaranteed to be the case for other theories. Here, we review gauge-invariant perturbation theory. Especially, we show how it can be applied and that it is little more complicated than conventional perturbation theory, and that it is often possible to utilize existing results of conventional perturbation theory. Finally, we present tests of the predictions of gauge-invariant perturbation theory, using lattice gauge theory, in three different settings. In ...
Gauge Theories in the Twentieth Century
2001-01-01
By the end of the 1970s, it was clear that all the known forces of nature (including, in a sense, gravity) were examples of gauge theories , characterized by invariance under symmetry transformations chosen independently at each position and each time. These ideas culminated with the finding of the W and Z gauge bosons (and perhaps also the Higgs boson). This important book brings together the key papers in the history of gauge theories, including the discoveries of: the role of gauge transformations in the quantum theory of electrically charged particles in the 1920s; nonabelian gauge groups
Gauge Invariants and Correlators in Flavoured Quiver Gauge Theories
Mattioli, Paolo
2016-01-01
In this paper we study the construction of holomorphic gauge invariant operators for general quiver gauge theories with flavour symmetries. Using a characterisation of the gauge invariants in terms of equivalence classes generated by permutation actions, along with representation theory results in symmetric groups and unitary groups, we give a diagonal basis for the 2-point functions of holomorphic and anti-holomorphic operators. This involves a generalisation of the previously constructed Quiver Restricted Schur operators to the flavoured case. The 3-point functions are derived and shown to be given in terms of networks of symmetric group branching coefficients. The networks are constructed through cutting and gluing operations on the quivers.
Algebraic deformations of toric varieties II. Noncommutative instantons
Cirio, Lucio; Szabo, Richard J
2011-01-01
We continue our study of the noncommutative algebraic and differential geometry of a particular class of deformations of toric varieties, focusing on aspects pertinent to the construction and enumeration of noncommutative instantons on these varieties. We develop a noncommutative version of twistor theory, which introduces a new example of a noncommutative four-sphere. We develop a braided version of the ADHM construction and show that it parametrizes a certain moduli space of framed torsion free sheaves on a noncommutative projective plane. We use these constructions to explicitly build instanton gauge bundles with canonical connections on the noncommutative four-sphere that satisfy appropriate anti-selfduality equations. We construct projective moduli spaces for the torsion free sheaves and demonstrate that they are smooth. We define equivariant partition functions of these moduli spaces, finding that they coincide with the usual instanton partition functions for supersymmetric gauge theories on C^2.
Supersymmetric gauge theories, intersecting branes and free fermions
Dijkgraaf, Robbert; Hollands, Lotte; Sułkowski, Piotr; Vafa, Cumrun
2008-02-01
We show that various holomorphic quantities in supersymmetric gauge theories can be conveniently computed by configurations of D4-branes and D6-branes. These D-branes intersect along a Riemann surface that is described by a holomorphic curve in a complex surface. The resulting I-brane carries two-dimensional chiral fermions on its world-volume. This system can be mapped directly to the topological string on a large class of non-compact Calabi-Yau manifolds. Inclusion of the string coupling constant corresponds to turning on a constant B-field on the complex surface, which makes this space non-commutative. Including all string loop corrections the free fermion theory is elegantly formulated in terms of holonomic D-modules that replace the classical holomorphic curve in the quantum case.
Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions
Dijkgraaf, Robbert; Sulkowski, Piotr; Vafa, Cumrun
2008-01-01
We show that various holomorphic quantities in supersymmetric gauge theories can be conveniently computed by configurations of D4-branes and D6-branes. These D-branes intersect along a Riemann surface that is described by a holomorphic curve in a complex surface. The resulting I-brane carries two-dimensional chiral fermions on its world-volume. This system can be mapped directly to the topological string on a large class of non-compact Calabi-Yau manifolds. Inclusion of the string coupling constant corresponds to turning on a constant B-field on the complex surface, which makes this space non-commutative. Including all string loop corrections the free fermion theory is elegantly formulated in terms of holonomic D-modules that replace the classical holomorphic curve in the quantum case.
Multiloop Noncommutative Open String Theory and their QFT limit
Chu, C S; Chu, Chong-Sun; Russo, Rodolfo
2001-01-01
The multiloop amplitudes for open bosonic string in presence of a constant B-field are derived from first principles. The basic ingredients of the construction are the commutation relations for the string modes and the Reggeon vertex describing the interaction among three generic string states. The modifications due to the presence of the B-field affect non--trivially only the zero modes. This makes it possible to write in a simple and elegant way the general expression for multiloop string amplitudes in presence of a constant B-field. The field theory limit of these string amplitudes is also considered. We show that it reproduces exactly the Feynman diagrams of noncommutative field theories. Issues of UV/IR are briefly discussed.
Noncommutative Common Cause Principles in algebraic quantum field theory
Hofer-Szabó, Gábor; Vecsernyés, Péter
2013-04-01
States in algebraic quantum field theory "typically" establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions VA and VB, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of VA and VB and the set {C, C⊥} screens off the correlation between A and B.
Noncommutative Common Cause Principles in Algebraic Quantum Field Theory
Hofer-Szabó, Gábor
2012-01-01
States in algebraic quantum field theory "typically" establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V_A and V_B, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V_A and V_B and the set {C, non-C} screens off the correlation between A and B.
One loop radiative corrections to the translation-invariant noncommutative Yukawa Theory
Bouchachia, Karim; Hachemane, Mahmoud; Schweda, Manfred
2015-01-01
We elaborate in this paper a translation-invariant model for fermions in 4-dimensional noncommutative Euclidean space. The construction is done on the basis of the renormalizable noncommutative translation-invariant Phi4 theory introduced by R. Gurau et al. We combine our model with the scalar model, in order to study the noncommutative pseudo-scalar Yukawa theory. After we derive the Feynman rules of the theory, we perform an explicit calculation of the quantum corrections at one loop level to the propagators and vertices.
$\\Phi$-derivable approximations in gauge theories
Arrizabalaga, A
2003-01-01
We discuss the method of $\\Phi$-derivable approximations in gauge theories. There, two complications arise, namely the violation of Bose symmetry in correlation functions and the gauge dependence. For the latter we argue that the error introduced by the gauge dependent terms is controlled, therefore not invalidating the method.
Lattice gauge theories and Monte Carlo simulations
Rebbi, Claudio
1983-01-01
This volume is the most up-to-date review on Lattice Gauge Theories and Monte Carlo Simulations. It consists of two parts. Part one is an introductory lecture on the lattice gauge theories in general, Monte Carlo techniques and on the results to date. Part two consists of important original papers in this field. These selected reprints involve the following: Lattice Gauge Theories, General Formalism and Expansion Techniques, Monte Carlo Simulations. Phase Structures, Observables in Pure Gauge Theories, Systems with Bosonic Matter Fields, Simulation of Systems with Fermions.
Gauge Invariant Cosmological Perturbation Theory
Durrer, R
1993-01-01
After an introduction to the problem of cosmological structure formation, we develop gauge invariant cosmological perturbation theory. We derive the first order perturbation equations of Einstein's equations and energy momentum ``conservation''. Furthermore, the perturbations of Liouville's equation for collisionless particles and Boltzmann's equation for Compton scattering are worked out. We fully discuss the propagation of photons in a perturbed Friedmann universe, calculating the Sachs--Wolfe effect and light deflection. The perturbation equations are extended to accommodate also perturbations induced by seeds. With these general results we discuss some of the main aspects of the texture model for the formation of large scale structure in the Universe (galaxies, clusters, sheets, voids). In this model, perturbations in the dark matter are induced by texture seeds. The gravitational effects of a spherically symmetric collapsing texture on dark matter, baryonic matter and photons are calculated in first orde...
Gauge Theory and Langlands Duality
Frenkel, Edward
2009-01-01
The Langlands Program was launched in the late 60s with the goal of relating Galois representations and automorphic forms. In recent years a geometric version has been developed which leads to a mysterious duality between certain categories of sheaves on moduli spaces of (flat) bundles on algebraic curves. Three years ago, in a groundbreaking advance, Kapustin and Witten have linked the geometric Langlands correspondence to the S-duality of 4D supersymmetric gauge theories. This and subsequent works have already led to striking new insights into the geometric Langlands Program, which in particular involve the Homological Mirror Symmetry of the Hitchin moduli spaces of Higgs bundles on algebraic curves associated to two Langlands dual Lie groups.
Moyal deformations of Clifford gauge theories of gravity
Castro, Carlos
2016-12-01
A Moyal deformation of a Clifford Cl(3, 1) Gauge Theory of (Conformal) Gravity is performed for canonical noncommutativity (constant Θμν parameters). In the very special case when one imposes certain constraints on the fields, there are no first-order contributions in the Θμν parameters to the Moyal deformations of Clifford gauge theories of gravity. However, when one does not impose constraints on the fields, there are first-order contributions in Θμν to the Moyal deformations in variance with the previous results obtained by other authors and based on different gauge groups. Despite that the generators of U(2, 2),SO(4, 2),SO(2, 3) can be expressed in terms of the Clifford algebra generators this does not imply that these algebras are isomorphic to the Clifford algebra. Therefore one should not expect identical results to those obtained by other authors. In particular, there are Moyal deformations of the Einstein-Hilbert gravitational action with a cosmological constant to first-order in Θμν. Finally, we provide a mechanism which furnishes a plausible cancellation of the huge vacuum energy density.
Non-commutative Iwasawa theory for modular forms
Coates, John; Liang, Zhibin; Stein, William; Sujatha, Ramdorai
2012-01-01
The aim of the present paper is to give evidence, largely numerical, in support of the non-commutative main conjecture of Iwasawa theory for the motive of a primitive modular form of weight k>2 over the Galois extension of Q obtained by adjoining to Q all p-power roots of unity, and all p-power roots of a fixed integer m>1. The predictions of the main conjecture are rather intricate in this case because there is more than one critical point, and also there is no canonical choice of periods. Nevertheless, our numerical data agrees perfectly with all aspects of the main conjecture, including Kato's mysterious congruence between the cyclotomic Manin p-adic L-function, and the cyclotomic p-adic L-function of a twist of the motive by a certain non-abelian Artin character of the Galois group of this extension.
Lattice Gauge Theories and Spin Models
Mathur, Manu
2016-01-01
The Wegner $Z_2$ gauge theory-$Z_2$ Ising spin model duality in $(2+1)$ dimensions is revisited and derived through a series of canonical transformations. These $Z_2$ results are directly generalized to SU(N) lattice gauge theory in $(2+1)$ dimensions to obtain a dual SU(N) spin model in terms of the SU(N) magnetic fields and electric scalar potentials. The gauge-spin duality naturally leads to a new gauge invariant disorder operator for SU(N) lattice gauge theory. A variational ground state of the dual SU(2) spin model with only nearest neighbour interactions is constructed to analyze SU(2) lattice gauge theory.
G_2 gauge theory at finite temperature
Cossu, Guido; Di Giacomo, Adriano; Lucini, Biagio; Pica, Claudio
2007-01-01
The gauge group being centreless, $G_2$ gauge theory is a good laboratory for studying the role of the centre of the group for colour confinement in Yang-Mills gauge theories. In this paper, we investigate $G_2$ pure gauge theory at finite temperature on the lattice. By studying the finite size scaling of the plaquette, the Polyakov loop and their susceptibilities, we show that a deconfinement phase transition takes place. The analysis of the pseudocritical exponents give strong evidence of the deconfinement transition being first order. Implications of our findings for scenarios of colour confinement are discussed.
Non-commutative standard model: model building
Chaichian, Masud; Presnajder, P
2003-01-01
A non-commutative version of the usual electro-weak theory is constructed. We discuss how to overcome the two major problems: (1) although we can have non-commutative U(n) (which we denote by U sub * (n)) gauge theory we cannot have non-commutative SU(n) and (2) the charges in non-commutative QED are quantized to just 0,+-1. We show how the latter problem with charge quantization, as well as with the gauge group, can be resolved by taking the U sub * (3) x U sub * (2) x U sub * (1) gauge group and reducing the extra U(1) factors in an appropriate way. Then we proceed with building the non-commutative version of the standard model by specifying the proper representations for the entire particle content of the theory, the gauge bosons, the fermions and Higgs. We also present the full action for the non-commutative standard model (NCSM). In addition, among several peculiar features of our model, we address the inherentCP violation and new neutrino interactions. (orig.)
Superfield quantization of general gauge theories
Lavrov, P M
1995-01-01
A superfield version on superspace (x^\\mu,\\theta^a) is proposed for the Sp(2)-- covariant Lagrangian quantization of general gauge theories. The BRST- and antiBRST- transformations are realized on superfields as supertranslations in the \\theta^a-- directions. A new (geometric) interpretation of the Ward identities in the quantum gauge theory is given.
Naka, S.; Toyoda, H.; Takanashi, T.; Umezawa, E.
2014-04-01
In kappa -Minkowski spacetime, the coordinates are Lie algebraic elements such that time and space coordinates do not commute, whereas space coordinates commute with each other. The noncommutativity is proportional to a Planck-length-scale constant kappa ^{-1}, which is a universal constant other than the velocity of light, under the kappa -Poincaré transformation. In this sense, the spacetime has a structure called "doubly special relativity." Such a noncommutative structure is known to be realized by SO(1,4) generators in 4-dimensional de Sitter space. In this paper, we try to construct a noncommutative spacetime having a commutative n-dimensional Minkowski spacetime based on AdS_{n+1} space with SO(2,n) symmetry. We also study an invariant wave equation corresponding to the first Casimir invariant of this symmetry as a nonlocal field equation expected to yield finite loop amplitudes.
Functional integration and gauge ambiguities in generalized abelian gauge theories
Kelnhofer, Gerald
2007-01-01
We consider the covariant quantization of generalized abelian gauge theories on a closed and compact n-dimensional manifold whose space of gauge invariant fields is the abelian group of Cheeger-Simons differential characters. The space of gauge fields is shown to be a non-trivial bundle over the orbits of the subgroup of smooth Cheeger-Simons differential characters. Furthermore each orbit itself has the structure of a bundle over a multi-dimensional torus. As a consequence there is a topological obstruction to the existence of a global gauge fixing condition. A functional integral measure is proposed on the space of gauge fields which takes this problem into account and provides a regularization of the gauge degrees of freedom. For the generalized p-form Maxwell theory closed expressions for all physical observables are obtained. The Greens functions are shown to be affected by the non-trivial bundle structure. Finally the vacuum expectation values of circle-valued homomorphisms, including the Wilson operato...
Invariant Regularization of Supersymmetric Chiral Gauge Theory
Suzuki, H
1999-01-01
We present a regularization scheme which respects the supersymmetry and the maximal background gauge covariance in supersymmetric chiral gauge theories. When the anomaly cancellation condition is satisfied, the effective action in the superfield background field method automatically restores the gauge invariance without counterterms. The scheme also provides a background gauge covariant definition of composite operators that is especially useful in analyzing anomalies. We present several applications: The minimal consistent gauge anomaly; the super-chiral anomaly and the superconformal anomaly; as the corresponding anomalous commutators, the Konishi anomaly and an anomalous supersymmetric transformation law of the supercurrent (the ``central extension'' of N=1 supersymmetry algebra) and of the R-current.
Toward a gauge field theory of gravity.
Yilmaz, H.
Joint use of two differential identities (Bianchi and Freud) permits a gauge field theory of gravity in which the gravitational energy is localizable. The theory is compatible with quantum mechanics and is experimentally viable.
A Nonperturbative Regulator for Chiral Gauge Theories
Grabowska, Dorota M
2015-01-01
We propose a nonperturbative gauge invariant regulator for $d$-dimensional chiral gauge theories on the lattice. The method involves simulating domain wall fermions in $d+1$ dimensions with quantum gauge fields that reside on one $d$-dimensional surface and are extended into the bulk via gradient flow. The result is a theory of gauged fermions plus mirror fermions, where the mirror fermions couple to the gauge fields via a form factor that becomes exponentially soft with the separation between domain walls. The resultant theory has a local $d$-dimensional interpretation if and only if the chiral fermion representation is anomaly free. A physical realization of this construction leads to mirror fermions in the Standard Model with soft form factors for gauge fields and gravity. These mirror particles could evade detection except by sensitive probes at extremely low energy, and yet still affect vacuum topology, and could gravitate differently than conventional matter.
Entanglement of Distillation for Lattice Gauge Theories
Van Acoleyen, Karel; Bultinck, Nick; Haegeman, Jutho; Marien, Michael; Scholz, Volkher B.; Verstraete, Frank
2016-09-01
We study the entanglement structure of lattice gauge theories from the local operational point of view, and, similar to Soni and Trivedi [J. High Energy Phys. 1 (2016) 1], we show that the usual entanglement entropy for a spatial bipartition can be written as the sum of an undistillable gauge part and of another part corresponding to the local operations and classical communication distillable entanglement, which is obtained by depolarizing the local superselection sectors. We demonstrate that the distillable entanglement is zero for pure Abelian gauge theories at zero gauge coupling, while it is in general nonzero for the non-Abelian case. We also consider gauge theories with matter, and show in a perturbative approach how area laws—including a topological correction—emerge for the distillable entanglement. Finally, we also discuss the entanglement entropy of gauge fixed states and show that it has no relation to the physical distillable entropy.
Graph Zeta function and gauge theories
He, Yang-Hui
2011-03-01
Along the recently trodden path of studying certain number theoretic properties of gauge theories, especially supersymmetric theories whose vacuum manifolds are non-trivial, we investigate Ihara's Graph Zeta Function for large classes of quiver theories and periodic tilings by bi-partite graphs. In particular, we examine issues such as the spectra of the adjacency and whether the gauge theory satisfies the strong and weak versions of the graph theoretical analogue of the Riemann Hypothesis.
Discussion on Lorentz invariance violation of noncommutative field theory and neutrino oscillation
Luo, Cui-Bai; Shi, Song; Du, Yi-Lun; Wang, Yong-Long; Zong, Hong-Shi
2017-03-01
Depending on deformed canonical anticommutation relations, massless neutrino oscillation based on Lorentz invariance violation in noncommutative field theory is discussed. It is found that the previous studies about massless neutrino oscillation within deformed canonical anticommutation relations should satisfy the condition of new Moyal product and new nonstandard commutation relations. Furthermore, comparing the Lorentz invariant violation parameters A in the previous studies with new Moyal product and new nonstandard commutation relations, we find that the orders of magnitude of noncommutative parameters (Lorentz invariant violation parameters A) is not self-consistent. This inconsistency means that the previous studies of Lorentz invariance violation in noncommutative field theory may not naturally explain massless neutrino oscillation. In other words, it should be impossible to explain neutrino oscillation by Lorentz invariance violation in noncommutative field theory. This conclusion is supported by the latest atmospheric neutrinos experimental results from the super-Kamiokande Collaboration, which show that no evidence of Lorentz invariance violation on atmospheric neutrinos was observed.
Exotic Newton-Hooke group, noncommutative plane and superconformal symmetry
Alvarez, Pedro D
2009-01-01
In this thesis we have studied some systems with exotic symmetries, which are a peculiarity in 2+1 space-time dimensions. Coded in the exotic structure appears noncommutative coordinates and a phases structure. This kind of systems has attracted attention from different areas of physics independently. Among them we can mention: theory of ray representations of Lie groups, anyons physics, some condensed matter systems, for instance the quantum Hall effect, planar gauge and gravitation theories, noncommutative field theory, noncommutative geometry and noncommutative quantum mechanics. We will focus our study in some topics on exotic nonrelativistic symmetries, such as the exotic Newton-Hooke group, the relation between the systems of exotic Newton-Hooke and the noncommutative Landau problem and the symmetries of noncommutative Landau problem, its conformal and supersymmetric extensions. The exotic Newton-Hooke group correspond to the nonrelativistic limit of the de Sitter groups, and has as a particular case (f...
Global anomalies in Chiral Lattice Gauge Theory
Bär, Oliver; Campos, Isabel
As first realized by Witten an SU(2) gauge theory coupled to a single Weyl fermion suffers from a global anomaly. This problem is addressed here in the context of the recent developments on chiral gauge theories on the lattice. We find Witten's anomaly manifests in the impossibility of defining globally a fermion measure that reproduces the proper continuum limit. Moreover, following Witten's original argument, we check numerically the crossing of the lowest eigenvalues of Neuberger's operator along a path connecting two gauge fields that differ by a topologically non-trivial gauge transformation.
Symmetry breaking in noncommutative finite temperature λphi4 theory with a nonuniform ground state
Hernández, J. M.; Ramírez, C.; Sánchez, M.
2014-05-01
We consider the CJT effective action at finite temperature for a noncommutative real scalar field theory, with noncommutativity among space and time variables. We study the solutions of a stripe type nonuniform background, which depends on space and time. The analysis in the first approximation shows that such solutions appear in the planar limit, but also under normal anisotropic noncommutativity. Further we show that the transition from the uniform ordered phase to the non uniform one is first order and that the critical temperature depends on the nonuniformity of the ground state.
Scattering Amplitudes in Gauge Theories
Schubert, Ulrich
2014-01-01
This thesis is focused on the development of new mathematical methods for computing multi-loop scattering amplitudes in gauge theories. In this work we combine, for the first time, the unitarity-based construction for integrands, and the recently introduced integrand-reduction through multivariate polynomial division. After discussing the generic features of this novel reduction algorithm, we will apply it to the one- and two-loop five-point amplitudes in ${\\cal N}=4$ sYM. The integrands of the multiple-cuts are generated from products of tree-level amplitudes within the super-amplitudes formalism. The corresponding expressions will be used for the analytic reconstruction of the polynomial residues. Their parametric form is known a priori, as derived by means of successive polynomial divisions using the Gr\\"obner basis associated to the on-shell denominators. The integrand reduction method will be exploited to investigate the color-kinematic duality for multi-loop ${\\cal N}=4$ sYM scattering amplitudes. Our a...
Noncommutative field theory and violation of translation invariance
Energy Technology Data Exchange (ETDEWEB)
Bertolami, Orfeu [Departamento de Fisica, Instituto Superior Tecnico, Lisbon (Portugal)]. E-mail: orfeu@cosmos.ist.utl.pt; Guisado, Luis [Departamento de Fisica, Instituto Superior Tecnico, Lisbon (Portugal)
2003-12-01
Noncommutative field theories with commutator of the coordinates of the form [x{sup {mu}}, x{sup {nu}}] = i {lambda}{sup {mu}}{sup {nu}}{sub {omega}}x{sup {omega}} with nilpotent structure constants are studied and shown that a free quantum field theory is not affected. Invariance under translations is broken and the conservation of energy-momentum is violated, obeying a new law which is expressed by a Poincare-invariant equation. The resulting new kinematics is studied and applied to simple examples and to astrophysical puzzles, such as the observed violation of the GZK cutoff. The {lambda}{phi}{sup 4} quantum field theory is also considered in this context. In particular, self interaction terms violate the usual conservation of energy-momentum and, hence, the radiative correction to the propagator is altered. The correction to first order in {lambda} is calculated. The usual UV divergent terms are still present, but a new type of term also emerges, which is IR divergent, violates momentum conservation and implies a correction to the dispersion relation. (author)
Tree amplitudes of noncommutative U(N) Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Huang Jiahui [Center of Mathematical Science, Zhejiang University, Hangzhou (China); Huang Rijun; Jia Yin, E-mail: huangjh19@gmail.com [Physics Department, Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou (China)
2011-10-21
Following the spirit of the S-matrix program, we propose a modified Britto-Cachazo-Feng-Witten recursion relation for tree amplitudes of noncommutative U(N) Yang-Mills theory. Starting from three-point amplitudes, one can use this modified BCFW recursion relation to compute or analyze color-ordered tree amplitudes without relying on any detailed information of noncommutative Yang-Mills theory. After clarifying the color structure of noncommutative tree amplitudes, we write down the noncommutative analogies of Kleiss-Kuijf and Bern-Carrasco-Johansson relations for color-ordered tree amplitudes and prove them using the modified BCFW recursion relation. This checks the consistency of the relation. (paper)
Tree amplitudes of noncommutative U(N) Yang-Mills theory
Huang, Jia-Hui; Huang, Rijun; Jia, Yin
2011-10-01
Following the spirit of the S-matrix program, we propose a modified Britto-Cachazo-Feng-Witten recursion relation for tree amplitudes of noncommutative U(N) Yang-Mills theory. Starting from three-point amplitudes, one can use this modified BCFW recursion relation to compute or analyze color-ordered tree amplitudes without relying on any detailed information of noncommutative Yang-Mills theory. After clarifying the color structure of noncommutative tree amplitudes, we write down the noncommutative analogies of Kleiss-Kuijf and Bern-Carrasco-Johansson relations for color-ordered tree amplitudes and prove them using the modified BCFW recursion relation. This checks the consistency of the relation.
Gauge dependence in Chern-Simons theory
Dilkes, F A; McKeon, D G C; Sherry, T N
1996-01-01
We compute the contribution to the modulus of the one-loop effective action in pure non-Abelian Chern-Simons theory in an arbitrary covariant gauge. We find that the results are dependent on both the gauge parameter (\\alpha) and the metric required in the gauge fixing. A contribution arises that has not been previously encountered; it is of the form (\\alpha / \\sqrt{p^2}) \\epsilon _{\\mu \\lambda \
Higher Gauge Theory and M-Theory
Palmer, Sam
2014-01-01
In this thesis, the emerging field of higher gauge theory will be discussed, particularly in relation to problems arising in M-theory, such as selfdual strings and the so-called (2,0) theory. This thesis will begin with a Nahm-like construction for selfdual strings using loop space, the space of loops on spacetime. This construction maps solutions of the Basu-Harvey equation, the BPS equation arising in the description of multiple M2-branes, to solutions of a selfdual string equation on loop space. Furthermore, all ingredients of the construction reduce to those of the ordinary Nahm construction when compactified on a circle with all loops restricted to those wrapping the circle. The rest of this thesis, however, will not involve loop space. We will see a Nahm-like construction for the case of infinitely many selfdual strings, suspended between two M5-branes. This is possible since the limit taken renders the fields describing the M5-branes abelian. This avoids the problem which the rest of this thesis focuse...
Motion in gauge theories of gravity
Tresguerres, Romualdo
2012-01-01
A description of motion is proposed, adapted to the composite bundle interpretation of Poincar\\'e Gauge Theory. Reference frames, relative positions and time evolution are characterized in gauge-theoretical terms. The approach is illustrated by an appropriate formulation of the familiar example of orbital motion induced by Schwarzschild spacetime.
Hayasaka, K; Hayasaka, Kiyoshi; Nakayama, Ryuichi
2002-01-01
We point out that when a D-brane is placed in an NS-NS B field background with non-vanishing field strength (H=dB) along the D-brane worldvolume, the coordinate of one end of the open string does not commute with that of the other in the low energy limit. The degrees of the freedom associated with both ends are not decoupled and accordingly, the effective action must be quite different from that of the ordinary noncommutative gauge theory for a constant B background. We construct an associative and noncommutative product which operates on the coordinates of both ends of the string and propose a new type of noncommutative gauge action for the low energy effective theory of a Dp-brane. This effective theory is bi-local and lives in twice as large dimensions (2D=2(p+1)) as in the H=0 case. When viewed as a theory in the D-dimensional space, this theory is non-local and we must force the two ends of the string to coincide. We will then propose a prescription for reducing this bi-local effective action to that in ...
Reducible gauge theories in very special relativity
Energy Technology Data Exchange (ETDEWEB)
Upadhyay, Sudhaker, E-mail: sudhakerupadhyay@gmail.com [Department of Physics, Indian Institute of Technology Kanpur, 208016, Kanpur (India)
2015-12-14
In this paper we analyze the tensor field (reducible gauge) theories in the context of very special relativity (VSR). Particularly, we study the VSR gauge symmetry as well as VSR BRST symmetry of Kalb–Ramond and Abelian 3-form fields involving a fixed null vector. We observe that the Kalb–Ramond and Abelian 3-form fields and corresponding ghosts get masses in the VSR framework. The effective action in VSR-type axial gauge is greatly simplified compared with the VSR-type Lorenz gauge. Further, we quantize these models using a Batalin–Vilkovisy (BV) formulation in VSR.
Reducible gauge theories in very special relativity
Energy Technology Data Exchange (ETDEWEB)
Upadhyay, Sudhaker [Indian Institute of Technology Kanpur, Department of Physics, Kanpur (India)
2015-12-15
In this paper we analyze the tensor field (reducible gauge) theories in the context of very special relativity (VSR). Particularly, we study the VSR gauge symmetry as well as VSR BRST symmetry of Kalb-Ramond and Abelian 3-form fields involving a fixed null vector. We observe that the Kalb-Ramond and Abelian 3-form fields and corresponding ghosts get masses in the VSR framework. The effective action in VSR-type axial gauge is greatly simplified compared with the VSR-type Lorenz gauge. Further, we quantize these models using a Batalin-Vilkovisy (BV) formulation in VSR. (orig.)
Invariant Regularization of Supersymmetric Chiral Gauge Theory
Hayashi, T; Okuyama, K; Suzuki, H; Hayashi, Takuya; Ohshima, Yoshihisa; Okuyama, Kiyoshi; Suzuki, Hiroshi
1998-01-01
We formulate a manifestly supersymmetric gauge-covariant regularization of supersymmetric chiral gauge theories. In our scheme, the effective action in the superfield background-field method above one-loop is always supersymmetric and gauge invariant. The gauge anomaly has the covariant form and can emerge only in one-loop diagrams with all the external lines are the background gauge superfield. We also present several illustrative applications in the one-loop approximation: The self-energy part of the chiral multiplet and the gauge multiplet; the super-chiral anomaly and the superconformal anomaly; as the corresponding anomalous commutators, the Konishi anomaly and the anomalous supersymmetric transformation law of the supercurrent (the ``central extension'' of N=1 supersymmetry algebra) and of the R-current.
Topological gauge theories and group cohomology
Dijkgraaf, Robbert; Witten, Edward
1990-04-01
We show that three dimensional Chern-Simons gauge theories with a compact gauge group G (not necessarily connected or simply connected) can be classified by the integer cohomology group H 4( BG, Z). In a similar way, possible Wess-Zumino interactions of such a group G are classified by H 3( G, Z). The relation between three dimensional Chern-Simons gauge theory and two dimensional sigma models involves a certain natural map from H 4( BG, Z) to H 3( G, Z). We generalize this correspondence to topological “spin” theories, which are defined on three manifolds with spin structure, and are related to what might be called Z 2 graded chiral algebras (or chiral superalgebras) in two dimensions. Finally we discuss in some detail the formulation of these topological gauge theories for the special case of a finite group, establishing links with two dimensional (holomorphic) orbifold models.
Gauge Theories on the Light-Front
Brodsky, S J
2004-01-01
The light-front quantization of gauge theories in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitary, and a trivial vacuum. The light-front Hamiltonian form of QCD provides an alternative to lattice gauge theory for the computation of nonperturbative quantities such as the hadronic spectrum and the corresponding eigenfunctions. In the case of the electroweak theory, spontaneous symmetry breaking is represented by the appearance of zero modes of the Higgs field. Light-front quantization then leads to an elegant ghost-free theory of massive gauge particles, automatically incorporating the Lorentz and 't Hooft conditions, as well as the Goldstone boson equivalence theorem.
Introduction to dualities in gauge theories
Energy Technology Data Exchange (ETDEWEB)
Kneipp, Marco A.C. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: kneipp@cbpf.br
2000-12-01
These notes present a pedagogical introduction to magnetic monopoles, supersymmetry and dualities in gauge theories. They are based on lectures given at the X Jorge Andre Swieca Summer School on Particles and Fields. (author)
Gauge/string duality in confining theories
Energy Technology Data Exchange (ETDEWEB)
Edelstein, J.D. [Departamento de Fi sica de Particulas, Universidade de Santiago de Compostela and Instituto Galego de Fisica de Altas Enerxias (IGFAE), 15782 Santiago de Compostela (Spain); Instituto de Fisica de La Plata (IFLP), Universidad Nacional de La Plata, La Plata (Argentina); Centro de Estudios Cientificos (CECS), Casilla 1469, Valdivia (Chile); Portugues, R. [Centro de Estudios Cientificos (CECS), Casilla 1469, Valdivia (Chile)
2006-07-03
This is the content of a set of lectures given at the ''XIII Jorge Andre Swieca Summer School on Particles and Fields'', Campos do Jordao, Brazil in January 2005. They intend to be a basic introduction to the topic of gauge/gravity duality in confining theories. We start by reviewing some key aspects of the low energy physics of non-Abelian gauge theories. Then, we present the basics of the AdS/CFT correspondence and its extension both to gauge theories in different spacetime dimensions with sixteen supercharges and to more realistic situations with less supersymmetry. We discuss the different options of interest: placing D-branes at singularities and wrapping D-branes in calibrated cycles of special holonomy manifolds. We finally present an outline of a number of non-perturbative phenomena in non-Abelian gauge theories as seen from supergravity. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Gauge/String Duality in Confining Theories
Edelstein, J D; Edelstein, Jose D.; Portugues, Ruben
2006-01-01
This is the content of a set of lectures given at the XIII Jorge Andre Swieca Summer School on Particles and Fields, held in Campos do Jordao, Brazil in January 2005. They intend to be a basic introduction to the topic of gauge/gravity duality in confining theories. We start by reviewing some key aspects of the low energy physics of non-Abelian gauge theories. Then, we present the basics of the AdS/CFT correspondence and its extension both to gauge theories in different spacetime dimensions with sixteen supercharges and to more realistic situations with less supersymmetry. We discuss the different options of interest: placing D-branes at singularities and wrapping D-branes in calibrated cycles of special holonomy manifolds. We finally present an outline of a number of non-perturbative phenomena in non-Abelian gauge theories as seen from supergravity.
From SU(2) gauge theory to qubits on the fuzzy sphere
Zizzi, Paola
2013-01-01
We consider a classical pure SU(2) gauge theory, and make an ansatz, which separates the space-temporal degrees of freedom from the internal ones. This ansatz is gauge-invariant but not Lorentz invariant. In a limit case of the ansatz, obtained through a contraction map, and corresponding to a vacuum solution, the SU(2) gauge field reduces to an operator, which is the product of the generator of a global U(1) group times a Pauli matrix. We give a geometrical interpretation of the ansatz and of the contraction map in the framework of principal fiber bundles. Then, we identify the internal degrees of freedom of the gauge field with the non-commutative coordinates of the fuzzy sphere in the fundamental representation and obtain a one qubit state.
Hidden simplicity of gauge theory amplitudes
Energy Technology Data Exchange (ETDEWEB)
Drummond, J M, E-mail: drummond@lapp.in2p3.f [LAPTH, Universite de Savoie, CNRS, B.P. 110, F-74941 Annecy-le-Vieux, Cedex (France)
2010-11-07
These notes were given as lectures at the CERN Winter School on Supergravity, Strings and Gauge Theory 2010. We describe the structure of scattering amplitudes in gauge theories, focussing on the maximally supersymmetric theory to highlight the hidden symmetries which appear. Using the Britto, Cachzo, Feng and Witten (BCFW) recursion relations we solve the tree-level S-matrix in N=4 super Yang-Mills theory and describe how it produces a sum of invariants of a large symmetry algebra. We review amplitudes in the planar theory beyond tree level, describing the connection between amplitudes and Wilson loops, and discuss the implications of the hidden symmetries.
Hidden simplicity of gauge theory amplitudes
Drummond, J. M.
2010-11-01
These notes were given as lectures at the CERN Winter School on Supergravity, Strings and Gauge Theory 2010. We describe the structure of scattering amplitudes in gauge theories, focussing on the maximally supersymmetric theory to highlight the hidden symmetries which appear. Using the Britto, Cachzo, Feng and Witten (BCFW) recursion relations we solve the tree-level S-matrix in \\ {N}=4 super Yang-Mills theory and describe how it produces a sum of invariants of a large symmetry algebra. We review amplitudes in the planar theory beyond tree level, describing the connection between amplitudes and Wilson loops, and discuss the implications of the hidden symmetries.
Gauge theory origins of supergravity causal structure
Kabat, D; Kabat, Daniel; Lifschytz, Gilad
1999-01-01
We discuss the gauge theory mechanisms which are responsible for the causal structure of the dual supergravity. For D-brane probes we show that the light cone structure and Killing horizons of supergravity emerge dynamically. They are associated with the appearance of new light degrees of freedom in the gauge theory, which we explicitly identify. This provides a picture of physics at the horizon of a black hole as seen by a D-brane probe.
Integrable Lattice Models From Gauge Theory
Witten, Edward
2016-01-01
These notes provide an introduction to recent work by Kevin Costello in which integrable lattice models of classical statistical mechanics in two dimensions are understood in terms of quantum gauge theory in four dimensions. This construction will be compared to the more familiar relationship between quantum knot invariants in three dimensions and Chern-Simons gauge theory. (Based on a Whittaker Colloquium at the University of Edinburgh and a lecture at Strings 2016 in Beijing.)
Softly Broken Supersymmetric Gauge Theories through Compactifications
Takenaga, K
1998-01-01
Effects of boundary conditions of fields for compactified space directions on the supersymmetric gauge theories are discussed. For general and possible boundary conditions the supersymmetry is explicitly broken to yield universal soft supersymmetry breaking terms, and the gauge symmetry of the theory can also be broken through the dynamics of non-integrable phases, depending on number and the representation under the gauge group of matters. The 4-dimensional supersymmetric QCD is studied as a toy model when one of the space coordinates is compactified on $S^1$.
Lattice gauge theories and spin models
Mathur, Manu; Sreeraj, T. P.
2016-10-01
The Wegner Z2 gauge theory-Z2 Ising spin model duality in (2 +1 ) dimensions is revisited and derived through a series of canonical transformations. The Kramers-Wannier duality is similarly obtained. The Wegner Z2 gauge-spin duality is directly generalized to SU(N) lattice gauge theory in (2 +1 ) dimensions to obtain the SU(N) spin model in terms of the SU(N) magnetic fields and their conjugate SU(N) electric scalar potentials. The exact and complete solutions of the Z2, U(1), SU(N) Gauss law constraints in terms of the corresponding spin or dual potential operators are given. The gauge-spin duality naturally leads to a new gauge invariant magnetic disorder operator for SU(N) lattice gauge theory which produces a magnetic vortex on the plaquette. A variational ground state of the SU(2) spin model with nearest neighbor interactions is constructed to analyze SU(2) gauge theory.
Gauge theories of gravity: the nonlinear framework
Tiemblo, A
2004-01-01
Nonlinear realizations of spacetime groups are presented as a versatile mathematical tool providing a common foundation for quite different formulations of gauge theories of gravity. We apply nonlinear realizations in particular to both the Poincar\\'e and the affine group in order to develop Poincar\\'e gauge theory (PGT) and metric-affine gravity (MAG) respectively. Regarding PGT, two alternative nonlinear treatments of the Poincar\\'e group are developed, one of them being suitable to deal with the Lagrangian and the other one with the Hamiltonian version of the same gauge theory. We argue that our Hamiltonian approach to PGT is closely related to Ashtekar's approach to gravity. On the other hand, a brief survey on MAG clarifies the role played by the metric--affine metric tensor as a Goldsone field. All gravitational quantities in fact --the metric as much as the coframes and connections-- are shown to acquire a simple gauge--theoretical interpretation in the nonlinear framework.
Quantum Critical Behaviour of Semisimple Gauge Theories
DEFF Research Database (Denmark)
Kamuk Esbensen, Jacob; Ryttov, Thomas A.; Sannino, Francesco
2016-01-01
We study the perturbative phase diagram of semi-simple fermionic gauge theories resembling the Standard Model. We investigate an $SU(N)$ gauge theory with $M$ Dirac flavors where we gauge first an $SU(M)_L$ and then an $SU(2)_L \\subset SU(M)_L$ of the original global symmetry $SU(M)_L\\times SU......(M)_R \\times U(1) $ of the theory. To avoid gauge anomalies we add lepton-like particles. At the two-loops level an intriguing phase diagram appears. We uncover phases in which one, two or three fixed points exist and discuss the associated flows of the coupling constants. We discover a phase featuring...
An alternative way to explain how non-commutativity arises in the bosonic string theory
De Andrade, M A
2015-01-01
In this work we will investigate how the non-commutativity arises into the string theory, \\textit{i.e.}, how the bosonic string theory attaches to a D3-brane in the presence of magnetic fields. In order to accomplish the proposal, we departure from the commutative two-dimensional harmonic oscillator, which after the application of the general Bopp's shifts Matrix Method, the non-commutative version of the two-dimensional harmonic oscillator is obtained. After that, this non-commutative harmonic oscillator will be mapped into the bosonic string theory in the light cone frame, which it now appears as a bosonic string theory attached to a D3-brane.
A gauge-invariant reorganization of thermal gauge theory
Energy Technology Data Exchange (ETDEWEB)
Su, Nan
2010-07-01
This dissertation is devoted to the study of thermodynamics for quantum gauge theories. The poor convergence of quantum field theory at finite temperature has been the main obstacle in the practical applications of thermal QCD for decades. In this dissertation I apply hard-thermal-loop perturbation theory, which is a gauge-invariant reorganization of the conventional perturbative expansion for quantum gauge theories to the thermodynamics of QED and Yang-Mills theory to three-loop order. For the Abelian case, I present a calculation of the free energy of a hot gas of electrons and photons by expanding in a power series in m{sub D}/T, m{sub f}/T and e{sup 2}, where m{sub D} and m{sub f} are the photon and electron thermal masses, respectively, and e is the coupling constant. I demonstrate that the hard-thermal-loop perturbation reorganization improves the convergence of the successive approximations to the QED free energy at large coupling, e {proportional_to} 2. For the non-Abelian case, I present a calculation of the free energy of a hot gas of gluons by expanding in a power series in m{sub D}/T and g{sup 2}, where m{sub D} is the gluon thermal mass and g is the coupling constant. I show that at three-loop order hard-thermal-loop perturbation theory is compatible with lattice results for the pressure, energy density, and entropy down to temperatures T {proportional_to} 2 - 3 T{sub c}. The results suggest that HTLpt provides a systematic framework that can be used to calculate static and dynamic quantities for temperatures relevant at LHC. (orig.)
Casimir effect in (2+1)dimensional noncommutative theories
Fosco, C D
2008-01-01
We study the Dirichlet Casimir effect for a complex scalar field on two noncommutative spatial coordinates plus a commutative time. To that end, we introduce Dirichlet-like boundary conditions on a curve contained in the spatial plane, in such a way that the correct commutative limit can be reached. We evaluate the resulting Casimir energy for two different curves: (a) Two parallel lines separated by a distance $L$, and (b) a circle of radius $R$. In the first case, the resulting Casimir energy agrees exactly with the one corresponding to the commutative case, regardless of the values of $L$ and of the noncommutativity scale $\\theta$, while for the latter the commutative behaviour is only recovered when $R >> \\sqrt{\\theta}$. Outside of that regime, the dependence of the energy with $R$ is substantially changed due to noncommutative corrections, becoming regular for $R \\to 0$.
Topological resolution of gauge theory singularities
Energy Technology Data Exchange (ETDEWEB)
Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo
2013-08-21
Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric S U ( 2 ) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.
Topological resolution of gauge theory singularities
Saracco, Fabio; Torroba, Gonzalo
2013-01-01
Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric SU(2) Yang-Mills-Chern-Simons theory. We calculate the one loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high energy metric (that would exhibit the singularity) and a regular singularity-free low energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.
Algebraic formulation of higher gauge theory
Zucchini, Roberto
2017-06-01
In this paper, we present a purely algebraic formulation of higher gauge theory and gauged sigma models based on the abstract theory of graded commutative algebras and their morphisms. The formulation incorporates naturally Becchi - Rouet -Stora - Tyutin (BRST) symmetry and is also suitable for Alexandrov - Kontsevich - Schwartz-Zaboronsky (AKSZ) type constructions. It is also shown that for a full-fledged Batalin-Vilkovisky formulation including ghost degrees of freedom, higher gauge and gauged sigma model fields must be viewed as internal smooth functions on the shifted tangent bundle of a space-time manifold valued in a shifted L∞-algebroid encoding symmetry. The relationship to other formulations where the L∞-algebroid arises from a higher Lie groupoid by Lie differentiation is highlighted.
Origin of gauge invariance in string theory
Horowitz, G. T.; Strominger, A.
1986-01-01
A first quantization of the space-time embedding Chi exp mu and the world-sheet metric rho of the open bosonic string. The world-sheet metric rho decouples from S-matrix elements in 26 dimensions. This formulation of the theory naturally includes 26-dimensional gauge transformations. The gauge invariance of S-matrix elements is a direct consequence of the decoupling of rho. Second quantization leads to a string field Phi(Chi exp mu, rho) with a gauge-covariant equation of motion.
Origin of gauge invariance in string theory
Horowitz, G. T.; Strominger, A.
1986-01-01
A first quantization of the space-time embedding Chi exp mu and the world-sheet metric rho of the open bosonic string. The world-sheet metric rho decouples from S-matrix elements in 26 dimensions. This formulation of the theory naturally includes 26-dimensional gauge transformations. The gauge invariance of S-matrix elements is a direct consequence of the decoupling of rho. Second quantization leads to a string field Phi(Chi exp mu, rho) with a gauge-covariant equation of motion.
Gauge theory of phase and scale
PAW\\LOWSKI, Marek
1999-01-01
Old Weyl's the idea of scale recalibration freedom and Infeld's and van der Waerden's (IW) ideas concerning geometrical interpretation of natural spinor phase gauge symmetry are discussed in the context of modern models of fundamental particle interactions. It is argued that (IW) gauge symmetry can be naturaly identified with the U(1) symmetry of the Weinberg-Salam model. It is also argued that there are no serious reasons to reject Weyl's gauge theory from consid...
Gravitational Goldstone fields from affine gauge theory
Tresguerres, R
2000-01-01
In order to facilitate the application of standard renormalization techniques, gravitation should be decribed, if possible, in pure connection formalism, as a Yang-Mills theory of a certain spacetime group, say the Poincare or the affine group. This embodies the translational as well as the linear connection. However, the coframe is not the standard Yang-Mills type gauge field of the translations, since it lacks the inhomogeneous gradient term in the gauge transformations. By explicitly restoring the "hidden" piece responsible for this behavior within the framework of nonlinear realizations, the usual geometrical interpretation of the dynamical theory becomes possible, and in addition one can avoid the metric or coframe degeneracy which would otherwise interfere with the integrations within the path integral. We claim that nonlinear realizations provide a general mathematical scheme clarifying the foundations of gauge theories of spacetime symmetries. When applied to construct the Yang-Mills theory of the aff...
String theory duals of Lifshitz-Chern-Simons gauge theories
Balasubramanian, Koushik
2011-01-01
We propose candidate gravity duals for a class of non-Abelian z=2 Lifshitz Chern-Simons (LCS) gauge theories studied by Mulligan, Kachru and Nayak. These are nonrelativistic gauge theories in 2+1 dimensions in which parity and time-reversal symmetries are explicitly broken by the presence of a Chern-Simons term. We show that these field theories can be realized as deformations of DLCQ N=4 super Yang-Mills theory. Using the holographic dictionary, we identify the bulk fields that are dual to these deformations. The geometry describing the groundstate of the non-Abelian LCS gauge theory realized here ends smoothly in the infrared region. This is a signal for confinement in the dual field theory, suggesting that non-Abelian Lifshitz gauge theories can indeed flow to strongly-coupled confining theories.
Deconstructing Noncommutativity with a Giant Fuzzy Moose
Energy Technology Data Exchange (ETDEWEB)
Adams, Allan W.
2001-12-05
We argue that the world volume theories of D-branes probing orbifolds with discrete torsion develop, in the large quiver limit, new non-commutative directions. This provides an explicit ''deconstruction'' of a wide class of noncommutative theories. This also provides insight into the physical meaning of discrete torsion and its relation to the T-dual B field. We demonstrate that the strict large quiver limit reproduces the matrix theory construction of higher-dimensional D-branes, and argue that finite ''fuzzy moose'' theories provide novel regularizations of non-commutative theories and explicit string theory realizations of gauge theories on fuzzy tori. We also comment briefly on the relation to NCOS, (2,0) and little string theories.
Deconstructing Noncommutativity with a Giant Fuzzy Moose
Adams, A; Adams, Allan; Fabinger, Michal
2002-01-01
We argue that the worldvolume theories of D-branes probing orbifolds with discrete torsion develop, in the large quiver limit, new non-commutative directions. This provides an explicit `deconstruction' of a wide class of noncommutative theories. This also provides a novel insight into the physical meaning of discrete torsion and its relation to the T-dual B field. We demonstrate that the strict large quiver limit reproduces the matrix theory construction of higher-dimensional D-branes, and argue that finite `fuzzy moose' theories provide novel regularizations of non-commutative theories and explicit string theory realizations of gauge theories on fuzzy tori. We also comment briefly on the relation to NCOS, (2,0) and little string theories.
Universally finite gravitational and gauge theories
Directory of Open Access Journals (Sweden)
Leonardo Modesto
2015-11-01
Full Text Available It is well known that standard gauge theories are renormalizable in D=4 while Einstein gravity is renormalizable in D=2. This is where the research in the field of two derivatives theories is currently standing. We hereby present a class of weakly non-local higher derivative gravitational and gauge theories universally consistent at quantum level in any spacetime dimension. These theories are unitary (ghost-free and perturbatively renormalizable. Moreover, we can always find a simple extension of these theories that is super-renormalizable or finite at quantum level in even and odd spacetime dimensions. Finally, we propose a super-renormalizable or finite theory for gravity coupled to matter laying the groundwork for a “finite standard model of particle physics” and/or a grand unified theory of all fundamental interactions.
Noncommutative Yang-Mills in IIB Matrix Model
Aoki, H; Iso, S; Kawai, H; Kitazawa, Y; Tada, T
2000-01-01
We show that twisted reduced models can be interpreted as noncommutative Yang-Mills theory. Based upon this correspondence, we obtain noncommutative Yang-Mills theory with D-brane backgrounds in IIB matrix model. We propose that IIB matrix model with D-brane backgrounds serve as a concrete definition of noncommutative Yang-Mills. We investigate D-instanton solutions as local excitations on D3-branes. When instantons overlap, their interaction can be well described in gauge theory and AdS/CFT correspondence. We show that IIB matrix model gives us the consistent potential with IIB supergravity when they are well separated.
Strong Field, Noncommutative QED
Directory of Open Access Journals (Sweden)
Anton Ilderton
2010-05-01
Full Text Available We review the effects of strong background fields in noncommutative QED. Beginning with the noncommutative Maxwell and Dirac equations, we describe how combined noncommutative and strong field effects modify the propagation of fermions and photons. We extend these studies beyond the case of constant backgrounds by giving a new and revealing interpretation of the photon dispersion relation. Considering scattering in background fields, we then show that the noncommutative photon is primarily responsible for generating deviations from strong field QED results. Finally, we propose a new method for constructing gauge invariant variables in noncommutative QED, and use it to analyse the physics of our null background fields.
One-Loop Calculations and Detailed Analysis of the Localized Non-Commutative p^{-2} U(1 Gauge Model
Directory of Open Access Journals (Sweden)
Daniel N. Blaschke
2010-05-01
Full Text Available This paper carries forward a series of articles describing our enterprise to construct a gauge equivalent for the θ-deformed non-commutative p^{-2} model originally introduced by Gurau et al. [Comm. Math. Phys. 287 (2009, 275-290]. It is shown that breaking terms of the form used by Vilar et al. [J. Phys. A: Math. Theor. 43 (2010, 135401, 13 pages] and ourselves [Eur. Phys. J. C: Part. Fields 62 (2009, 433-443] to localize the BRST covariant operator (D^2θ^2D^2^{-1} lead to difficulties concerning renormalization. The reason is that this dimensionless operator is invariant with respect to any symmetry of the model, and can be inserted to arbitrary power. In the present article we discuss explicit one-loop calculations, and analyze the mechanism the mentioned problems originate from.
String states, loops and effective actions in noncommutative field theory and matrix models
Directory of Open Access Journals (Sweden)
Harold C. Steinacker
2016-09-01
Full Text Available Refining previous work by Iso, Kawai and Kitazawa, we discuss bi-local string states as a tool for loop computations in noncommutative field theory and matrix models. Defined in terms of coherent states, they exhibit the stringy features of noncommutative field theory. This leads to a closed form for the 1-loop effective action in position space, capturing the long-range non-local UV/IR mixing for scalar fields. The formalism applies to generic fuzzy spaces. The non-locality is tamed in the maximally supersymmetric IKKT or IIB model, where it gives rise to supergravity. The linearized supergravity interactions are obtained directly in position space at one loop using string states on generic noncommutative branes.
String states, loops and effective actions in noncommutative field theory and matrix models
Energy Technology Data Exchange (ETDEWEB)
Steinacker, Harold C., E-mail: harold.steinacker@univie.ac.at
2016-09-15
Refining previous work by Iso, Kawai and Kitazawa, we discuss bi-local string states as a tool for loop computations in noncommutative field theory and matrix models. Defined in terms of coherent states, they exhibit the stringy features of noncommutative field theory. This leads to a closed form for the 1-loop effective action in position space, capturing the long-range non-local UV/IR mixing for scalar fields. The formalism applies to generic fuzzy spaces. The non-locality is tamed in the maximally supersymmetric IKKT or IIB model, where it gives rise to supergravity. The linearized supergravity interactions are obtained directly in position space at one loop using string states on generic noncommutative branes.
Curving Yang-Mills-Higgs Gauge Theories
Kotov, Alexei
2015-01-01
Established fundamental physics can be described by fields, which are maps. The source of such a map is space-time, which can be curved due to gravity. The map itself needs to be curved in its gauge field part so as to describe interaction forces like those mediated by photons and gluons. In the present article, we permit non-zero curvature also on the internal space, the target of the field map. The action functional and the symmetries are constructed in such a way that they reduce to those of standard Yang-Mills-Higgs (YMH) gauge theories precisely when the curvature on the target of the fields is turned off. For curved targets one obtains a new theory, a curved YMH gauge theory. It realizes in a mathematically consistent manner an old wish in the community: replacing structures constants by functions depending on the scalars of the theory. In addition, we provide a simple 4d toy model, where the gauge symmetry is abelian, but turning off the gauge fields, no rigid symmetry remains---another possible manife...
Local Poincaré Symmetry in Gauge Theory of Gravity
Institute of Scientific and Technical Information of China (English)
MA Jian-Feng; MA Yong-Ge
2009-01-01
It is well known that the Poincaré gauge theories of gravity do not have the structure of a standard gauge theory. Nevertheless, we show that a general form of action for the gravitational gauge fields in the gauge theory does possess local Poincaré invariance.
A gauge theory of massive spin one particles
Vyas, Vivek M
2015-01-01
An Abelian gauge theory describing dynamics of massive spin one bosons is constructed. This is achieved by appending to the Maxwell action, a gauge invariant mass term. The theory is quantised in temporal as well as Lorentz gauge, and the corresponding Hilbert spaces are constructed. In both the gauges, it is found that, the theory respects Lorentz invariance, locality, causality and unitarity.
Renormalizable supersymmetric gauge theory in six dimensions
Energy Technology Data Exchange (ETDEWEB)
Ivanov, E.A. [Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna (Russian Federation)]. E-mail: eivanov@theor.jinr.ru; Smilga, A.V. [SUBATECH, Universite de Nantes, 4 rue Alfred Kastler, BP 20722, Nantes 44307 (France)]. E-mail: smilga@subatech.in2p3.fr; Zupnik, B.M. [Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna (Russian Federation)]. E-mail: zupnik@theor.jinr.ru
2005-10-17
We construct and discuss a 6D supersymmetric gauge theory involving four derivatives in the action. The theory involves a dimensionless coupling constant and is renormalizable. At the tree level, it enjoys N=(1,0) superconformal symmetry, but the latter is broken by quantum anomaly. Our study should be considered as preparatory for seeking an extended version of this theory which would hopefully preserve conformal symmetry at the full quantum level and be ultraviolet-finite.
Recursion equations in gauge field theories
Migdal, A. A.
An approximate recursion equation is formulated, describing the scale transformation of the effective action of a gauge field. In two-dimensional space-time the equation becomes exact. In four-dimensional theories it reproduces asymptotic freedom to an accuracy of 30% in the coefficients of the β-function. In the strong-coupling region the β-function remains negative and this results in an asymptotic prison in the infrared region. Possible generalizations and applications to the quark-gluon gauge theory are discussed.
Classical Loop Actions of Gauge Theories
Armand-Ugon, D; Griego, J R; Setaro, L; Armand-Ugon, Daniel; Gambini, Rodolfo; Griego, Jorge; Setaro, Leonardo
1994-01-01
Since the first attempts to quantize Gauge Theories and Gravity in the loop representation, the problem of the determination of the corresponding classical actions has been raised. Here we propose a general procedure to determine these actions and we explicitly apply it in the case of electromagnetism. Going to the lattice we show that the electromagnetic action in terms of loops is equivalent to the Wilson action, allowing to do Montecarlo calculations in a gauge invariant way. In the continuum these actions need to be regularized and they are the natural candidates to describe the theory in a ``confining phase''.
Jarzynski's theorem for lattice gauge theory
Caselle, Michele; Nada, Alessandro; Panero, Marco; Toniato, Arianna
2016-01-01
Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a non-equilibrium transformation of a system, to the free-energy difference between two equilibrium states. In this article, we extend Jarzynski's theorem to lattice gauge theory, and present examples of applications for two challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schroedinger functional and for simulations at finite density using reweighting techniques.
Towards Noncommutative Topological Quantum Field Theory - Hodge theory for cyclic cohomology
Zois, I. P.
2014-03-01
Some years ago we initiated a program to define Noncommutative Topological Quantum Field Theory (see [1]). The motivation came both from physics and mathematics: On the one hand, as far as physics is concerned, following the well-known holography principle of 't Hooft (which in turn appears essentially as a generalisation of the Hawking formula for black hole entropy), quantum gravity should be a topological quantum field theory. On the other hand as far as mathematics is concerned, the motivation came from the idea to replace the moduli space of flat connections with the Gabai moduli space of codim-1 taut foliations for 3 dim manifolds. In most cases the later is finite and much better behaved and one might use it to define some version of Donaldson-Floer homology which, hopefully, would be easier to compute. The use of foliations brings noncommutative geometry techniques immediately into the game. The basic tools are two: Cyclic cohomology of the corresponding foliation C*-algebra and the so called "tangential cohomology" of the foliation. A necessary step towards this goal is to develop some sort of Hodge theory both for cyclic (and Hochschild) cohomology and for tangential cohomology. Here we present a method to develop a Hodge theory for cyclic and Hochschild cohomology for the corresponding C*-algebra of a foliation.
National Computational Infrastructure for Lattice Gauge Theory
Energy Technology Data Exchange (ETDEWEB)
Brower, Richard C.
2014-04-15
SciDAC-2 Project The Secret Life of Quarks: National Computational Infrastructure for Lattice Gauge Theory, from March 15, 2011 through March 14, 2012. The objective of this project is to construct the software needed to study quantum chromodynamics (QCD), the theory of the strong interactions of sub-atomic physics, and other strongly coupled gauge field theories anticipated to be of importance in the energy regime made accessible by the Large Hadron Collider (LHC). It builds upon the successful efforts of the SciDAC-1 project National Computational Infrastructure for Lattice Gauge Theory, in which a QCD Applications Programming Interface (QCD API) was developed that enables lattice gauge theorists to make effective use of a wide variety of massively parallel computers. This project serves the entire USQCD Collaboration, which consists of nearly all the high energy and nuclear physicists in the United States engaged in the numerical study of QCD and related strongly interacting quantum field theories. All software developed in it is publicly available, and can be downloaded from a link on the USQCD Collaboration web site, or directly from the github repositories with entrance linke http://usqcd-software.github.io
Higher Gauge Theory with String 2-Groups
Demessie, Getachew Alemu
2016-01-01
We give a complete and explicit description of the kinematical data of higher gauge theory on principal 2-bundles with the string 2-group model of Schommer-Pries as structure 2-group. We start with a self-contained review of the weak 2-category Bibun of Lie groupoids, bibundles and bibundle morphisms. We then construct categories internal to Bibun, which allow us to define principal 2-bundles with 2-groups internal to Bibun as structure 2-groups. Using these, we Lie-differentiate the 2-group model of the string group and we obtain the well-known string Lie 2-algebra. Generalizing the differentiation process, we find Maurer-Cartan forms leading us to higher non-abelian Deligne cohomology, encoding the kinematical data of higher gauge theory together with their (finite) gauge symmetries. We end by discussing an example of non-abelian self-dual strings in this setting.
Local subsystems in gauge theory and gravity
Donnelly, William
2016-01-01
We consider the problem of defining localized subsystems in gauge theory and gravity. Such systems are associated to spacelike hypersurfaces with boundaries and provide the natural setting for studying entanglement entropy of regions of space. We present a general formalism to associate a gauge-invariant classical phase space to a spatial slice with boundary by introducing new degrees of freedom on the boundary. In Yang-Mills theory the new degrees of freedom are a choice of gauge on the boundary, transformations of which are generated by the normal component of the nonabelian electric field. In general relativity the new degrees of freedom are the location of a codimension-2 surface and a choice of conformal normal frame. These degrees of freedom transform under a group of surface symmetries, consisting of diffeomorphisms of the codimension-2 boundary, and position-dependent linear deformations of its normal plane. We find the observables which generate these symmetries, consisting of the conformal normal me...
Gauge Field Theories, 2nd Edition
Frampton, Paul H.
2000-08-01
The first edition of Gauge Field Theories, published in 1985, quickly became widely used in universities and other institutions of higher learning around the world. Written by well-known physicist Paul Frampton, the new edition continues to offer a first-rate mathematical treatment of gauge field theories, while thoroughly updating all chapters to keep pace with developments in the field. Frampton emphasizes formalism rather than experiments and provides sufficient detail for readers wishing to do their own calculations or pursue theoretical physics research. Special features of the Second Edition include: * Improved, logical organization of the material on gauge invariance, quantization, and renormalization * Major revision of the chapter on electroweak interactions, incorporating the latest precision data and discovery of the top quark * Discussions of renormalization group and quantum chromodynamics * A completely new chapter on model building
Holography of charges in gauge theories
Julia, B L
2001-01-01
In this short review we compare the rigid Noether charges to topological gauge charges. One important extension is that one should consider each boundary component of spacetime independently. The argument that relates bulk charges to surface terms can be adapted to the perfect fluid situation where one can recognise the helicity and enstrophies as Noether charges. More generally a forcing procedure that increases for instance any Noether charge is demonstrated. In the gauge theory situation, the key idea can be summarized by one sentence: ``go to infinity and stay there''. A new variational formulation of Einstein's gravity is given that allows for local GL(D,R) invariance. The a priori indeterminacy of the Noether charges is emphasized and a covariant ansatz due to S. Silva for the surface charges of gauge theories is analysed, it replaces the (non-covariant) Regge-Teitelboim procedure.
Anatomy of One-Loop Effective Action in Noncommutative Scalar Field Theories
Kiem, Youngjai; Sato, Haru-Tada; Yee, Jung-Tay; Kiem, Youngjai; Rey, Soo-Jong; Sato, Haru-Tada; Yee, Jung-Tay
2002-01-01
One-loop effective action of noncommutative scalar field theory with cubic self-interaction is studied. Utilizing worldline formulation, both planar and nonplanar part of the effective action are computed explicitly. We find complete agreement of the result with Seiberg-Witten limit of string worldsheet computation and standard Feynman diagrammatics. We prove that, at low-energy and large noncommutativity limit, nonplanar part of the effective action is simplified enormously and is resummable into a quadratic action of scalar open Wilson line operators.
Field Theory on Noncommutative Space-Time and the Deformed Virasoro Algebra
Chaichian, Masud; Presnajder, P
2000-01-01
First we briefly describe the link between the Virasoro algebra and the free scalar field on a two-dimensional space-time given as a standard commutative cylinder, and in the Euclidean version on a complex plane. The field-theoretical model generalized then to the noncommutative cylinder leads to discrete time-evolution. Its Euclidean version is shown to be equivalent to a model on a complex $q$-plane. There is a direct link between the model on a noncommutative cylinder and the deformed Virasoro algebra suggested earlier, which describes the symmetry of the theory. The problems with the supersymmetric extension of the model on a noncommutative super-space are briefly discussed.
Topologically Massive Gauge Theory: A Lorentzian Solution
Saygili, K
2006-01-01
We obtain a lorentzian solution for the topologically massive non-abelian gauge theory on AdS space by means of a SU(1, 1) gauge transformation of the previously found abelian solution. There exists a natural scale of length which is determined by the inverse topological mass. The topological mass is proportional to the square of the gauge coupling constant. In the topologically massive electrodynamics the field strength locally determines the gauge potential up to a closed 1-form via the (anti-)self-duality equation. We introduce a transformation of the gauge potential using the dual field strength which can be identified with an abelian gauge transformation. Then we present the map from the AdS space to the pseudo-sphere including the topological mass. This is the lorentzian analog of the Hopf map. This map yields a global decomposition of the AdS space as a trivial circle bundle over the upper portion of the pseudo-sphere which is the the Hyperboloid model for the Lobachevski geometry. This leads to a redu...
T-Duality in Type II String Theory via Noncommutative Geometry and Beyond
Mathai, V.
This brief survey on how nocommutative and nonassociative geometry appears naturally in the study of T-duality in type II string theory, is essentially a transcript of my talks given at the 21st Nishinomiya-Yukawa Memorial Symposium on Theoretical Physics: Noncommutative Geometry and Quantum Spacetime in Physics, Japan, 11--15 November 2006.
Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories
Sasai, Yuya; Sasakura, Naoki
2008-02-01
Domain wall solitons are the simplest topological objects in field theories. The conventional translational symmetry in a field theory is the generator of a one-parameter family of domain wall solutions, and induces a massless moduli field which propagates along a domain wall. We study similar issues in braided noncommutative field theories possessing Hopf algebraic translational symmetries. As a concrete example, we discuss a domain wall soliton in the scalar ϕ4 braided noncommutative field theory in Lie-algebraic noncommutative space-time, [xi,xj]=2iκγijkxk (i,j,k=1,2,3), which has a Hopf algebraic translational symmetry. We first discuss the existence of a domain wall soliton in view of Derrick’s theorem, and construct explicitly a one-parameter family of solutions in perturbation of the noncommutativity parameter κ. We then find the massless moduli field which propagates on the domain wall soliton. We further extend our analysis to the general Hopf algebraic translational symmetry.
Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories
Sasai, Yuya
2007-01-01
Domain wall solitons are the simplest topological objects in field theories. The conventional translational symmetry in a field theory is the generator of a one-parameter family of domain wall solutions, and induces a massless moduli field which propagates along a domain wall. We study similar issues in braided noncommutative field theories possessing Hopf algebraic translational symmetries. As a concrete example, we discuss a domain wall soliton in the scalar phi^4 braided noncommutative field theory in Lie-algebraic noncommutative spacetime, [x^i,x^j]=2i kappa epsilon^{ijk}x_k (i,j,k=1,2,3), which has a Hopf algebraic translational symmetry. We first discuss the existence of a domain wall soliton in view of Derrick's theorem, and construct explicitly a one-parameter family of solutions in perturbation of the noncommutativity parameter kappa. We then find the massless moduli field which propagates on the domain wall soliton. We further extend our analysis to the general Hopf algebraic translational symmetry.
On the stringy nature of winding states in noncommutative thermal field theories
Arcioni, G.; Barbon, J.L.F.; Gomis, J.; Vazquez-Mozo, M.A.
2000-01-01
We show that thermal noncommutative field theories admit a version of `channel duality' reminiscent of open/closed string duality, where non-planar thermal loops can be replaced by an infinite tower of tree-level exchanges of effective fields. These effective fields resemble closed strings in three
Unification of Non-Abelian SU(N) Gauge Theory and Gravitational Gauge Theory
Institute of Scientific and Technical Information of China (English)
WU Ning
2002-01-01
In this paper, a general theory on unification of non-Abelian SU(N) gauge interactions and gravitationalinteractions is discussed. SU(N) gauge interactions and gravitational interactions are formulated on the similar basisand are unified in a semi-direct product group GSU(N). Based on this model, we can discuss unification of fundamentalinteractions of Nature.
New Dualities in Supersymmetric Chiral Gauge Theories
Energy Technology Data Exchange (ETDEWEB)
Craig, Nathaniel; /Princeton, Inst. Advanced Study /Rutgers U., Piscataway; Essig, Rouven; Hook, Anson; Torroba, Gonzalo; /Stanford U., Phys. Dept. /SLAC
2011-08-15
We analyze the phase structure of supersymmetric chiral gauge theories with gauge group SU(N), an antisymmetric, and F {le} N + 3 flavors, in the presence of a cubic superpotential. When F = N + 3 the theory flows to a superconformal fixed point in the infrared, and new dual descriptions of this theory are uncovered. The theory with odd N admits a self-dual magnetic description. For general N, we find an infinite family of magnetic dual descriptions, characterized by arbitrarily large gauge groups and additional classical global symmetries that are truncated by nonperturbative effects. The infrared dynamics of these theories are analyzed using a-maximization, which supports the claim that all these theories flow to the same superconformal fixed point. A very rich phase structure is found when the number of flavors is reduced below N + 3, including a new self-dual point, transitions from conformal to confining, and a nonperturbative instability for F {le} N. We also give examples of chiral theories with antisymmetrics that have nonchiral duals.
Topological gauge theories and group cohomology
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, R. (Rijksuniversiteit Utrecht (Netherlands). Inst. voor Theoretische Fysica); Witten, E. (Institute for Advanced Study, Princeton, NJ (USA). School of Natural Sciences)
1990-04-01
We show that three dimensional Chern-Simons gauge theories with a compact gauge group G (not necessarily connected or simply connected) can be classified by the integer cohomology group H{sup 4}(BG, Z). In a similar way, possible Wess-Zumino interactions of such a group G are classified by H{sup 3}(G, Z). The relation between three dimensional Chern-Simons gauge theory and two dimensional sigma models involves a certain natural map from H{sup 4}(BG, Z) to H{sup 3}(G, Z). We generalize this correspondence to topological 'spin' theories, which are defined on three manifolds with spin structure, and are related to what might be called Z{sub 2} graded chiral algebras (or chiral superalgebras) in two dimensions. Finally we discuss in some detail the formulation of these topological gauge theories for the special case of a finite group, establishing links with two dimensional (holomorphic) orbifold models. (orig.).
Recent advances in lattice gauge theories
Indian Academy of Sciences (India)
R V Gavai
2000-04-01
Recent progress in the ﬁeld of lattice gauge theories is brieﬂy reviewed for a nonspecialist audience. While the emphasis is on the latest and more deﬁnitive results that have emerged prior to this symposium, an effort has been made to provide them with minimal technicalities.
Compositeness Condition for Dynamically Induced Gauge Theories
Akama, K; Akama, Keiichi; Hattori, Takashi
1997-01-01
We show that the compositeness condition for the induced gauge boson in the four-fermion interaction theory actually works beyond the one-loop approximation. The next-to-leading contributions are calculated, and turn out to be reasonably suppressed, so that the leading-order approximation is justified.
Unified Gauge Field Theory and Topological Transitions
Patwardhan, A
2004-01-01
The search for a Unified description of all interactions has created many developments of mathematics and physics. The role of geometric effects in the Quantum Theory of particles and fields and spacetime has been an active topic of research. This paper attempts to obtain the conditions for a Unified Gauge Field Theory, including gravity. In the Yang Mills type of theories with compactifications from a 10 or 11 dimensional space to a spacetime of 4 dimensions, the Kaluza Klein and the Holonomy approach has been used. In the compactifications of Calabi Yau spaces and sub manifolds, the Euler number Topological Index is used to label the allowed states and the transitions. With a SU(2) or SL(2,C) connection for gravity and the U(1)*SU(2)*SU(3) or SU(5) gauge connection for the other interactions, a Unified gauge field theory is expressed in the 10 or 11 dimension space. Partition functions for the sum over all possible configurations of sub spaces labeled by the Euler number index and the Action for gauge and m...
M-theory and gauged supergravities
Roest, D
2005-01-01
We present a pedagogical discussion of the emergence of gauged supergravities from M-theory. First, a review of maximal supergravity and its global symmetries and supersymmetric solutions is given. Next, different procedures of dimensional reduction are explained: reductions over a torus, a group ma
Vanishing Vierbein in Gauge Theories of Gravitation
Jadczyk, A
1999-01-01
We discuss the problem of a degenerate vierbein in the framework of gauge theories of gravitation (thus including torsion). We discuss two examples: Hanson-Regge gravitational instanton and Einstein-Rose bridge.We argue that a region of space-time with vanishing vierbein but smooth principal connection can be, in principle, detected by scattering experiments.
M-theory and Gauged Supergravities
Roest, D.
2004-01-01
Abstract: We present a pedagogical discussion of the emergence of gauged supergravities from M-theory. First, a review of maximal supergravity and its global symmetries and supersymmetric solutions is given. Next, different procedures of dimensional reduction are explained: reductions over a torus,
M-theory and Gauged Supergravities
Roest, D.
2004-01-01
Abstract: We present a pedagogical discussion of the emergence of gauged supergravities from M-theory. First, a review of maximal supergravity and its global symmetries and supersymmetric solutions is given. Next, different procedures of dimensional reduction are explained: reductions over a torus,
Short distance properties of cascading gauge theories
Aharony, O; Yarom, A; Aharony, Ofer; Buchel, Alex; Yarom, Amos
2006-01-01
We study the short distance (large momentum) properties of correlation functions of cascading gauge theories by performing a tree-level computation in their dual gravitational background. We prove that these theories are holographically renormalizable; the correlators have only analytic ultraviolet divergences, which may be removed by appropriate local counterterms. We find that n-point correlation functions of properly normalized operators have the expected scaling in the semi-classical gravity (large N) limit: they scale as N_{eff}^{2-n} with N_{eff} proportional to ln(k/Lambda) where k is a typical momentum. Our analysis thus confirms the interpretation of the cascading gauge theories as renormalizable four-dimensional quantum field theories with an effective number of degrees of freedom which logarithmically increases with the energy.
Coset space dimensional reduction of gauge theories
Energy Technology Data Exchange (ETDEWEB)
Kapetanakis, D. (Physik Dept., Technische Univ. Muenchen, Garching (Germany)); Zoupanos, G. (CERN, Geneva (Switzerland))
1992-10-01
We review the attempts to construct unified theories defined in higher dimensions which are dimensionally reduced over coset spaces. We employ the coset space dimensional reduction scheme, which permits the detailed study of the resulting four-dimensional gauge theories. In the context of this scheme we present the difficulties and the suggested ways out in the attempts to describe the observed interactions in a realistic way. (orig.).
Loop Equations in Abelian Gauge Theories
Di Bartolo, C; Pe~na, F; Bartolo, Cayetano Di; Leal, Lorenzo; Peña, Francisco
2005-01-01
The equations obeyed by the vacuum expectation value of the Wilson loop of Abelian gauge theories are considered from the point of view of the loop-space. An approximative scheme for studying these loop-equations for lattice Maxwell theory is presented. The approximation leads to a partial difference equation in the area and length variables of the loop, and certain physically motivated ansatz is seen to reproduce the mean field results from a geometrical perspective.
Quantum topology change and large-N gauge theories
Energy Technology Data Exchange (ETDEWEB)
Albuquerque, Luiz C. de [Faculdade de Tecnologia de Sao Paulo - DEG - CEETEPS - UNESP, Praca Fernando Prestes, 30, 01124-060 Sao Paulo, SP (Brazil)]. E-mail: lclaudio@fatecsp.br; Teotonio-Sobrinho, [Universidade de Sao Paulo, Instituto de Fisica - DFMA, Caixa Postal 66318, 05315-970, Sao Paulo, SP (Brazil); Vaidya, Sachindeo [Centre for High Energy Physics, Indian Institute of Science, 560012, Bangalore (India)
2004-10-01
We study a model for dynamical localization of topology using ideas from non-commutative geometry and topology in quantum mechanics. We consider a collection X of N one-dimensional manifolds and the corresponding set of boundary conditions (self-adjoint extensions) of the Dirac operator D. The set of boundary conditions encodes the topology and is parameterized by unitary matrices g. A particular geometry is described by a spectral triple x(g)=(A{sub X},H{sub X},D(g)). We define a partition function for the sum over all g. In this model topology fluctuates but the dimension is kept fixed. We use the spectral principle to obtain an action for the set of boundary conditions. Together with invariance principles the procedure fixes the partition function for fluctuating topologies. The model has one free-parameter {beta} and it is equivalent to a one plaquette gauge theory. We argue that topology becomes localized at {beta}={infinity} for any value of N. Moreover, the system undergoes a third-order phase transition at {beta}=1 for large-N. We give a topological interpretation of the phase transition by looking how it affects the topology. (author)
Gauge theories and integrable lattice models
Witten, Edward
1989-08-01
Investigations of new knot polynomials discovered in the last few years have shown them to be intimately connected with soluble models of two dimensional lattice statistical mechanics. In this paper, these results, which in time may illuminate the whole question of why integrable lattice models exist, are reconsidered from the point of view of three dimensional gauge theory. Expectation values of Wilson lines in three dimensional Chern-Simons gauge theories can be computed by evaluating the partition functions of certain lattice models on finite graphs obtained by projecting the Wilson lines to the plane. The models in question — previously considered in both the knot theory and statistical mechanics — are IRF models in which the local Boltzmann weights are the matrix elements of braiding matrices in rational conformal field theories. These matrix elements, in turn, can be presented in three dimensional gauge theory in terms of the expectation value of a certain tetrahedral configuration of Wilson lines. This representation makes manifest a surprising symmetry of the braiding matrix elements in conformal field theory.
The shear viscosity of gauge theory plasma with chemical potentials
Benincasa, P; Naryshkin, R; Benincasa, Paolo; Buchel, Alex; Naryshkin, Roman
2007-01-01
We consider strongly coupled gauge theory plasma with conserved global charges that allow for a dual gravitational description. We study the shear viscosity of the gauge theory plasma in the presence of chemical potentials for these charges. Using gauge theory/string theory correspondence we prove that at large 't Hooft coupling the ratio of the shear viscosity to the entropy density is universal.
The shear viscosity of gauge theory plasma with chemical potentials
Benincasa, Paolo; Buchel, Alex; Naryshkin, Roman
2007-02-01
We consider strongly coupled gauge theory plasma with conserved global charges that allow for a dual gravitational description. We study the shear viscosity of the gauge theory plasma in the presence of chemical potentials for these charges. Using gauge theory/string theory correspondence we prove that at large 't Hooft coupling the ratio of the shear viscosity to the entropy density is universal.
Quiver gauge theories and integrable lattice models
Yagi, Junya
2015-01-01
We discuss connections between certain classes of supersymmetric quiver gauge theories and integrable lattice models from the point of view of topological quantum field theories (TQFTs). The relevant classes include 4d $\\mathcal{N} = 1$ theories known as brane box and brane tilling models, 3d $\\mathcal{N} = 2$ and 2d $\\mathcal{N} = (2,2)$ theories obtained from them by compactification, and 2d $\\mathcal{N} = (0,2)$ theories closely related to these theories. We argue that their supersymmetric indices carry structures of TQFTs equipped with line operators, and as a consequence, are equal to the partition functions of lattice models. The integrability of these models follows from the existence of extra dimension in the TQFTs, which emerges after the theories are embedded in M-theory. The Yang-Baxter equation expresses the invariance of supersymmetric indices under Seiberg duality and its lower-dimensional analogs.
Quiver gauge theories and integrable lattice models
Energy Technology Data Exchange (ETDEWEB)
Yagi, Junya [International School for Advanced Studies (SISSA),via Bonomea 265, 34136 Trieste (Italy); INFN - Sezione di Trieste,via Valerio 2, 34149 Trieste (Italy)
2015-10-09
We discuss connections between certain classes of supersymmetric quiver gauge theories and integrable lattice models from the point of view of topological quantum field theories (TQFTs). The relevant classes include 4d N=1 theories known as brane box and brane tilling models, 3d N=2 and 2d N=(2,2) theories obtained from them by compactification, and 2d N=(0,2) theories closely related to these theories. We argue that their supersymmetric indices carry structures of TQFTs equipped with line operators, and as a consequence, are equal to the partition functions of lattice models. The integrability of these models follows from the existence of extra dimension in the TQFTs, which emerges after the theories are embedded in M-theory. The Yang-Baxter equation expresses the invariance of supersymmetric indices under Seiberg duality and its lower-dimensional analogs.
Workshop on Non-Associative & Non-Commutative Algebra and Operator Theory
Molina, Mercedes
2016-01-01
Presenting the collaborations of over thirty international experts in the latest developments in pure and applied mathematics, this volume serves as an anthology of research with a common basis in algebra, functional analysis and their applications. Special attention is devoted to non-commutative algebras, non-associative algebras, operator theory and ring and module theory. These themes are relevant in research and development in coding theory, cryptography and quantum mechanics. The topics in this volume were presented at the Workshop on Non-Associative & Non-Commutative Algebra and Operator Theory, held May 23—25, 2014 at Cheikh Anta Diop University in Dakar, Senegal in honor of Professor Amin Kaidi. The workshop was hosted by the university's Laboratory of Algebra, Cryptology, Algebraic Geometry and Applications, in cooperation with the University of Almería and the University of Málaga. Dr. Kaidi's work focuses on non-associative rings and algebras, operator theory and functional analysis, and he...
Planar Zeros in Gauge Theories and Gravity
Jimenez, Diego Medrano; Vazquez-Mozo, Miguel A
2016-01-01
Planar zeros are studied in the context of the five-point scattering amplitude for gauge bosons and gravitons. In the case of gauge theories, it is found that planar zeros are determined by an algebraic curve in the projective plane spanned by the three stereographic coordinates labelling the direction of the outgoing momenta. This curve depends on the values of six independent color structures. Considering the gauge group SU(N) with N=2,3,5 and fixed color indices, the class of curves obtained gets broader by increasing the rank of the group. For the five-graviton scattering, on the other hand, we show that the amplitude vanishes whenever the process is planar, without imposing further kinematic conditions. A rationale for this result is provided using color-kinematics duality.
Noncommutative Symmetries and Gravity
Aschieri, P
2006-01-01
Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now star-multiplied. Consistently, spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms. Their deformed Lie algebra structure and that of infinitesimal Poincare' transformations is defined and explicitly constructed. This allows to construct a noncommutative theory of gravity.
Konisi, G; Mäki, Z; Nakahara, M
1999-01-01
The left-right symmetric model (LRSM) with gauge group $SU(2)_{L} \\times SU(2)_{R} \\times U(1)_{B-L}$ is reconstructed from the geometric formulation of gauge theory in $M_4 \\times Z_2 \\times Z_2$ where $M_4$ is the four-dimensional Minkowski space and $Z_2 \\times Z_2$ the discrete space with four points. The geometrical structure of this model becomes clearer compared with other works based on noncommutative geometry. As a result, the Yukawa coupling terms and the Higgs potential are derived in more restricted forms than in the standard LRSM.
Entanglement in Weakly Coupled Lattice Gauge Theories
Radicevic, Djordje
2015-01-01
We present a direct lattice gauge theory computation that, without using dualities, demonstrates that the entanglement entropy of Yang-Mills theories with arbitrary gauge group $G$ contains a generic logarithmic term at sufficiently weak coupling $e$. In two spatial dimensions, for a region of linear size $r$, this term equals $\\frac{1}{2} \\dim(G) \\log\\left(e^2 r\\right)$ and it dominates the universal part of the entanglement entropy. Such logarithmic terms arise from the entanglement of the softest mode in the entangling region with the environment. For Maxwell theory in two spatial dimensions, our results agree with those obtained by dualizing to a compact scalar with spontaneous symmetry breaking.
Integrability in N=2 superconformal gauge theorie
Energy Technology Data Exchange (ETDEWEB)
Pomoni, Elli [Deutsches Elektronen-Synchrotron DESY, Hamburg (Germany). Theory Group; National Technical Univ. of Athens (Greece). Physics Div.
2013-10-15
Any N=2 superconformal gauge theory (including N=4 SYM) contains a set of local operators made only out of fields in the N=2 vector multiplet that is closed under renormalization to all loops, namely the SU(2,1 vertical stroke 2) sector. For planar N=4 SYM the spectrum of local operators can be obtained by mapping the problem to an integrable model (a spin chain in perturbation theory), in principle for any value of the coupling constant. We present a diagrammatic argument that for any planar N=2 superconformal gauge theory the SU(2,1 vertical stroke 2) Hamiltonian acting on infinite spin chains is identical to all loops to that of N=4 SYM, up to a redefinition of the coupling constant. Thus, this sector is integrable and anomalous dimensions can be, in principle, read off from the N=4 ones up to this redefinition.
The Gribov problem in noncommutative QED
Canfora, Fabrizio; Kurkov, Maxim A.; Rosa, Luigi; Vitale, Patrizia
2016-01-01
It is shown that in the noncommutative version of QED (NCQED) Gribov copies induced by the noncommutativity of space-time appear in the Landau gauge. This is a genuine effect of noncommutative geometry which disappears when the noncommutative parameter vanishes.
Noncommutative spectral geometry, dissipation and the origin of quantization
Sakellariadou, Mairi; Vitiello, Giuseppe
2012-01-01
We present a physical interpretation of the doubling of the algebra, which is the basic ingredient of the noncommutative spectral geometry, developed by Connes and collaborators as an approach to unification. We discuss its connection to dissipation and to the gauge structure of the theory. We then argue, following 't Hooft's conjecture, that noncommutative spectral geometry classical construction carries implicit in its feature of the doubling of the algebra the seeds of quantization.
Gravity, Gauge Theories and Geometric Algebra
Lasenby, A; Gull, S F; Lasenby, Anthony; Doran, Chris; Gull, Stephen
1998-01-01
A new gauge theory of gravity is presented. The theory is constructed in a flat background spacetime and employs gauge fields to ensure that all relations between physical quantities are independent of the positions and orientations of the matter fields. In this manner all properties of the background spacetime are removed from physics, and what remains are a set of `intrinsic' relations between physical fields. The properties of the gravitational gauge fields are derived from both classical and quantum viewpoints. Field equations are then derived from an action principle, and consistency with the minimal coupling procedure selects an action that is unique up to the possible inclusion of a cosmological constant. This in turn singles out a unique form of spin-torsion interaction. A new method for solving the field equations is outlined and applied to the case of a time-dependent, spherically-symmetric perfect fluid. A gauge is found which reduces the physics to a set of essentially Newtonian equations. These e...
Conformal field theory with gauge symmetry
Ueno, Kenji
2008-01-01
This book presents a systematic approach to conformal field theory with gauge symmetry from the point of view of complex algebraic geometry. After presenting the basic facts of the theory of compact Riemann surfaces and the representation theory of affine Lie algebras in Chapters 1 and 2, conformal blocks for pointed Riemann surfaces with coordinates are constructed in Chapter 3. In Chapter 4 the sheaf of conformal blocks associated to a family of pointed Riemann surfaces with coordinates is constructed, and in Chapter 5 it is shown that this sheaf supports a projective flat connection-one of
Noncommuting observables in quantum detection and estimation theory
Helstrom, C. W.
1972-01-01
Basing decisions and estimates on simultaneous approximate measurements of noncommuting observables in a quantum receiver is shown to be equivalent to measuring commuting projection operators on a larger Hilbert space than that of the receiver itself. The quantum-mechanical Cramer-Rao inequalities derived from right logarithmic derivatives and symmetrized logarithmic derivatives of the density operator are compared, and it is shown that the latter give superior lower bounds on the error variances of individual unbiased estimates of arrival time and carrier frequency of a coherent signal. For a suitably weighted sum of the error variances of simultaneous estimates of these, the former yield the superior lower bound under some conditions.
Light-Front Quantization of Gauge Theories
Energy Technology Data Exchange (ETDEWEB)
Brodskey, Stanley
2002-12-01
Light-front wavefunctions provide a frame-independent representation of hadrons in terms of their physical quark and gluon degrees of freedom. The light-front Hamiltonian formalism provides new nonperturbative methods for obtaining the QCD spectrum and eigensolutions, including resolvant methods, variational techniques, and discretized light-front quantization. A new method for quantizing gauge theories in light-cone gauge using Dirac brackets to implement constraints is presented. In the case of the electroweak theory, this method of light-front quantization leads to a unitary and renormalizable theory of massive gauge particles, automatically incorporating the Lorentz and 't Hooft conditions as well as the Goldstone boson equivalence theorem. Spontaneous symmetry breaking is represented by the appearance of zero modes of the Higgs field leaving the light-front vacuum equal to the perturbative vacuum. I also discuss an ''event amplitude generator'' for automatically computing renormalized amplitudes in perturbation theory. The importance of final-state interactions for the interpretation of diffraction, shadowing, and single-spin asymmetries in inclusive reactions such as deep inelastic lepton-hadron scattering is emphasized.
Large-Nc Gauge Theory and Chiral Random Matrix Theory
Hanada, Masanori; Lee, Jong-Wan; Yamada, Norikazu
Effective theory approaches and the large-Nc limit are useful for studying the strongly coupled gauge theories. In this talk we consider how the chiral random matrix theory (χRMT) can be used in the study of large-Nc gauge theories. It turns out the parameter regions, in which each of these two approaches are valid, are different. Still, however, we show that the breakdown of chiral symmetry can be detected by combining the large-Nc argument and the χRMT with some cares. As a demonstration, we numerically study the four dimensional SU(Nc) gauge theory with Nf = 2 heavy adjoint fermions on a 24 lattice by using Monte-Carlo simulations, which is related to the infinite volume lattice through the Eguchi-Kawai equivalence.
Analytic Variational Investigation of Euclidean SU(3) Gauge Theory
Dass, N D H
1993-01-01
Analytic variational techniques for lattice gauge theories based on the Rayleigh-Ritz(RR) method were previously developed for euclidean SU(2) gauge theories in 3 and 4 dimensions. Their extensions to SU(3) gauge theory including applications to correlation functions and mass gaps are presented here.
Planar Gravitational Corrections For Supersymmetric Gauge Theories
Dijkgraaf, R; Ooguri, H; Vafa, C; Zanon, D
2004-01-01
In this paper we discuss the contribution of planar diagrams to gravitational F-terms for N=1 supersymmetric gauge theories admitting a large N description. We show how the planar diagrams lead to a universal contribution at the extremum of the glueball superpotential, leaving only the genus one contributions, as was previously conjectured. We also discuss the physical meaning of gravitational F-terms.
Chiral symmetry and lattice gauge theory
Creutz, M
1994-01-01
I review the problem of formulating chiral symmetry in lattice gauge theory. I discuss recent approaches involving an infinite tower of additional heavy states to absorb Fermion doublers. For hadronic physics this provides a natural scheme for taking quark masses to zero without requiring a precise tuning of parameters. A mirror Fermion variation provides a possible way of extending the picture to chirally coupled light Fermions. Talk presented at "Quark Confinement and the Hadron Spectrum," Como, Italy, 20-24 June 1994.
Constraining differential renormalization in abelian gauge theories
del Águila, F; Tapia, R M; Pérez-Victoria, M
1998-01-01
We present a procedure of differential renormalization at the one loop level which avoids introducing unnecessary renormalization constants and automatically preserves abelian gauge invariance. The amplitudes are expressed in terms of a basis of singular functions. The local terms appearing in the renormalization of these functions are determined by requiring consistency with the propagator equation. Previous results in abelian theories, with and without supersymmetry, are discussed in this context.
Gauge theories with non-trivial backgrounds
Binosi, Daniele
2014-01-01
We review our most recent results in formulating gauge theories in the presence of a background field on the basis of symmetry arguments only. In particular we show how one can gain full control over the dependence on the background field of the effective action, and how the so-called background field method emerges naturally from the requirement of invariance under the BRST and antiBRST symmetries.
Quantum gravity from noncommutative spacetime
Energy Technology Data Exchange (ETDEWEB)
Lee, Jungjai [Daejin University, Pocheon (Korea, Republic of); Yang, Hyunseok [Korea Institute for Advanced Study, Seoul (Korea, Republic of)
2014-12-15
We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative *-algebra) of quantum gravity.
Dark matter in the hidden gauge theory
Yamanaka, Nodoka; Gongyo, Shinya; Iida, Hideaki
2014-01-01
The cosmological scenario of the dark matter generated in the hidden gauge theory based on the grand unification is discussed. It is found that the stability of the dark matter halo of our Galaxy and the cosmic ray observation constrain, respectively, the dark matter mass and the unification scale between the standard model and the hidden gauge theory sectors. To obtain a phenomenologically consistent thermal evolution, the entropy of the standard model sector needs to be increased. We therefore propose a scenario where the mini-inflation is induced from the potential coupled to the Standard model sector, in particular the Higgs sector. This scenario makes consistent the current dark matter density as well as the baryon-to-photon ratio for the case of pion dark matter. For the glueball or heavy pion of hidden gauge theory, an additional mini-inflation in the standard model sector before the leptogenesis is required. We also propose the possibility to confirm this scenario by known prospective experimental app...
Dynamical symmetry breaking in chiral gauge theories with direct-product gauge groups
Shi, Yan-Liang; Shrock, Robert
2016-09-01
We analyze patterns of dynamical symmetry breaking in strongly coupled chiral gauge theories with direct-product gauge groups G . If the gauge coupling for a factor group Gi⊂G becomes sufficiently strong, it can produce bilinear fermion condensates that break the Gi symmetry itself and/or break other gauge symmetries Gj⊂G . Our comparative study of a number of strongly coupled direct-product chiral gauge theories elucidates how the patterns of symmetry breaking depend on the structure of G and on the relative sizes of the gauge couplings corresponding to factor groups in the direct product.
Dynamical Symmetry Breaking in Chiral Gauge Theories with Direct-Product Gauge Groups
Shi, Yan-Liang
2016-01-01
We analyze patterns of dynamical symmetry breaking in strongly coupled chiral gauge theories with direct-product gauge groups $G$. If the gauge coupling for a factor group $G_i \\subset G$ becomes sufficiently strong, it can produce bilinear fermion condensates that break the $G_i$ symmetry itself and/or break other gauge symmetries $G_j \\subset G$. Our comparative study of a number of strongly coupled direct-product chiral gauge theories elucidates how the patterns of symmetry breaking depend on the structure of $G$ and on the relative sizes of the gauge couplings corresponding to factor groups in the direct product.
N=2 gauge theories and degenerate fields of Toda theory
Kanno, Shoichi; Shiba, Shotaro; Tachikawa, Yuji
2009-01-01
We discuss the correspondence between degenerate fields of the W_N algebra and punctures of Gaiotto's description of the Seiberg-Witten curve of N=2 superconformal gauge theories. Namely, we find that the type of degenerate fields of the W_N algebra, with null states at level one, is classified by Young diagrams with N boxes, and that the singular behavior of the Seiberg-Witten curve near the puncture agrees with that of W_N generators. We also find how to translate mass parameters of the gauge theory to the momenta of the Toda theory.
Nonequilibrium formulation of abelian gauge theories
Energy Technology Data Exchange (ETDEWEB)
Zoeller, Thorsten
2013-09-01
This work is about a formulation of abelian gauge theories out-of-equilibrium. In contrast to thermal equilibrium, systems out-of-equilibrium are not constant in time, and the interesting questions in such systems refer to time evolution problems. After a short introduction to quantum electrodynamics (QED), the two-particle irreducible (2PI) effective action is introduced as an essential technique for the study of quantum field theories out-of-equilibrium. The equations of motion (EOMs) for the propagators of the theory are then derived from it. It follows a discussion of the physical degrees of freedom (DOFs) of the theory, in particular with respect to the photons, since in covariant formulations of gauge theories unphysical DOFs are necessarily contained. After that the EOMs for the photon propagator are examined more closely. It turns out that they are structurally complicated, and a reformulation of the equations is presented which for the untruncated theory leads to an essential structural simplification of the EOMs. After providing the initial conditions which are necessary in order to solve the EOMs, the free photon EOMs are solved with the help of the reformulated equations. It turns out that the solutions diverge in time, i.e. they are secular. This is a manifestation of the fact that gauge theories contain unphysical DOFs. It is reasoned that these secularities exist only in the free case and are therefore ''artificial''. It is however emphasized that they may not be a problem in principle, but certainly are in practice, in particular for the numerical solution of the EOMs. Further, the origin of the secularities, for which there exists an illustrative explanation, is discussed in more detail. Another characteristic feature of 2PI formulations of gauge theories is the fact that quantities calculated from approximations of the 2PI effective action, which are gauge invariant in the exact theory as well as in an approximated theory at
Gauge theory and defects in solids
Edelen, DGB
2012-01-01
This new series Mechanics and Physics of Discrete Systems aims to provide a coherent picture of the modern development of discrete physical systems. Each volume will offer an orderly perspective of disciplines such as molecular dynamics, crystal mechanics and/or physics, dislocation, etc. Emphasized in particular are the fundamentals of mechanics and physics that play an essential role in engineering applications.Volume 1, Gauge Theory and Defects in Solids, presents a detailed development of a rational theory of the dynamics of defects and damage in solids. Solutions to field e
Exceptional Confinement in G(2) Gauge Theory
Holland, K; Pepé, M; Wiese, U J
2003-01-01
We study theories with the exceptional gauge group G(2). The 14 adjoint "gluons" of a G(2) gauge theory transform as {3}, {3bar} and {8} under the subgroup SU(3), and hence have the color quantum numbers of ordinary quarks, anti-quarks and gluons in QCD. Since G(2) has a trivial center, a "quark" in the {7} representation of G(2) can be screened by "gluons". As a result, in G(2) Yang-Mills theory the string between a pair of static "quarks" can break. In G(2) QCD there is a hybrid consisting of one "quark" and three "gluons". In supersymmetric G(2) Yang-Mills theory with a {14} Majorana "gluino" the chiral symmetry is Z(4)_\\chi. Chiral symmetry breaking gives rise to distinct confined phases separated by confined-confined domain walls. A scalar Higgs field in the {7} representation breaks G(2) to SU(3) and allows us to interpolate between theories with exceptional and ordinary confinement. We also present strong coupling lattice calculations that reveal basic features of G(2) confinement. Just as in QCD, wher...
Gravitons, Inflatons, Twisted Bits: A Noncommutative Bestiary
Pearson, J
2004-01-01
In this work, we examine ideas connected with the noncommutativity of spacetime and its realizations in string theory. Motivated by Matrix Theory and the AdS-CFT correspondence, we propose a survey of selected noncommutative objects, assessing their implications for inflation, gauge theory duals, and solvable backgrounds. Our initial pair of examples, related to the Myers effect, incorporate elements of so-called “giant graviton” behavior. In the first, the formation of an extended, supersymmetry-restoring domain wall from point-brane sources in a flux background is related to a nonperturbative process of brane-flux annihilation. In the second, we reexamine these phenomena from a cosmological vantage, investigating the prospect of slow- roll inflation in the noncommutative configuration space of multiple d-branes. For our third and final example, we turn to the solvable pp-wave background, outlining a combinatorial, permutation-based approach to string physics which interpolates between ga...
Flavour singlets in gauge theory as Permutations
Kimura, Yusuke; Suzuki, Ryo
2016-01-01
Gauge-invariant operators can be specified by equivalence classes of permutations. We develop this idea concretely for the singlets of the flavour group $SO(N_f)$ in $U(N_c)$ gauge theory by using Gelfand pairs and Schur-Weyl duality. The singlet operators, when specialised at $N_f =6$, belong to the scalar sector of ${\\cal N}=4$ SYM. A simple formula is given for the two-point functions in the free field limit of $g_{YM}^2 =0$. The free two-point functions are shown to be equal to the partition function on a 2-complex with boundaries and a defect, in a topological field theory of permutations. The permutation equivalence classes are Fourier transformed to a representation basis which is orthogonal for the two-point functions at finite $N_c , N_f$. Counting formulae for the gauge-invariant operators are described. The one-loop mixing matrix is derived as a linear operator on the permutation equivalence classes.
Coproduct and star product in field theories on Lie-algebra noncommutative space-times
Amelino-Camelia, Giovanni; Arzano, Michele
2002-04-01
We propose a new approach to field theory on κ-Minkowski noncommutative space-time, a popular example of Lie-algebra space-time. Our proposal is essentially based on the introduction of a star product, a technique which is proving to be very fruitful in analogous studies of canonical noncommutative space-times, such as the ones recently found to play a role in the description of certain string-theory backgrounds. We find to be incorrect the expectation, previously reported in the literature, that the lack of symmetry of the κ-Poincaré coproduct should lead to interaction vertices that are not symmetric under exchanges of the momenta of identical particles entering the relevant processes. We show that in κ-Minkowski the coproduct and the star product must indeed treat momenta in a nonsymmetric way, but the overall structure of interaction vertices is symmetric under exchange of identical particles. We also show that in κ-Minkowski field theories it is convenient to introduce the concepts of ``planar'' and ``nonplanar'' Feynman loop diagrams, again in close analogy with the corresponding concepts previously introduced in the study of field theories in canonical noncommutative space-times.
Matrix product states for gauge field theories.
Buyens, Boye; Haegeman, Jutho; Van Acoleyen, Karel; Verschelde, Henri; Verstraete, Frank
2014-08-29
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study (1+1)-dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground-state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study full quantum nonequilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field.
Double Compactified d = 11 Supermembrane Dual as a Non-Commutative Super-Maxwell Theory
Martin, I; Restuccia, A
2000-01-01
The physical hamiltonian of the double compactified D=11 supermembrane dual with non trivial wrapping is explicitly obtained. It contains cubic and quartic interacting terms. It exactly agrees with the hamiltonian formulation of non-commutative super-Maxwell theory on the world volume, minimally coupled to seven scalars fields corresponding to the transverse coordinates to the brane. The non commutative star product is intrinsically obtained from the simplectic 2-form defined by the minimal configuration of the hamiltonian, that is by the pull-back to the world volume of the canonical conection 1-form on the Hopf fibring over $CP_n$. The constraint generating the area preserving diffeomorphism is reformulated as the Gauss constraint of the non-commutative super-Maxwell theory.
Higher-dimensional gauge theories from string theory
Energy Technology Data Exchange (ETDEWEB)
Tomasiello, Alessandro [Dipartimento di Fisica, Universita di Milano-Bicocca, Milano (Italy); INFN, Sezione di Milano-Bicocca, Milano (Italy)
2016-04-15
We review some recent developments regarding supersymmetric field theories in six and five dimensions. In particular, we will describe the classification of supersymmetric six-dimensional theories with a holographic IIA dual; they are ''linear quivers'' consisting of chains of many SU (or SO/Sp) gauge groups connected by hypermultiplets and tensor multiplets. We will also describe the wider classification of supersymmetric six-dimensional theories that can be engineered in F-theory; these are also chains, but they include exceptional gauge groups and copies of a more exotic ''E-string'' theory with a single tensor and E{sub 8} flavor symmetry. Finally we discuss some properties of these theories under compactification to lower dimensions. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Bassetto, A; Torrielli, A; Vian, F
2005-01-01
We present an investigation on the invariance properties of noncommutative Yang-Mills theory in two dimensions under area preserving diffeomorphisms. Stimulated by recent remarks by Ambjorn, Dubin and Makeenko who found a breaking of such an invariance, we confirm both on a fairly general ground and by means of perturbative analytical and numerical calculations that indeed invariance under area preserving diffeomorphisms is lost. However a remnant survives, namely invariance under linear unimodular tranformations.
Supersymmetry algebra and BPS states of super Yang-Mills theories on noncommutative tori
Konechny, Anatoly; Schwarz, Albert
1999-04-01
We consider 10-dimensional super Yang-Mills theory with topological terms compactified on a noncommutative torus. We calculate supersymmetry algebra and derive BPS energy spectra from it. The cases of d-dimensional tori with d=2,3,4 are considered in full detail. SO(d,d,Z)-invariance of the BPS spectrum and relation of new results to the previous work in this direction are discussed.
N=1 Supersymmetry, Deconstruction, and Bosonic Gauge Theories
Dijkgraaf, R; Dijkgraaf, Robbert; Vafa, Cumrun
2003-01-01
We show how the full holomorphic geometry of local Calabi-Yau threefold compactifications with N=1 supersymmetry can be obtained from matrix models. In particular for the conifold geometry we relate F-terms to the general amplitudes of c=1 non-critical bosonic string theory, and express them in a quiver or, equivalently, super matrix model. Moreover we relate, by deconstruction, the uncompactified c=1 theory to the six-dimensional conformal (2,0) theory. Furthermore, we show how we can use the idea of deconstruction to connect 4+k dimensional supersymmetric gauge theories to a k-dimensional internal bosonic gauge theory, generalizing the relation between 4d theories and matrix models. Examples of such bosonic systems include unitary matrix models and gauged matrix quantum mechanics, which deconstruct 5-dimensional supersymmetric gauge theories, and Chern-Simons gauge theories, which deconstruct gauge theories living on branes wrapped over cycles in Calabi-Yau threefolds.
Strong Coupling Gauge Theories in LHC ERA
Fukaya, H.; Harada, M.; Tanabashi, M.; Yamawaki, K.
2011-01-01
AdS/QCD, light-front holography, and the nonperturbative running coupling / Stanley J. Brodsky, Guy de Teramond and Alexandre Deur -- New results on non-abelian vortices - Further insights into monopole, vortex and confinement / K. Konishi -- Study on exotic hadrons at B-factories / Toru Iijima -- Cold compressed baryonic matter with hidden local symmetry and holography / Mannque Rho -- Aspects of baryons in holographic QCD / T. Sakai -- Nuclear force from string theory / K. Hashimoto -- Integrating out holographic QCD back to hidden local symmetry / Masayasu Harada, Shinya Matsuzaki and Koichi Yamawaki -- Holographic heavy quarks and the giant Polyakov loop / Gianluca Grignani, Joanna Karczmarek and Gordon W. Semenoff -- Effect of vector-axial-vector mixing to dilepton spectrum in hot and/or dense matter / Masayasu Harada and Chihiro Sasaki -- Infrared behavior of ghost and gluon propagators compatible with color confinement in Yang-Mills theory with the Gribov horizon / Kei-Ichi Kondo -- Chiral symmetry breaking on the lattice / Hidenori Fukaya [for JLQCD and TWQCD collaborations] -- Gauge-Higgs unification: Stable Higgs bosons as cold dark matter / Yutaka Hosotani -- The limits of custodial symmetry / R. Sekhar Chivukula ... [et al.] -- Higgs searches at the tevatron / Kazuhiro Yamamoto [for the CDF and D[symbol] collaborations] -- The top triangle moose / R. S. Chivukula ... [et al.] -- Conformal phase transition in QCD like theories and beyond / V. A. Miransky -- Gauge-Higgs unification at LHC / Nobuhito Maru and Nobuchika Okada -- W[symbol]W[symbol] scattering in Higgsless models: Identifying better effective theories / Alexander S. Belyaev ... [et al.] -- Holographic estimate of Muon g - 2 / Deog Ki Hong -- Gauge-Higgs dark matter / T. Yamashita -- Topological and curvature effects in a multi-fermion interaction model / T. Inagaki and M. Hayashi -- A model of soft mass generation / J. Hosek -- TeV physics and conformality / Thomas Appelquist -- Conformal
Four-Fermion Limit of Gauge-Yukawa Theories
DEFF Research Database (Denmark)
Krog, Jens; Mojaza, Matin; Sannino, Francesco
2015-01-01
perturbative gauge-Yukawa theories can have a strongly coupled limit at high-energy, that can be mapped into a four-fermion theory. Interestingly, we are able to precisely carve out a region of the perturbative parameter space supporting such a composite limit. This has interesting implications on our current......We elucidate and extend the conditions that map gauge-Yukawa theories at low energies into time-honoured gauged four-fermion interactions at high energies. These compositeness conditions permit to investigate theories of composite dynamics through gauge-Yukawa theories. Here we investigate whether...... view on models of particle physics. As a template model we use an $SU(N_C)$ gauge theory with $N_F$ Dirac fermions transforming according to the fundamental representation of the gauge group. The fermions further interact with a gauge singlet complex $N_F\\times N_F$ Higgs that ceases to be a physical...
Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space
Energy Technology Data Exchange (ETDEWEB)
Zahn, J.W.
2006-12-15
We study field theories on the noncommutative Minkowski space with noncommuting time. The focus lies on dispersion relations in quantized interacting models in the Yang-Feldman formalism. In particular, we compute the two-point correlation function of the field strength in noncommutative quantum electrodynamics to second order. At this, we take into account the covariant coordinates that allow the construction of local gauge invariant quantities (observables). It turns out that this does not remove the well-known severe infrared problem, as one might have hoped. Instead, things become worse, since nonlocal divergences appear. We also show that these cancel in a supersymmetric version of the theory if the covariant coordinates are adjusted accordingly. Furthermore, we study the {phi}{sup 3} and the Wess-Zumino model and show that the distortion of the dispersion relations is moderate for parameters typical for the Higgs field. We also discuss the formulation of gauge theories on noncommutative spaces and study classical electrodynamics on the noncommutative Minkowski space using covariant coordinates. In particular, we compute the change of the speed of light due to nonlinear effects in the presence of a background field. Finally, we examine the so-called twist approach to quantum field theory on the noncommutative Minkowski space and point out some conceptual problems of this approach. (orig.)
On the Structure of Quantum Gauge Theories with External Fields
Falkenberg, S; Lavrov, P M; Moshin, P
1998-01-01
We consider generating functionals of Green's functions with external fields in the framework of BV and BLT quantization schemes for general gauge theories. The corresponding Ward identities are obtained, and the gauge dependence is studied.
The Gribov ambiguity for maximal abelian and center gauges in SU(2) lattice gauge theory
Energy Technology Data Exchange (ETDEWEB)
Stack, John D.; Tucker, William W
2001-03-01
We present results for the fundamental string tension in SU(2) lattice gauge theory after projection to maximal abelian and direct maximal center gauges. We generate 20 Gribov copies/configuration. Abelian and center projected string tensions slowly decrease as higher values of the gauge functionals are reached.
Noncommutative Algebraic Equations and Noncommutative Eigenvalue Problem
Schwarz, A
2000-01-01
We analyze the perturbation series for noncommutative eigenvalue problem $AX=X\\lambda$ where $\\lambda$ is an element of a noncommutative ring, $ A$ is a matrix and $X$ is a column vector with entries from this ring. As a corollary we obtain a theorem about the structure of perturbation series for Tr $x^r$ where $x$ is a solution of noncommutative algebraic equation (for $r=1$ this theorem was proved by Aschieri, Brace, Morariu, and Zumino, hep-th/0003228, and used to study Born-Infeld lagrangian for the gauge group $U(1)^k$).
Exceptional Deconfinement in G(2) Gauge Theory
Pepé, M
2006-01-01
The Z(N) center symmetry plays an important role in the deconfinement phase transition of SU(N) Yang-Mills theory at finite temperature. The exceptional group G(2) is the smallest simply connected gauge group with a trivial center. Hence, there is no symmetry reason why the low- and high-temperature regimes in G(2) Yang-Mills theory should be separated by a phase transition. Still, we present numerical evidence for the presence of a first order deconfinement phase transition at finite temperature. Via the Higgs mechanism, G(2) breaks to its SU(3) subgroup when a scalar field in the fundamental {7} representation acquires a vacuum expectation value v. Varying v we investigate how the G(2) deconfinement transition is related to the one in SU(3) Yang-Mills theory. Interestingly, the two transitions seem to be disconnected. We also discuss a potential dynamical mechanism that may explain this behavior.
2d Gauge Theories and Generalized Geometry
Kotov, Alexei; Strobl, Thomas
2014-01-01
We show that in the context of two-dimensional sigma models minimal coupling of an ordinary rigid symmetry Lie algebra $\\mathfrak{g}$ leads naturally to the appearance of the "generalized tangent bundle" $\\mathbb{T}M \\equiv TM \\oplus T^*M$ by means of composite fields. Gauge transformations of the composite fields follow the Courant bracket, closing upon the choice of a Dirac structure $D \\subset \\mathbb{T}M$ (or, more generally, the choide of a "small Dirac-Rinehart sheaf" $\\cal{D}$), in which the fields as well as the symmetry parameters are to take values. In these new variables, the gauge theory takes the form of a (non-topological) Dirac sigma model, which is applicable in a more general context and proves to be universal in two space-time dimensions: A gauging of $\\mathfrak{g}$ of a standard sigma model with Wess-Zumino term exists, \\emph{iff} there is a prolongation of the rigid symmetry to a Lie algebroid morphism from the action Lie algebroid $M \\times \\mathfrak{g}\\to M$ into $D\\to M$ (or the algebra...
Dualities in all-order finite N=1 gauge theories
Energy Technology Data Exchange (ETDEWEB)
Karch, A.; Luest, D.; Zoupanos, G. [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik
1998-09-28
We search for dual gauge theories of all-loop finite, N=1 supersymmetric gauge theories. It is shown how to find explicitly the dual gauge theories of almost all chiral, N=1, all-loop finite gauge theories, while several models have been discussed in detail, including a realistic finite SU(5) unified theory. Out of our search only one all-loop, N=1 finite SO(10) theory emerges, so far, as a candidate for exhibiting also S-duality. (orig.) 60 refs.
Lattice gauge theories and Monte Carlo algorithms
Energy Technology Data Exchange (ETDEWEB)
Creutz, M. (Brookhaven National Lab., Upton, NY (USA). Physics Dept.)
1989-07-01
Lattice gauge theory has become the primary tool for non-perturbative calculations in quantum field theory. These lectures review some of the foundations of this subject. The first lecture reviews the basic definition of the theory in terms of invariant integrals over group elements on lattice bonds. The lattice represents an ultraviolet cutoff, and renormalization group arguments show how the bare coupling must be varied to obtain the continuum limit. Expansions in the inverse of the coupling constant demonstrate quark confinement in the strong coupling limit. The second lecture turns to numerical simulation, which has become an important approach to calculating hadronic properties. Here I discuss the basic algorithms for obtaining appropriately weighted gauge field configurations. The third lecture turns to algorithms for treating fermionic fields, which still require considerably more computer time than needed for purely bosonic simulations. Some particularly promising recent approaches are based on global accept-reject steps and should display a rather favorable dependence of computer time on the system volume. (orig.).
Gauge fixing and BRST formalism in non-Abelian gauge theories
Ghiotti, Marco; Williams, A G
2007-01-01
In this Thesis we present a comprehensive study of perturbative and non-perturbative non-Abelian gauge theories in the light of gauge-fixing procedures, focusing our attention on the BRST formalism in Yang-Mills theory. We propose first a model to re-write the Faddeev-Popov quantisation method in terms of group-theoretical techniques and then we give a possible way to solve the no-go theorem of Neuberger for lattice Yang-Mills theory with double BRST symmetry. In the final part we present a study of the Batalin-Vilkovisky quantisation method for non-linear gauges in non-Abelian gauge theories.
Noncompact lattice formulation of gauge theories
Friedberg, R; Pang, Y; Ren, H C
1995-01-01
We expand the gauge field in terms of a suitably constructed complete set of Bloch wave functions, each labeled by a band designation \\,n\\, and a wave number \\,\\vec K\\, restricted to the Brillouin zone. A noncompact formulation of lattice QCD (or QED) can be derived by restricting the expansion only to the \\,0^{th}-band (\\,n = 0\\,) functions, which are simple continuum interpolations of discrete values associated with sites or links on a lattice. The exact continuum theory can be reached through the inclusion of all \\,n = 0\\, and \\,n \
Screening in two-dimensional gauge theories
Korcyl, Piotr
2012-01-01
We analyze the problem of screening in 1+1 dimensional gauge theories. Using QED2 as a warm-up for the non-abelian models we show the mechanism of the string breaking, in particular the vanishing overlap of the Wilson loops to the broken-string ground state that has been conjectured in higher-dimensional analyses. We attempt to extend our analysis to non-integer charges in the quenched and unquenched cases, in pursuit of the numerical check of a renowned result for the string tension between arbitrarily-charged fermions in the massive Schwinger model.
Screening in two-dimensional gauge theories
Energy Technology Data Exchange (ETDEWEB)
Korcyl, Piotr [Uniwersytet Jagiellonski, Cracow (Poland). Inst. Fizyki; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Koren, Mateusz [Uniwersytet Jagiellonski, Cracow (Poland). Inst. Fizyki
2012-12-15
We analyze the problem of screening in 1+1 dimensional gauge theories. Using QED{sub 2} as a warmup for the non-abelian models we show the mechanism of the string breaking, in particular the vanishing overlap of the Wilson loops to the broken-string ground state that has been conjectured in higher-dimensional analyses. We attempt to extend our analysis to non-integer charges in the quenched and unquenched cases, in pursuit of the numerical check of a renowned result for the string tension between arbitrarily-charged fermions in the massive Schwinger model.
Lattice Gauge Field Theory and Prismatic Sets
DEFF Research Database (Denmark)
Akyar, Bedia; Dupont, Johan Louis
as and in particular the latter we use to study lattice gauge theory in the sense of Phillips and Stone. Thus for a Lie group and a set of parallel transport functions defining the transition over faces of the simplices, we define a classifying map from the prismatic star to a prismatic version of the classifying......We study prismatic sets analogously to simplicial sets except that realization involves prisms, i.e., products of simplices rather than just simplices. Particular examples are the prismatic subdivision of a simplicial set and the prismatic star of . Both have the same homotopy type...
Parallel supercomputers for lattice gauge theory.
Brown, F R; Christ, N H
1988-03-18
During the past 10 years, particle physicists have increasingly employed numerical simulation to answer fundamental theoretical questions about the properties of quarks and gluons. The enormous computer resources required by quantum chromodynamic calculations have inspired the design and construction of very powerful, highly parallel, dedicated computers optimized for this work. This article gives a brief description of the numerical structure and current status of these large-scale lattice gauge theory calculations, with emphasis on the computational demands they make. The architecture, present state, and potential of these special-purpose supercomputers is described. It is argued that a numerical solution of low energy quantum chromodynamics may well be achieved by these machines.
Nonperturbative Solution of Yukawa Theory and Gauge Theories
Hiller, John R.
2004-11-01
Recent progress in the nonperturbative solution of (3+1)-dimensional Yukawa theory and quantum electrodynamics (QED) and (1+1)-dimensional super Yang-Mills (SYM) theory will be summarized. The work on Yukawa theory has been extended to include two-boson contributions to the dressed fermion state and has inspired similar work on QED, where Feynman gauge has been found surprisingly convenient. In both cases, the theories are regulated in the ultraviolet by the inclusion of Pauli-Villars particles. For SYM theory, new high-resolution calculations of spectra have been used to obtain thermodynamic functions and improved results for a stress-energy correlator.
The shear viscosity of gauge theory plasma with chemical potentials
Energy Technology Data Exchange (ETDEWEB)
Benincasa, Paolo [Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7 (Canada); Buchel, Alex [Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7 (Canada) and Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2J 2W9 (Canada)]. E-mail: abuchel@perimeterinstitute.ca; Naryshkin, Roman [Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7 (Canada); Physics Department, Taras Shevchenko Kiev National University, Prosp. Glushkova 6, Kiev 03022 (Ukraine)
2007-02-08
We consider strongly coupled gauge theory plasma with conserved global charges that allow for a dual gravitational description. We study the shear viscosity of the gauge theory plasma in the presence of chemical potentials for these charges. Using gauge theory/string theory correspondence we prove that at large 't Hooft coupling the ratio of the shear viscosity to the entropy density is universal.
Three Instanton Computations In Gauge Theory And String Theory
Beasley, C E
2005-01-01
We employ a variety of ideas from geometry and topology to perform three new instanton computations in gauge theory and string theory. First, we consider supersymmetric QCD with gauge group SU( Nc) and with Nf flavors. In this theory, it is well known that instantons generate a superpotential if Nf = Nc − 1 and deform the moduli space of supersymmetric vacua if Nf = Nc. We extend these results to supersymmetric QCD with Nf > Nc flavors, for which we show that instantons generate a hierarchy of new, multi- fermion F-terms in the effective action. Second, we revisit the question of which Calabi-Yau compactifications of the heterotic string are stable under worldsheet instanton corrections to the effective space-time superpotential. For instance, compactifications described by (0, 2) linear sigma models are believed to be stable, suggesting a remarkable cancellation among the instanton effects in these theories. We show that this cancellation follows directly from a residue theorem, whose proof relie...
Berman, DS; Campos, VL; Cederwall, M; Gran, U; Larsson, H; Nielsen, M; Nilsson, BEW; Sundell, P
2001-01-01
We examine noncommutative Yang-Mills and open string theories using magnetically and electrically deformed supergravity duals. The duals are near horizon regions of Dp-brane bound state solutions which are obtained by using O(p + 1; p + 1) transformations of Dp-branes. The action of the T-duality gr
Relations between Non-Commutative and Commutative Spacetime
Tezuka, K I
2001-01-01
Spacetime non-commutativity appears in string theory. In this paper, the non-commutativity in string theory is reviewed. At first we review that a Dp-brane is equivalent to a configuration of infinitely many D($p-2$)-branes. If we consider the worldvolume as that of the Dp-brane, coordinates of the Dp-brane is commutative. On the other hand if we deal with the worldvolume as that of the D($p-2$)-branes, since coordinates of many D-branes are promoted to matrices the worldvolume theory is non-commutative one. Next we see that using a point splitting reguralization gives a non-commutative D-brane, and a non-commutative gauge field can be rewritten in terms of an ordinary gauge field. The transformation is called the Seiberg-Witten map. And we introduce second class constraints as boundary conditions of an open string. Since Neumann and Dirichlet boundary conditions are mixed in the constraints when the open string is coupled to a NS B field, the end points of the open string is non-commutative.
Algebraic differential calculus for gauge theories
Energy Technology Data Exchange (ETDEWEB)
Landi, G.; Marmo, G. (Naples Univ. (Italy). Dipt. di Scienze Fisiche Istituto Nazionale di Fisica Nucleare, Naples (Italy))
1990-12-01
The guiding idea in this paper is that, from the point of view of physics, functions and fields are more important than the (space time) manifold over which they are defined. The line pursued in these notes belongs to the general framework of ideas that replaces the space M by the ring of functions on it. Our essential observation, underlying this work, is that much of mathematical physics requires only a few differential operators (Lie derivative, d, {delta}) operating on modules of sections of suitable bundles. A connection (=gauge potential) can be described by a lift of vector fields from the base to the total space of a principal bundle. Much of the information can be encoded in the lift without reference to the bundle structures. In this manner, one arrives at an 'algebraic differential calculus' and its graded generalization that we are going to discuss. We are going to give an exposition of 'algebraic gauge theory' in both ungraded and graded versions. We show how to deal with the essential features of electromagnetism, Dirac, Kaluza-Klein and 't Hooft-Polyakov monopoles. We also show how to break the symmetry from SU(2) to U(1) without Higgs field. We briefly show how to deal with tests particles in external fields and with the Lagrangian formulation of field theories. (orig./HSI).
Gravitational Quantum Foam and Supersymmetric Gauge Theories
Maeda, T; Noma, Y; Tamakoshi, T; Maeda, Takashi; Nakatsu, Toshio; Noma, Yui; Tamakoshi, Takeshi
2005-01-01
We study K\\"{a}hler gravity on local SU(N) geometry and describe precise correspondence with certain supersymmetric gauge theories and random plane partitions. The local geometry is discretized, via the geometric quantization, to a foam of an infinite number of gravitational quanta. We count these quanta in a relative manner by measuring a deviation of the local geometry from a singular Calabi-Yau threefold, that is a A_{N-1} singularity fibred over \\mathbb{P}^1. With such a regularization prescription, the number of the gravitational quanta becomes finite and turns to be the perturbative prepotential for five-dimensional \\mathcal{N}=1 supersymmetric SU(N) Yang-Mills. These quanta are labelled by lattice points in a certain convex polyhedron on \\mathbb{R}^3. The polyhedron becomes obtainable from a plane partition which is the ground state of a statistical model of random plane partition that describes the exact partition function for the gauge theory. Each gravitational quantum of the local geometry is shown...
Chaos in Chiral Condensates in Gauge Theories
Hashimoto, Koji; Murata, Keiju; Yoshida, Kentaroh
2016-12-01
Assigning a chaos index for dynamics of generic quantum field theories is a challenging problem because the notion of a Lyapunov exponent, which is useful for singling out chaotic behavior, works only in classical systems. We address the issue by using the AdS /CFT correspondence, as the large Nc limit provides a classicalization (other than the standard ℏ→0 ) while keeping nontrivial quantum condensation. We demonstrate the chaos in the dynamics of quantum gauge theories: The time evolution of homogeneous quark condensates ⟨q ¯q ⟩ and ⟨q ¯γ5q ⟩ in an N =2 supersymmetric QCD with the S U (Nc) gauge group at large Nc and at a large 't Hooft coupling λ ≡NcgYM2 exhibits a positive Lyapunov exponent. The chaos dominates the phase space for energy density E ≳(6 ×1 02)×mq4(Nc/λ2), where mq is the quark mass. We evaluate the largest Lyapunov exponent as a function of (Nc,λ ,E ) and find that the N =2 supersymmetric QCD is more chaotic for smaller Nc.
Application of Noncommutative Differential Geometry on Lattice to Anomaly
Fujiwara, T; Wu, K; Fujiwara, Takanori; Suzuki, Hiroshi; Wu, Ke
1999-01-01
The chiral anomaly in lattice abelian gauge theory is investigated by applying the geometric and topological method in noncommutative differential geometry(NCDG). A new kind of double complex and descent equation are proposed on infinite hypercubic lattice in arbitrary even dimensional Euclidean space, in the framework of NCDG. Using the general solutions to proposed descent equation, we derive the chiral anomaly in Abelian lattice gauge theory. The topological origin of anomaly is nothing but the Chern classes in NCDG.
Gauge invariance and radiative corrections in an extra dimensional theory
Novales-Sánchez, H.; Toscano, J. J.
2011-04-01
The gauge structure of the four dimensional effective theory originated in a pure five dimensional Yang-Mills theory compactified on the orbifold S1 /Z2, is discussed on the basis of the BRST symmetry. If gauge parameters propagate in the bulk, the excited Kaluza-Klein (KK) modes are gauge fields and the four dimensional theory is gauge invariant only if the compactification is carried out by using curvatures as fundamental objects. The four dimensional theory is governed by two types of gauge transformations, one determined by the KK zero modes of the gauge parameters and the other by the excited ones. Within this context, a gauge-fixing procedure to quantize the KK modes that is covariant under the first type of gauge transformations is shown and the ghost sector induced by the gauge-fixing functions is presented. If the gauge parameters are confined to the usual four dimensional space-time, the known result in the literature is reproduced with some minor variants, although it is emphasized that the excited KK modes are not gauge fields, but matter fields transforming under the adjoint representation of SU4(N). A calculation of the one-loop contributions of the excited KK modes of the SUL(2) gauge group on the off-shell W+W-V, with V a photon or a Z boson, is exhibited. Such contributions are free of ultraviolet divergences and well-behaved at high energies.
Derivatives and the Role of the Drinfel'd Twist in Noncommutative String Theory
Watts, P
2000-01-01
We consider the derivatives which appear in the context of noncommutative string theory. First, we identify the correct derivations to use when the underlying structure of the theory is a quasitriangular Hopf algebra. Then we show that this is a specific case of a more general structure utilising the Drinfel'd twist. We go on to present reasons as to why we feel that the low-energy effective action, when written in terms of the original commuting coordinates, should explicitly exhibit this twisting.
Noncommutative Self-dual Gravity
García-Compéan, H; Ramírez, C; Sabido, M
2003-01-01
Starting from a self-dual formulation of gravity, we obtain a noncommutative theory of pure Einstein theory in four dimensions. In order to do that, we use Seiberg-Witten map. It is shown that the noncommutative torsion constraint is solved by the vanishing of commutative torsion. Finally, the noncommutative corrections to the action are computed up to second order.
Wilson loop expectations in $SU(N)$ lattice gauge theory
Jafarov, Jafar
2016-01-01
This article gives a rigorous formulation and proof of the $1/N$ expansion for Wilson loop expectations in strongly coupled $SU(N)$ lattice gauge theory in any dimension. The coefficients of the expansion are represented as absolutely convergent sums over trajectories in a string theory on the lattice, establishing a kind of gauge-string duality. Moreover, it is shown that in large $N$ limit, calculations in $SU(N)$ lattice gauge theory with coupling strength $2\\beta$ corresponds to those in $SO(N)$ lattice gauge theory with coupling strength $\\beta$ when $|\\beta|$ is sufficiently small.
Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver Gauge Theories
Bonelli, Giulio; Tanzini, Alessandro; Vasko, Petr
2015-01-01
We study the connection between N = 2 supersymmetric gauge theories, quantum cohomology and quantum integrable systems of hydrodynamic type. We consider gauge theories on ALE spaces of A and D-type and discuss how they describe the quantum cohomology of the corresponding Nakajima's quiver varieties. We also discuss how the exact evaluation of local BPS observables in the gauge theory can be used to calculate the spectrum of quantum Hamiltonians of spin Calogero integrable systems and spin Intermediate Long Wave hydrodynamics. This is explicitly obtained by a Bethe Ansatz Equation provided by the quiver gauge theory in terms of its adjacency matrix.
Quantum cohomology and quantum hydrodynamics from supersymmetric quiver gauge theories
Bonelli, Giulio; Sciarappa, Antonio; Tanzini, Alessandro; Vasko, Petr
2016-11-01
We study the connection between N = 2 supersymmetric gauge theories, quantum cohomology and quantum integrable systems of hydrodynamic type. We consider gauge theories on ALE spaces of A and D-type and discuss how they describe the quantum cohomology of the corresponding Nakajima's quiver varieties. We also discuss how the exact evaluation of local BPS observables in the gauge theory can be used to calculate the spectrum of quantum Hamiltonians of spin Calogero integrable systems and spin Intermediate Long Wave hydrodynamics. This is explicitly obtained by a Bethe Ansatz Equation provided by the quiver gauge theory in terms of its adjacency matrix.
He, Huan; von Keyserlingk, Curt
2016-01-01
Dijkgraaf-Witten (DW) theories are of recent interest to the condensed matter community, in part because they represent topological phases of matter, but also because they characterize the response theory of certain symmetry protected topological (SPT) phases. However, as yet there has not been a comprehensive treatment of the spectra of these models in the field theoretic setting -- the goal of this work is to fill the gap in the literature, at least for a selection of DW models with abelian gauge groups but non-abelian topological order. As applications, various correlation functions and fusion rules of line operators are calculated. We discuss for example the appearance of non-abelian statistics in DW theories with abelian gauge groups.
A gauge field theory of fermionic continuous-spin particles
Directory of Open Access Journals (Sweden)
X. Bekaert
2016-09-01
Full Text Available In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continuous-Spin Particles (CSPs. The action is invariant under gauge transformations without any constraint on both the gauge field and the gauge transformation parameter. The Fang–Fronsdal equations for a tower of massless fields with all half-integer spins arise as a particular limit of the equation of motion of fermionic CSPs.
From lattice gauge theories to hydrogen atoms
Directory of Open Access Journals (Sweden)
Manu Mathur
2015-10-01
Full Text Available We construct canonical transformations to obtain a complete and most economical realization of the physical Hilbert space Hp of pure SU(22+1 lattice gauge theory in terms of Wigner coupled Hilbert spaces of hydrogen atoms. One hydrogen atom is assigned to every plaquette of the lattice. A complete orthonormal description of the Wilson loop basis in Hp is obtained by all possible angular momentum Wigner couplings of hydrogen atom energy eigenstates |n l m〉 describing electric fluxes on the loops. The SU(2 gauge invariance implies that the total angular momenta of all hydrogen atoms vanish. The canonical transformations also enable us to rewrite the Kogut–Susskind Hamiltonian in terms of fundamental Wilson loop operators and their conjugate electric fields. The resulting loop Hamiltonian has a global SU(2 invariance and a simple weak coupling (g2→0 continuum limit. The canonical transformations leading to the loop Hamiltonian are valid for any SU(N. The ideas and techniques can also be extended to higher dimension.
A Formulation of Lattice Gauge Theories for Quantum Simulations
Zohar, Erez
2014-01-01
We examine the Kogut-Susskind formulation of lattice gauge theories under the light of fermionic and bosonic degrees of freedom that provide a description useful to the development of quantum simulators of gauge invariant models. We consider both discrete and continuous gauge groups and adopt a realistic multi-component Fock space for the definition of matter degrees of freedom. In particular, we express the Hamiltonian of the gauge theory and the Gauss law in terms of Fock operators. The gauge fields are described in two different bases, based on either group elements or group representations. This formulation allows for a natural scheme to achieve a consistent truncation of the Hilbert space for continuous groups, and provides helpful tools to study the connections of gauge theories with topological quantum double and string-net models for discrete groups. Several examples, including the case of the discrete $D_3$ gauge group, are presented.
Remarks on quiver gauge theories from open topological string theory
Carqueville, Nils
2009-01-01
We study effective quiver gauge theories arising from a stack of D3-branes on certain Calabi-Yau singularities. Our point of view is a first principle approach via open topological string theory. This means that we construct the natural A-infinity-structure of open string amplitudes in the associated D-brane category. Then we show that it precisely reproduces the results of the method of brane tilings, without having to resort to any effective field theory computations. In particular, we prove a general and simple formula for effective superpotentials.
Dimensionally continued multi-loop gauge theory
Broadhurst, D J
1999-01-01
A dimensionally continued background-field method makes the rationality of the 4-loop quenched QED beta function far more reasonable than had previously appeared. After 33 years of quest, dating from Rosner's discovery of 3-loop rationality, one finally sees cancellation of zeta values by the trace structure of individual diagrams. At 4-loops, diagram-by-diagram cancellation of $\\zeta(5)$ does not even rely on the values of integrals at d=4. Rather, it is a property of the rational functions of $d$ that multiply elements of the full d-dimensional basis. We prove a lemma: the basis consists of slices of wheels. We explain the previously mysterious suppression of $\\pi^4$ in massless gauge theory. The 4-loop QED result $\\beta_4=-46$ is obtained by setting d=4 in a precisely defined rational polynomial of d, with degree 11. The other 5 rational functions vanish at d=4.
Quantum Critical Behaviour of Semisimple Gauge Theories
DEFF Research Database (Denmark)
Esbensen, Jacob Kamuk; Ryttov, Thomas A.; Sannino, Francesco
2016-01-01
(M)_R \\times U(1) $ of the theory. To avoid gauge anomalies we add lepton-like particles. At the two-loops level an intriguing phase diagram appears. We uncover phases in which one, two or three fixed points exist and discuss the associated flows of the coupling constants. We discover a phase featuring...... complete asymptotic freedom and simultaneously an interacting infrared fixed point in both couplings. The analysis further reveals special renormalisation group trajectories along which one coupling displays asymptotic freedom and the other asymptotic safety, while both flowing in the infrared...... to an interacting fixed point. These are \\emph{safety free} trajectories. We briefly sketch out possible phenomenological implications, among which an independent way to generate near-conformal dynamics a l\\'a walking is investigated....
Towards Noncommutative Topological Quantum Field Theory: Tangential Hodge-Witten cohomology
Zois, I. P.
2014-03-01
Some years ago we initiated a program to define Noncommutative Topological Quantum Field Theory (see [1]). The motivation came both from physics and mathematics: On the one hand, as far as physics is concerned, following the well-known holography principle of 't Hooft (which in turn appears essentially as a generalisation of the Hawking formula for black hole entropy), quantum gravity should be a topological quantum field theory. On the other hand as far as mathematics is concerned, the motivation came from the idea to replace the moduli space of flat connections with the Gabai moduli space of codim-1 taut foliations for 3 dim manifolds. In most cases the later is finite and much better behaved and one might use it to define some version of Donaldson-Floer homology which, hopefully, would be easier to compute. The use of foliations brings noncommutative geometry techniques immediately into the game. The basic tools are two: Cyclic cohomology of the corresponding foliation C*-algebra and the so called "tangential cohomology" of the foliation. A necessary step towards this goal is to develop some sort of Hodge theory both for cyclic (and Hochschild) cohomology and for tangential cohomology. Here we present a method to develop a Hodge theory for tangential cohomology of foliations by mimicing Witten's approach to ordinary Morse theory by perturbations of the Laplacian.
A Mathematical Theory of the Gauged Linear Sigma Model
Fan, Huijun; Ruan, Yongbin
2015-01-01
We construct a rigorous mathematical theory of Witten's Gauged Linear Sigma Model (GLSM). Our theory applies to a wide range of examples, including many cases with non-Abelian gauge group. Both the Gromov-Witten theory of a Calabi-Yau complete intersection X and the Landau-Ginzburg dual (FJRW-theory) of X can be expressed as gauged linear sigma models. Furthermore, the Landau-Ginzburg/Calabi-Yau correspondence can be interpreted as a variation of the moment map or a deformation of GIT in the GLSM. This paper focuses primarily on the algebraic theory, while a companion article will treat the analytic theory.
Gauge dependence of the fermion quasiparticle poles in hot gauge theories
Wang, Shang-Yung
2004-09-01
The gauge dependence of the complex fermion quasiparticle poles corresponding to soft collective excitations is studied in hot gauge theories at one-loop order and next-to-leading order in the high-temperature expansion, with a view towards going beyond the leading order hard thermal loops and resummations thereof. We find that for collective excitations of momenta k˜eT the dispersion relations are gauge independent, but the corresponding damping rates are gauge dependent. For k≪eT and in the k→0 limit, both the dispersion relations and the damping rates are found to be gauge dependent. The gauge dependence of the position of the complex quasiparticle poles signals the need for resummation. Possible cancellation of the leading gauge dependence at two-loop order in the case of QED is briefly discussed.
On the definition of entanglement entropy in lattice gauge theories
Aoki, Sinya; Iritani, Takumi; Nozaki, Masahiro; Numasawa, Tokiro; Shiba, Noburo; Tasaki, Hal
2015-06-01
We focus on the issue of proper definition of entanglement entropy in lattice gauge theories, and examine a naive definition where gauge invariant states are viewed as elements of an extended Hilbert space which contains gauge non-invariant states as well. Working in the extended Hilbert space, we can define entanglement entropy associated with an arbitrary subset of links, not only for abelian but also for non-abelian theories. We then derive the associated replica formula. We also discuss the issue of gauge invariance of the entanglement entropy. In the Z N gauge theories in arbitrary space dimensions, we show that all the standard properties of the entanglement entropy, e.g. the strong subadditivity, hold in our definition. We study the entanglement entropy for special states, including the topological states for the Z N gauge theories in arbitrary dimensions. We discuss relations of our definition to other proposals.
On the definition of entanglement entropy in lattice gauge theories
Aoki, Sinya; Nozaki, Masahiro; Numasawa, Tokiro; Shiba, Noburo; Tasaki, Hal
2015-01-01
We focus on the issue of proper definition of entanglement entropy in lattice gauge theories, and examine a naive definition where gauge invariant states are viewed as elements of an extended Hilbert space which contain gauge non-invariant states as well. Working in the extended Hilbert space, we can define entanglement entropy associated with an arbitrary subset of links, not only for abelian but also for non-abelian theories. We then derive the associated replica formula. We also discuss the issue of gauge invariance of the entanglement entropy. In the $Z_N$ gauge theories in arbitrary space dimensions, we show that all the standard properties of the entanglement entropy, e.g. the strong subadditivity, hold in our definition. We study the entanglement entropy for special states, including the topological states for the $Z_N$ gauge theories in arbitrary dimensions. We discuss relations of our definition to other proposals.
Noncommutative Valuation of Options
Herscovich, Estanislao
2016-12-01
The aim of this note is to show that the classical results in finance theory for pricing of derivatives, given by making use of the replication principle, can be extended to the noncommutative world. We believe that this could be of interest in quantum probability. The main result called the First fundamental theorem of asset pricing, states that a noncommutative stock market admits no-arbitrage if and only if it admits a noncommutative equivalent martingale probability.
An Analysis of the First Order Form of Gauge Theories
Kiriushcheva, N; McKeon, D G C
2011-01-01
The first order form of a Maxwell theory and U(1) gauge theory in which a gauge invariant mass term appears is analyzed using the Dirac procedure. The form of the gauge transformation which leaves the action invariant is derived from the constraints present. A non-Abelian generalization is similarly analyzed. This first order three dimensional massive gauge theory is rewritten in terms of two interacting vector fields. The constraint structure when using light-cone coordinates is considered. The relationship between first and second order forms of the two-dimensional Einstein-Hilbert action is explored where a Lagrange multiplier is used to ensure their equivalence.
Integrable Models, SUSY Gauge Theories, and String Theory
Nam, S
1996-01-01
We consider the close relation between duality in N=2 SUSY gauge theories and integrable models. Vario us integrable models ranging from Toda lattices, Calogero models, spinning tops, and spin chains are re lated to the quantum moduli space of vacua of N=2 SUSY gauge theories. In particular, SU(3) gauge t heories with two flavors of massless quarks in the fundamental representation can be related to the spec tral curve of the Goryachev-Chaplygin top, which is a Nahm's equation in disguise. This can be generaliz ed to the cases with massive quarks, and N_f = 0,1,2, where a system with seven dimensional phas e space has the relevant hyperelliptic curve appear in the Painlevé test. To understand the stringy o rigin of the integrability of these theories we obtain exact nonperturbative point particle limit of ty pe II string compactified on a Calabi-Yau manifold, which gives the hyperelliptic curve of SU(2) QCD w ith N_f =1 hypermultiplet.
Strings, branes, and gravity duals of gauge theories
Lovis, K J
2002-01-01
We study the correspondence between certain supersymmetric gauge theories and their dual supergravity descriptions. Using low-energy brane probes of the supergravity geometries we find moduli spaces of vacua, as expected from considering the dual gauge theories. The metrics on these spaces can be put into a form consistent with field theory expectations. This provides a non-trivial check on the supergravity solutions, in addition to strong-coupling predictions for the gauge theories. In the case of N = 2 supersymmetric gauge theory, proposed supergravity duals have previously been shown, using brane probe techniques, to display the 'enhancon mechanism'. In particular, the supergravity geometries correctly reproduce the perturbative behaviour of the gauge theory. We calculate exact non-perturbative results at low-energies using the method of Seiberg and Witten. These correctly reproduce the perturbative results in the supergravity limit, but also make predictions for when the supergravity approximation is not ...
Axial Anomaly in Lattice Abelian Gauge Theory in Arbitrary Dimensions
Fujiwara, T; Wu, K; Fujiwara, Takanori; Suzuki, Hiroshi; Wu, Ke
1999-01-01
Axial anomaly of lattice abelian gauge theory in hyper-cubic regular lattice in arbitrary even dimensions is investigated by applying the method of exterior differential calculus. The topological invariance, gauge invariance and locality of the axial anomaly determine the explicit form of the topological part. The anomaly is obtained up to a multiplicative constant for finite lattice spacing and can be interpreted as the Chern character of the abelian lattice gauge theory.
Vacuum structure of bifundamental gauge theories at finite topological angles
Tanizaki, Yuya; Kikuchi, Yuta
2017-06-01
We discuss possible vacuum structures of SU( n) × SU( n) gauge theories with bifundamental matters at finite θ angles. In order to give a precise constraint, a mixed 't Hooft anomaly is studied in detail by gauging the center ℤ n one-form symmetry of the bifundamental gauge theory. We propose phase diagrams that are consistent with the con-straints, and also give a heuristic explanation of the result based on the dual superconductor scenario of confinement.
Yelnykov, O V
2005-01-01
This thesis addresses three topics: calculation of the invariant measure for the pure Yang-Mills configuration space in (3 + 1) dimensions, Hamiltonian analysis of the pure Chern-Simons theory on the noncommutative plane and noncommutative quantum mechanics in the presence of singular potentials. In Chapter 1 we consider a gauge-invariant Hamiltonian analysis for Yang-Mills theories in three spatial dimensions. The gauge potentials are parameterized in terms of a matrix variable which facilitates the elimination of the gauge degrees of freedom. We develop an approximate calculation of the volume element on the gauge-invariant configuration space. We also make a rough estimate of the ratio of 0++ glueball mass and the square root of string tension by comparison with (2 + 1)-dimensional Yang-Mills theory. In Chapter 2 the Hamiltonian analysis of the pure Chern- Simons theory on the noncommutative plane is performed. We use the techniques of geometric quantization to show that the classical reduced phase space o...
Seiberg-Witten equations and non-commutative spectral curves in Liouville theory
Energy Technology Data Exchange (ETDEWEB)
Chekhov, Leonid [Department of Theoretical Physics, Steklov Mathematical Institute, Moscow, 119991 Russia and School of Mathematics, Loughborough University, LE11 3TU Leicestershire (United Kingdom); Eynard, Bertrand [Institut de Physique Theorique, IPhT, CNRS, URA 2306, F-91191 Gif-sur-Yvette (France); Ribault, Sylvain [Institut de Physique Theorique, IPhT, CNRS, URA 2306, F-91191 Gif-sur-Yvette (France); Laboratoire Charles Coulomb UMR 5221 CNRS-UM2, Universite Montpellier 2, Place Eugene Bataillon, F-34095 Montpellier Cedex 5 (France)
2013-02-15
We propose that there exist generalized Seiberg-Witten equations in the Liouville conformal field theory, which allow the computation of correlation functions from the resolution of certain Ward identities. These identities involve a multivalued spin one chiral field, which is built from the energy-momentum tensor. We solve the Ward identities perturbatively in an expansion around the heavy asymptotic limit, and check that the first two terms of the Liouville three-point function agree with the known result of Dorn, Otto, Zamolodchikov, and Zamolodchikov. We argue that such calculations can be interpreted in terms of the geometry of non-commutative spectral curves.
On higher holonomy invariants in higher gauge theory I
Zucchini, Roberto
2015-01-01
This is the first of a series of two technical papers devoted to the analysis of holonomy invariants in strict higher gauge theory with end applications in higher Chern--Simons theory. For a flat 2--connection, we define the 2-holonomy of surface knots of arbitrary genus and determine its covariance properties under 1--gauge transformation and change of base data.
Two-loop beta functions for supersymmetric gauge theories
Energy Technology Data Exchange (ETDEWEB)
Jack, I. (Imperial Coll. of Science and Technology, London (UK). Blackett Lab.)
1984-11-15
The two-loop ..beta.. functions in the dimensional regularisation framework for a general gauge theory coupled to scalar and spinor fields are presented and by means of a finite transformation of the couplings are converted into a form which vanishes for special cases corresponding to supersymmetric gauge theories.
Conformal Gauge-Yukawa Theories away From Four Dimensions
DEFF Research Database (Denmark)
Codello, Alessandro; Langaeble, Kasper; Litim, Daniel
2016-01-01
We present the phase diagram and associated fixed points for a wide class of Gauge-Yukawa theories in $d=4+\\epsilon$ dimensions. The theories we investigate involve non-abelian gauge fields, fermions and scalars in the Veneziano-Witten limit. The analysis is performed in steps, we start with QCD...
CERN Theory Institute: Future directions in lattice gauge theory
2010-01-01
The main goal of the Institute is to bring together researchers in lattice gauge theory and in its applications to phenomenology to discuss interesting future directions of research. The focus will be on new ideas rather than on the latest computation of the usual quantities. The aim is to identify calculations in QCD, flavour physics, other strongly-interacting theories, etc. which are of high physics interest, and to clarify the theoretical and technical difficulties which, at present, prevent us from carrying them out.
Directory of Open Access Journals (Sweden)
Marco Panero
2006-11-01
Full Text Available We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to different commutative or non-commutative spaces. We present some of the theories which have been investigated in this framework, with a particular attention to the scalar model. Then we comment on the results recently obtained from Monte Carlo simulations, and show a preview of new numerical data, which are consistent with the expected transition between two phases characterised by the topology of the support of a matrix eigenvalue distribution.
Field Equations and Radial Solution in a Noncommutative Spherically Symmetric Geometry
Yazdani, Aref
2014-01-01
We study a noncommutative theory of gravity in the framework of torsional spacetime. This theory is based on a Lagrangian obtained by applying the technique of dimensional reduction of noncommutative gauge theory and that the yielded diffeomorphism invariant field theory can be made equivalent to a teleparallel formulation of gravity. Field equations are derived in the framework of teleparallel gravity through Weitzenbock geometry. We solve these field equations by considering a mass that is distributed spherically symmetrically in a stationary static spacetime in order to obtain a noncommutative line element.This new line element interestingly reaffirms the coherent state theory for a noncommutative Schwarzschild black hole. For the first time, we derive the Newtonian gravitational force equation in the commutative relativity framework, and this result could provide the possibility to investigate examples in various topics in quantum and ordinary theories of gravity.
Invariant Regularization of Supersymmetric Chiral Gauge Theory, 2
Hayashi, T; Okuyama, K; Suzuki, H; Hayashi, Takuya; Ohshima, Yoshihisa; Okuyama, Kiyoshi; Suzuki, Hiroshi
1998-01-01
By supplementing additional analyses postponed in the previous paper, we complete our construction of manifestly supersymmetric gauge-covariant regularization of supersymmetric chiral gauge theories. We present: An evaluation of the covariant gauge anomaly; the proof of integrability of the covariant gauge current in anomaly-free cases; a calculation of one-loop superconformal anomaly in the gauge supermultiplet sector. On the last point, we find that the ghost-anti-ghost supermultiplet and the Nakanishi-Lautrup supermultiplet give rise to BRST exact contributions which, due to the Slavnov-Taylor identities in our regularization scheme, can safely be neglected.
Noncommutative geometry with graded differential Lie algebras
Wulkenhaar, Raimar
1997-06-01
Starting with a Hilbert space endowed with a representation of a unitary Lie algebra and an action of a generalized Dirac operator, we develop a mathematical concept towards gauge field theories. This concept shares common features with the Connes-Lott prescription of noncommutative geometry, differs from that, however, by the implementation of unitary Lie algebras instead of associative * -algebras. The general scheme is presented in detail and is applied to functions ⊗ matrices.
Duality and Superconvergence Relation in Supersymmetric Gauge Theories
Tachibana, M
1998-01-01
We investigate the phase structures of various N=1 supersymmetric gauge theories including even the exceptional gauge group from the viewpoint of superconvergence of the gauge field propagator. Especially we analyze in detail whether a new type of duality recently discovered by Oehme in $SU(N_c)$ gauge theory coupled to fundamental matter fields can be found in more general gauge theories with more general matter representations or not. The result is that in the cases of theories including matter fields in only the fundamental representation, Oehme's duality holds but otherwise it does not. In the former case, superconvergence relation might give good criterion to describe the interacting non-Abelian Coulomb phase without using some information from dual magnetic theory.
6d strings from new chiral gauge theories
Kim, Hee-Cheol; Park, Jaemo
2016-01-01
We study the 6d $\\mathcal{N}=(1,0)$ superconformal field theory with smallest non-Higgsable gauge symmetry $SU(3)$. In particular, we propose new 2d gauge theory descriptions of its self-dual strings in the tensor branch. We use our gauge theories to compute the elliptic genera of the self-dual strings, which completely agree with the partial data known from topological strings. We further study the strings of the $(E_6,E_6)$ conformal matter by generalizing our 2d gauge theories. We also show that anomalies of all our gauge theories agree with the self-dual string anomalies computed by inflows from 6d.
Noncommutativity, Extra Dimensions, and Power Law Running in the Infrared
Abel, Steven A.; Jaeckel, Joerg; Khoze, Valentin V.; Ringwald, Andreas
2005-01-01
We investigate the running gauge couplings of U(N) noncommutative gauge theories with compact extra dimensions. Power law running of the trace-U(1) gauge coupling in the ultraviolet is communicated to the infrared by ultraviolet/infrared mixing, whereas the SU(N) factors run exactly as in the commutative theory. This results in theories where the experimentally excluded trace-U(1) factors decouple with a power law running of the momentum in the extreme infrared, effectively hiding them from d...
Non-Abelian discrete gauge symmetries in F-theory
Grimm, Thomas W; Regalado, Diego
2015-01-01
The presence of non-Abelian discrete gauge symmetries in four-dimensional F-theory compactifications is investigated. Such symmetries are shown to arise from seven-brane configurations in genuine F-theory settings without a weak string coupling description. Gauge fields on mutually non-local seven-branes are argued to gauge both R-R and NS-NS two-form bulk axions. The gauging is completed into a generalisation of the Heisenberg group with either additional seven-brane gauge fields or R-R bulk gauge fields. The former case relies on having seven-brane fluxes, while the latter case requires torsion cohomology and is analysed in detail through the M-theory dual. Remarkably, the M-theory reduction yields an Abelian theory that becomes non-Abelian when translated into the correct duality frame to perform the F-theory limit. The reduction shows that the gauge coupling function depends on the gauged scalars and transforms non-trivially as required for the groups encountered. This field dependence agrees with the exp...
Holism and structuralism in U(1) gauge theory
Lyre, Holger
After decades of neglect philosophers of physics have discovered gauge theories-arguably the paradigm of modern field physics-as a genuine topic for foundational and philosophical research. Incidentally, in the last couple of years interest from the philosophy of physics in structural realism-in the eyes of its proponents the best suited realist position towards modern physics-has also raised. This paper tries to connect both topics and aims to show that structural realism gains further credence from an ontological analysis of gauge theories-in particular U (1) gauge theory. In the first part of the paper the framework of fiber bundle gauge theories is briefly presented and the interpretation of local gauge symmetry will be examined. In the second part, an ontological underdetermination of gauge theories is carved out by considering the various kinds of non-locality involved in such typical effects as the Aharonov-Bohm effect. The analysis shows that the peculiar form of non-separability figuring in gauge theories is a variant of spatiotemporal holism and can be distinguished from quantum theoretic holism. In the last part of the paper the arguments for a gauge theoretic support of structural realism are laid out and discussed.
Gravitons, inflatons, twisted bits: A noncommutative bestiary
Pearson, John
In this work, we examine ideas connected with the noncommutativity of spacetime and its realizations in string theory. Motivated by Matrix Theory and the AdS-CFT correspondence, we propose a survey of selected noncommutative objects, assessing their implications for inflation, gauge theory duals, and solvable backgrounds. Our initial pair of examples, related to the Myers effect, incorporate elements of so-called "giant graviton" behavior. In the first, the formation of an extended, supersymmetry-restoring domain wall from point-brane sources in a flux background is related to a nonperturbative process of brane-flux annihilation. In the second, we reexamine these phenomena from a cosmological vantage, investigating the prospect of slow-roll inflation in the noncommutative configuration space of multiple d-branes. For our third and final example, we turn to the solvable pp-wave background, outlining a combinatorial, permutation-based approach to string physics which interpolates between gauge theory and worldsheet methods. This "string bit" language will allow us to find exact agreement between Yang-Mills theory in the large R-charge sector and string field theory on the light cone, resolving some previous discrepancies in the literature.
Local gauge theory and coarse graining
Zapata, Jose A
2012-01-01
Within the discrete gauge theory which is the basis of spin foam models, the problem of macroscopically faithful coarse graining is studied. Macroscopic data is identified; it contains the holonomy evaluation along a discrete set of loops and the homotopy classes of certain maps. When two configurations share this data they are related by a local deformation. The interpretation is that such configurations differ by "microscopic details". In many cases the homotopy type of the relevant maps is trivial for every connection; two important cases in which the homotopy data is composed by a set of integer numbers are: (i) a two dimensional base manifold and structure group U(1), (ii) a four dimensional base manifold and structure group SU(2). These cases are relevant for spin foam models of two dimensional gravity and four dimensional gravity respectively. This result suggests that if spin foam models for two-dimensional and four-dimensional gravity are modified to include all the relevant macroscopic degrees of fr...
Noncommutative Nonlinear Supersymmetry
Nishino, H; Nishino, Hitoshi; Rajpoot, Subhash
2002-01-01
We present noncommutative nonlinear supersymmetric theories. The first example is a non-polynomial Akulov-Volkov-type lagrangian with noncommutative nonlinear global supersymmetry in arbitrary space-time dimensions. The second example is the generalization of this lagrangian to Dirac-Born-Infeld lagrangian with nonlinear supersymmetry realized in dimensions D=2,3,4 and 6 (mod 8).
Twisted gauge theories in 3D Walker-Wang models
Wang, Zitao
2016-01-01
Three dimensional gauge theories with a discrete gauge group can emerge from spin models as a gapped topological phase with fractional point excitations (gauge charge) and loop excitations (gauge flux). It is known that 3D gauge theories can be "twisted", in the sense that the gauge flux loops can have nontrivial braiding statistics among themselves and such twisted gauge theories are realized in models discovered by Dijkgraaf and Witten. A different framework to systematically construct three dimensional topological phases was proposed by Walker and Wang and a series of examples have been studied. Can the Walker Wang construction be used to realize the topological order in twisted gauge theories? This is not immediately clear because the Walker-Wang construction is based on a loop condensation picture while the Dijkgraaf-Witten theory is based on a membrane condensation picture. In this paper, we show that the answer to this question is Yes, by presenting an explicit construction of the Walker Wang models wh...
The Gribov problem in Noncommutative QED
Canfora, Fabrizio; Rosa, Luigi; Vitale, Patrizia
2016-01-01
It is shown that in the noncommutative version of QED {(NCQED)} Gribov copies induced by the noncommutativity of space-time do appear in the Landau gauge. This is a genuine effect of noncommutative geometry which disappears when the noncommutative parameter vanishes. On the basis of existing applications of the Gribov-Zwanziger propagator in NCQED to deal with the UV/IR mixing problem, we argue that the two problems may have a common origin and possibly a common solution.
A bound on the scale of spacetime noncommutativity from the reheating phase after inflation
Horvat, R
2011-01-01
In an approach to noncommutative gauge theories, where the full noncommutative behavior is delimited by the presence of the UV and IR cutoffs, we consider the possibility of describing a system at a temperature T in a box of size L. Employing a specific form of UV/IR relationship inherent in such an approach of restrictive noncommutativity, we derive, for a given temperature T, an upper bound on the parameter of spacetime noncommutativity Lambda_NC ~ |theta|^{-1/2}. Considering such epochs in the very early universe which are expected to reflect spacetime noncommutativity to a quite degree, like the reheating stage after inflation, or believable pre-inflation radiation-dominated epochs, the best limits on Lambda_NC are obtained. We also demonstrate how the nature and size of the thermal system (for instance, the Hubble distance versus the future event horizon) can affect our bounds.
A bound on the scale of spacetime noncommutativity from the reheating phase after inflation
Energy Technology Data Exchange (ETDEWEB)
Horvat, R., E-mail: horvat@lei3.irb.hr [Institute Ruder Boskovic, Bijenicka 54, 10000 Zagreb (Croatia); Trampetic, J., E-mail: josipt@rex.irb.hr [Institute Ruder Boskovic, Bijenicka 54, 10000 Zagreb (Croatia); Max-Planck-Institut fuer Physik (Werner-Heisenberg-Institut), Foehringer Ring 6, D-80805 Muenchen (Germany)
2012-03-29
In an approach to noncommutative gauge theories, where the full noncommutative behavior is delimited by the presence of the UV and IR cutoffs, we consider the possibility of describing a system at a temperature T in a box of size L. Employing a specific form of UV/IR relationship inherent in such an approach of restrictive noncommutativity, we derive, for a given temperature T, an upper bound on the parameter of spacetime noncommutativity {Lambda}{sub NC}{approx}|{theta}|{sup -1/2}. Considering such epochs in the very early universe which are expected to reflect spacetime noncommutativity to a quite degree, like the reheating stage after inflation, or believable pre-inflation radiation-dominated epochs, the best limits on {Lambda}{sub NC} are obtained. We also demonstrate how the nature and size of the thermal system (for instance, the Hubble distance versus the future event horizon) can affect our bounds.
Quantized equations of motion in non-commutative theories
Heslop, P; Heslop, Paul; Sibold, Klaus
2004-01-01
Quantum field theories based on interactions which contain the Moyal star product suffer, in the general case when time does not commute with space, from several diseases: quantum equation of motions contain unusual terms, conserved currents can not be defined and the residual spacetime symmetry is not maintained. All these problems have the same origin: time ordering does not commute with taking the star product. Here we show that these difficulties can be circumvented by a new definition of time ordering: namely with respect to a light-cone variable. In particular the original spacetime symmetries SO(1,1) x SO(2) and translation invariance turn out to be respected. Unitarity is guaranteed as well.
Gauge fluxes in F-theory compactifications
Energy Technology Data Exchange (ETDEWEB)
Lin, Ling
2016-07-13
In this thesis, we study the geometry and physics of gauge fluxes in F-theory compactifications to four dimensions. Motivated by the phenomenological requirement of chiral matter in realistic model building scenarios, we develop methods for a systematic analysis of primary vertical G{sub 4}-fluxes on torus-fibred Calabi-Yau fourfolds. In particular, we extend the well-known description of fluxes on elliptic fibrations with sections to the more general set-up of genus-one fibrations with multi-sections. The latter are known to give rise to discrete abelian symmetries in F-theory. We test our proposal for constructing fluxes in such geometries on an explicit model with SU(5) x Z{sub 2} symmetry, which is connected to an ordinary elliptic fibration with SU(5) x U(1) symmetry by a conifold transition. With our methods we systematically verify anomaly cancellation and tadpole matching in both models. Along the way, we find a novel way of understanding anomaly cancellation in 4D F-theory in purely geometric terms. This observation is further strengthened by a similar analysis of an SU(3) x SU(2) x U(1){sup 2} model. The obvious connection of this particular model with the Standard Model is then investigated in a more phenomenologically motivated survey. There, we will first provide possible matchings of the geometric spectrum with the Standard Model states, which highlights the role of the additional U(1) factor as a selection rule. In a second step, we then utilise our novel methods on flux computations to set up a search algorithm for semi-realistic chiral spectra in our Standard- Model-like fibrations over specific base manifolds B. As a demonstration, we scan over three choices P{sup 3}, Bl{sub 1}P{sup 3} and Bl{sub 2}P{sup 3} for the base. As a result we find a consistent flux that gives the chiral Standard Model spectrum with a vector-like triplet exotic, which may be lifted by a Higgs mechanism.
Perturbative Gravity and Gauge Theory Relations: A Review
Directory of Open Access Journals (Sweden)
Thomas Søndergaard
2012-01-01
Full Text Available This paper is dedicated to the amazing Kawai-Lewellen-Tye relations, connecting perturbative gravity and gauge theories at tree level. The main focus is on n-point derivations and general properties both from a string theory and pure field theory point of view. In particular, the field theory part is based on some very recent developments.
Gauge theory renormalizations from the open bosonic string
Di Vecchia, P; Magnea, L; Marotta, R; Di Vecchia, P; Lerda, A; Magnea, L; Marotta, R
1995-01-01
We present a unified point of view on the different methods available in the literature to extract gauge theory renormalization constants from the low-energy limit of string theory. The Bern-Kosower method, based on an off-shell continuation of string theory amplitudes, and the construction of low-energy string theory effective actions for gauge particles, can both be understood in terms of strings interacting with background gauge fields, and thus reproduce, in the low-energy limit, the field theory results of the background field method. We present in particular a consistent off-shell continuation of the one-loop gluon amplitudes in the open bosonic string that reproduces exactly the results of the background field method in the Feynman gauge.
Ordinary matter in nonlinear affine gauge theories of gravitation
Tiemblo, A; Tiemblo, A; Tresguerres, R
1994-01-01
We present a general framework to include ordinary fermionic matter in the metric--affine gauge theories of gravity. It is based on a nonlinear gauge realization of the affine group, with the Lorentz group as the classification subgroup of the matter and gravitational fields.
A non-perturbative study of massive gauge theories
DEFF Research Database (Denmark)
Della Morte, Michele; Hernandez, Pilar
2013-01-01
We consider a non-perturbative formulation of an SU(2) massive gauge theory on a space-time lattice, which is also a discretised gauged non-linear chiral model. The lattice model is shown to have an exactly conserved global SU(2) symmetry. If a scaling region for the lattice model exists and the ...
Tanaka, S
2004-01-01
Noncommutative field theory on Yang's quantized space-time algebra (YSTA) is studied. It gives a theoretical framework to reformulate the matrix model as quantum mechanics of $D_0$ branes in a Lorentz-covariant form. The so-called kinetic term ($\\sim {\\hat{P_i}}^2)$ and potential term ($\\sim {[\\hat{X_i},\\hat{X_j}]}^2)$ of $D_0$ branes in the matrix model are described now in terms of Casimir operator of $SO(D,1)$, a subalgebra of the primary algebra $SO(D+1,1)$ which underlies YSTA with two contraction- parameters, $\\lambda$ and $R$. $D$-dimensional noncommutative space-time and momentum operators $\\hat{X_\\mu}$ and $\\hat{P_\\mu}$ in YSTA show a distinctive spectral structure, that is, space-components $\\hat{X_i}$ and $\\hat{P_i}$ have discrete eigenvalues, and time-components $\\hat{X_0}$ and $\\hat{P_0}$ continuous eigenvalues, consistently with Lorentz-covariance. According to the method of Lorentz-covariant Moyal star product proper to YSTA, the field equation of $D_0$ brane on YSTA is derived in a nontrivial ...
Deformed supersymmetric gauge theories from the fluxtrap background
Orlando, Domenico
2013-01-01
The fluxtrap background of string theory provides a transparent and algorithmic way of constructing supersymmetric gauge theories with both mass and Omega-type deformations in various dimensions. In this article, we review a number of deformed supersymmetric gauge theories in two and four dimensions which can be obtained via the fluxtrap background from string or M-theory. Such theories, the most well-known being Omega-deformed super Yang-Mills theory in four dimensions, have met with a lot of interest in the recent literature. The string theory treatment offers many new avenues of analysis and applications, such as for example the study of the gravity duals for deformed N=4 gauge theories.
Gauge origin independence in finite basis sets and perturbation theory
Sørensen, Lasse Kragh; Lindh, Roland; Lundberg, Marcus
2017-09-01
We show that origin independence in finite basis sets for the oscillator strengths is possibly in any gauge contrary to what is stated in literature. This is proved from a discussion of the consequences in perturbation theory when the exact eigenfunctions and eigenvalues to the zeroth order Hamiltonian H0 cannot be found. We demonstrate that the erroneous conclusion for the lack of gauge origin independence in the length gauge stems from not transforming the magnetic terms in the multipole expansion leading to the use of a mixed gauge. Numerical examples of exact origin dependence are shown.
E8 Gauge Theory and Gerbes in String Theory
Sati, H
2006-01-01
The reduction of the E8 gauge theory to ten dimensions leads to a loop group, which in relation to twisted K-theory has a Dixmier-Douady class identified with the Neveu-Schwarz H-field. We give an interpretation of the degree two part of the eta-form by comparing the adiabatic limit of the eta invariant with the one loop term in type IIA. More generally, starting with a G-bundle, the comparison for manifolds with String Structure identifies G with E8 and the representation as the adjoint, due to an interesting appearance of the dual Coxeter number. This makes possible a description in terms of a generalized WZW model at the critical level. We also discuss the relation to the index gerbe, the possibility of obtaining such bundles from loop space, and the symmetry breaking to finite-dimensional bundles. We discuss the implications of this and we give several proposals.
Roiban, Radu; Spradlin, Marcus; Volovich, Anastasia
2011-11-01
This issue aims to serve as an introduction to our current understanding of the structure of scattering amplitudes in gauge theory, an area which has seen particularly rapid advances in recent years following decades of steady progress. The articles contained herein provide a snapshot of the latest developments which we hope will serve as a valuable resource for graduate students and other scientists wishing to learn about the current state of the field, even if our continually evolving understanding of the subject might soon render this compilation incomplete. Why the fascination with scattering amplitudes, which have attracted the imagination and dedicated effort of so many physicists? Part of it stems from the belief, supported now by numerous examples, that unexpected simplifications of otherwise apparently complicated calculations do not happen by accident. Instead they provide a strong motivation to seek out an underlying explanation. The insight thereby gained can subsequently be used to make the next class of seemingly impossible calculations not only possible, but in some cases even trivial. This two-pronged strategy of exploring and exploiting the structure of gauge theory amplitudes appeals to a wide audience from formal theorists interested in mathematical structure for the sake of its own beauty to more phenomenologically-minded physicists eager to speed up the next generation of analysis software. Understandably it is the maximally supersymmetric 𝒩 = 4 Yang-Mills theory (SYM) which has the simplest structure and has correspondingly received the most attention. Rarely in theoretical physics are we fortunate enough to encounter a toy model which is simple enough to be solved completely yet rich enough to possess interesting non-trivial structure while simultaneously, and most importantly, being applicable (even if only as a good approximation) to a wide range of 'real' systems. The canonical example in quantum mechanics is of course the harmonic
Topological and differential geometrical gauge field theory
Saaty, Joseph
between bosons (quantized) and fermions (not quantized). Thus I produced results that were previously unobtainable. Furthermore, since topological charge takes place in Flat Spacetime, I investigated the quantization of the Curved Spacetime version of topological charge (Differential Geometrical Charge) by developing the differential geometrical Gauge Field Theory. It should be noted that the homotopy classification method is not at all applicable to Curved Spacetime. I also modified the Dirac equation in Curved Spacetime by using Einstein's field equation in order to account for the presence of matter. As a result, my method has allowed me to address four cases of topological charge (both spinless and spin one- half, in both Flat and in Curved Spacetime) whereas earlier methods had been blind to all but one of these cases (spinless in Flat Spacetime). (Abstract shortened by UMI.)
Extended Nambu models: Their relation to gauge theories
Escobar, C. A.; Urrutia, L. F.
2017-05-01
Yang-Mills theories supplemented by an additional coordinate constraint, which is solved and substituted in the original Lagrangian, provide examples of the so-called Nambu models, in the case where such constraints arise from spontaneous Lorentz symmetry breaking. Some explicit calculations have shown that, after additional conditions are imposed, Nambu models are capable of reproducing the original gauge theories, thus making Lorentz violation unobservable and allowing the interpretation of the corresponding massless gauge bosons as the Goldstone bosons arising from the spontaneous symmetry breaking. A natural question posed by this approach in the realm of gauge theories is to determine under which conditions the recovery of an arbitrary gauge theory from the corresponding Nambu model, defined by a general constraint over the coordinates, becomes possible. We refer to these theories as extended Nambu models (ENM) and emphasize the fact that the defining coordinate constraint is not treated as a standard gauge fixing term. At this level, the mechanism for generating the constraint is irrelevant and the case of spontaneous Lorentz symmetry breaking is taken only as a motivation, which naturally bring this problem under consideration. Using a nonperturbative Hamiltonian analysis we prove that the ENM yields the original gauge theory after we demand current conservation for all time, together with the imposition of the Gauss laws constraints as initial conditions upon the dynamics of the ENM. The Nambu models yielding electrodynamics, Yang-Mills theories and linearized gravity are particular examples of our general approach.
Higher Gauge Theory and Gravity in (2+1) Dimensions
Mann, R B; Popescu, Eugeniu M.
2006-01-01
Non-abelian higher gauge theory has recently emerged as a generalization of standard gauge theory to higher dimensional (2-dimensional in the present context) connection forms, and as such, it has been successfully applied to the non-abelian generalizations of the Yang-Mills theory and 2-form electrodynamics. (2+1)-dimensional gravity, on the other hand, has been a fertile testing ground for many concepts related to classical and quantum gravity, and it is therefore only natural to investigate whether we can find an application of higher gauge theory in this latter context. In the present paper we investigate the possibility of applying the formalism of higher gauge theory to gravity in (2+1) dimensions, and we show that a nontrivial model of (2+1)-dimensional gravity coupled to scalar and tensorial matter fields - the $\\Sigma\\Phi EA$ model - can be formulated both as a standard gauge theory and as a higher gauge theory. Since the model has a very rich structure - it admits as solutions black-hole BTZ-like ge...
Thermalization and confinement in strongly coupled gauge theories
Ishii, Takaaki; Rosen, Christopher
2016-01-01
Quantum field theories of strongly interacting matter sometimes have a useful holographic description in terms of the variables of a gravitational theory in higher dimensions. This duality maps time dependent physics in the gauge theory to time dependent solutions of the Einstein equations in the gravity theory. In order to better understand the process by which "real world" theories such as QCD behave out of thermodynamic equilibrium, we study time dependent perturbations to states in a model of a confining, strongly coupled gauge theory via holography. Operationally, this involves solving a set of non-linear Einstein equations supplemented with specific time dependent boundary conditions. The resulting solutions allow one to comment on the timescale by which the perturbed states thermalize, as well as to quantify the properties of the final state as a function of the perturbation parameters. We comment on the influence of the dual gauge theory's confinement scale on these results, as well as the appearance ...
Next-to-Maximal Helicity Violating Amplitudes in Gauge Theory
Kosower, D A
2004-01-01
Using the novel diagrammatic rules recently proposed by Cachazo, Svrcek, and Witten, I give a compact, manifestly Lorentz-invariant form for tree-level gauge-theory amplitudes with three opposite helicities.
Gauge Natural Formulation of Conformal Theory of Gravity
Campigotto, M.; Fatibene, L.
2014-01-01
We consider conformal gravity as a gauge natural theory. We study its conservation laws and superpotentials. We also consider the Mannheim and Kazanas spherically symmetric vacuum solution and discuss conserved quantities associated to conformal and diffeomorphism symmetries.
Dirac equation in gauge and affine-metric gravitation theories
Giachetta, G
1995-01-01
We show that the covariant derivative of Dirac fermion fields in the presence of a general linear connection on a world manifold is universal for Einstein's, gauge and affine-metric gravitation theories.
Multi-flux warped throats and cascading gauge theories
Franco, S; Uranga, Angel M; Franco, Sebastian; Hanany, Amihay; Uranga, Angel M.
2005-01-01
We describe duality cascades and their infrared behavior for systems of D3-branes at singularities given by complex cones over del Pezzo surfaces (and related examples), in the presence of fractional branes. From the gauge field theory viewpoint, we show that D3-branes probing the infrared theory have a quantum deformed moduli space, given by a complex deformation of the initial geometry to a simpler one. This implies that for the dual supergravity viewpoint, the gauge theory strong infrared dynamics smoothes out the naked singularities of the recently constructed warped throat solutions with 3-form fluxes, describing the cascading RG flow of the gauge theory. This behavior thus generalizes the Klebanov-Strassler deformation of the conifold. We describe several explicit examples, including models with several scales of strong gauge dynamics. In the regime of widely separated scales, the dual supergravity solutions should correspond to throats with several radial regions with different exponential warp factors...
Dark matter in the nonabelian hidden gauge theory
Yamanaka, Nodoka; Gongyo, Shinya; Iida, Hideaki
2015-01-01
We discuss the dark matter in the hidden gauge theory. We propose a scenario where the mini-inflation dilutes the dark matter density. This scenario is consistent with the current baryon number asymmetry.
Two-color gauge theory with novel infrared behavior.
Appelquist, T; Brower, R C; Buchoff, M I; Cheng, M; Fleming, G T; Kiskis, J; Lin, M F; Neil, E T; Osborn, J C; Rebbi, C; Schaich, D; Schroeder, C; Syritsyn, S; Voronov, G; Vranas, P; Witzel, O
2014-03-21
Using lattice simulations, we study the infrared behavior of a particularly interesting SU(2) gauge theory, with six massless Dirac fermions in the fundamental representation. We compute the running gauge coupling derived nonperturbatively from the Schrödinger functional of the theory, finding no evidence for an infrared fixed point up through gauge couplings g(2) of order 20. This implies that the theory either is governed in the infrared by a fixed point of considerable strength, unseen so far in nonsupersymmetric gauge theories, or breaks its global chiral symmetries producing a large number of composite Nambu-Goldstone bosons relative to the number of underlying degrees of freedom. Thus either of these phases exhibits novel behavior.
Generally covariant vs. gauge structure for conformal field theories
Energy Technology Data Exchange (ETDEWEB)
Campigotto, M., E-mail: martacostanza.campigotto@to.infn.it [Dipartimento di Fisica, University of Torino, Via P. Giuria 1, 10125, Torino (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Via P. Giuria 1, 10125, Torino (Italy); Fatibene, L. [Dipartimento di Matematica, University of Torino, Via C. Alberto 10, 10123, Torino (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Via P. Giuria 1, 10125, Torino (Italy)
2015-11-15
We introduce the natural lift of spacetime diffeomorphisms for conformal gravity and discuss the physical equivalence between the natural and gauge natural structure of the theory. Accordingly, we argue that conformal transformations must be introduced as gauge transformations (affecting fields but not spacetime point) and then discuss special structures implied by the splitting of the conformal group. -- Highlights: •Both a natural and a gauge natural structure for conformal gravity are defined. •Global properties and natural lift of spacetime transformations are described. •The possible definitions of physical state are considered and discussed. •The gauge natural theory has less physical states than the corresponding natural one. •The dynamics forces to prefer the gauge natural structure over the natural one.
Hamiltonian Formulation of Jackiw-Pi 3-Dimensional Gauge Theories
Dayi, O F
1998-01-01
A 3-dimensional non-abelian gauge theory was proposed by Jackiw and Pi to create mass for the gauge fields. However, the set of gauge invariances of the quadratic action obtained by switching off the non-abelian interactions is larger than the original one. This inconsistency in the gauge invariances causes some problems in quantization. Jackiw and Pi proposed another action by enlarging the space of states whose gauge invariances are consistent with the quadratic part. It is shown that all of these theories yield the same number of physical degrees of freedom in the hamiltonian framework. Hence, as far as the physical states are considered there is no inconsistency. Nevertheless, perturbation expansion is still problamatic.
Geometrical hyperbolic systems for general relativity and gauge theories
Abrahams, A M; Choquet-Bruhat, Y; York, J W
1996-01-01
The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural characteristic directions and speeds for the dynamical variables. Quantities representing gauge degrees of freedom [the spatial shift vector \\beta^{i}(t,x^{j}) and the spatial scalar potential \\phi(t,x^{j}), respectively] are not among the dynamical variables: the gauge and the physical quantities in the evolution equations are effectively decoupled. For example, the gauge quantities could be obtained as functions of (t,x^{j}) from subsidiary equations that are not part of the evolution equations. Propagation of certain (``radiative'') dynamical variables along the physical light cone is gauge invariant while the remaining dynamical variables are dragged along the axes orthogonal to the spacelike time slices by the propagating variables. We obtain these results by (1) taking a furth...
Cabra, D C; Rossini, L; Schaposnik, F A; Fradkin, Eduardo
1995-01-01
We discuss the behavior of theories of fermions coupled to Chern-Simons gauge fields with a non-abelian gauge group in three dimensions and at finite temperature. Using non-perturbative arguments and gauge invariance, and in contradiction with perturbative results, we show that the coefficient of the Chern-Simons term of the effective actions for the gauge fields at finite temperature can be {\\it at most} an integer function of the temperature. This is in a sense a generalized no-renormalization theorem. We also discuss the case of abelian theories and give indications that a similar condition should hold there too. We discuss consequences of our results to the thermodynamics of anyon superfluids and fractional quantum Hall systems.
Bloch Waves in Minimal Landau Gauge and the Infinite-Volume Limit of Lattice Gauge Theory
Cucchieri, Attilio; Mendes, Tereza
2017-05-01
By exploiting the similarity between Bloch's theorem for electrons in crystalline solids and the problem of Landau gauge fixing in Yang-Mills theory on a "replicated" lattice, we show that large-volume results can be reproduced by simulations performed on much smaller lattices. This approach, proposed by Zwanziger [Nucl. Phys. B412, 657 (1994), 10.1016/0550-3213(94)90396-4], corresponds to taking the infinite-volume limit for Landau-gauge field configurations in two steps: first for the gauge transformation alone, while keeping the lattice volume finite, and second for the gauge-field configuration itself. The solutions to the gauge-fixing condition are then given in terms of Bloch waves. Applying the method to data from Monte Carlo simulations of pure SU(2) gauge theory in two and three space-time dimensions, we are able to evaluate the Landau-gauge gluon propagator for lattices of linear extent up to 16 times larger than that of the simulated lattice. This approach is reminiscent of the Fisher-Ruelle construction of the thermodynamic limit in classical statistical mechanics.
Large field inflation models from higher-dimensional gauge theories
Furuuchi, Kazuyuki; Koyama, Yoji
2015-02-01
Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante's Inferno model turns out to be the most preferred model in this framework.
Large field inflation models from higher-dimensional gauge theories
Energy Technology Data Exchange (ETDEWEB)
Furuuchi, Kazuyuki [Manipal Centre for Natural Sciences, Manipal University, Manipal, Karnataka 576104 (India); Koyama, Yoji [Department of Physics, National Tsing-Hua University, Hsinchu 30013, Taiwan R.O.C. (China)
2015-02-23
Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher-dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante’s Inferno model turns out to be the most preferred model in this framework.
Seiberg Duality, Quiver Gauge Theories, and Ihara Zeta Function
Zhou, Da; He, Yang-Hui
2015-01-01
We study Ihara zeta function for graphs in the context of quivers arising from gauge theories, especially under Seiberg duality transformations. The distribution of poles is studied as we proceed along the duality tree, in light of the weak and strong graph versions of the Riemann Hypothesis. As a by-product, we find a refined version of Ihara zeta function to be the generating function for the generic superpotential of the gauge theory.
Closed String Amplitudes from Gauge Fixed String Field Theory
Drukker, Nadav
2002-01-01
Closed string diagrams are derived from cubic open string field theory using a gauge fixed kinetic operator. The basic idea is to use a string propagator that does not generate a boundary to the world sheet. Using this propagator and the closed string vertex, the moduli space of closed string surfaces is covered, so closed string scattering amplitudes should be reproduced. This kinetic operator could be a gauge fixed form of the string field theory action around the closed string vacuum.
Closed String Amplitudes from Gauge Fixed String Field Theory
Drukker, Nadav
2002-01-01
Closed string diagrams are derived from cubic open string field theory using a gauge fixed kinetic operator. The basic idea is to use a string propagator that does not generate a boundary to the world sheet. Using this propagator and the closed string vertex, the moduli space of closed string surfaces is covered, so closed string scattering amplitudes should be reproduced. This kinetic operator could be a gauge fixed form of the string field theory action around the closed string vacuum.
Large Field Inflations from Higher Dimensional Gauge Theories
Furuuchi, Kazuyuki
2015-01-01
Motivated by the recent detection of B-mode polarization of CMB by BICEP2 which is possibly of primordial origin, we study large field inflation models which can be obtained from higher dimensional gauge theories. The constraints from CMB observations on the gauge theory parameters are given, and their naturalness are discussed. Among the models analyzed, Dante's Inferno model appears as the most promising model in this framework.
Gauge Invariant Effective Action in Abelian Chiral Gauge Theory on the Lattice
Suzuki, H
1999-01-01
Lüscher's recent formulation of Abelian chiral gauge theories on the lattice, in the vacuum (or perturbative) sector in infinite lattice volume, is re-interpreted in terms of the lattice covariant regularization. The gauge invariance of the effective action and the integrability of the gauge current in anomaly-free cases become transparent then. The real part of the effective action is simply one-half of that of the Dirac fermion and, when the Dirac operator has proper properties in the continuum limit, the imaginary part in the continuum limit reproduces the $\\eta$-invariant.}
Algebra of Noncommutative Riemann Surfaces
2006-01-01
We examine several algebraic properties of the noncommutive $z$-plane and Riemann surfaces. The starting point of our investigation is a two-dimensional noncommutative field theory, and the framework of the theory will be converted into that of a complex coordinate system. The basis of noncommutative complex analysis is obtained thoroughly, and the considerations on functional analysis are also given before performing the examination of the conformal mapping and the Teichm\\"{u}ller theory. (K...
Gauge and motion in perturbation theory
Pound, Adam
2015-01-01
Through second order in perturbative general relativity, a small compact object in an external vacuum spacetime obeys a generalized equivalence principle: although it is accelerated with respect to the external background geometry, it is in free fall with respect to a certain \\emph{effective} vacuum geometry. However, this single principle takes very different mathematical forms, with very different behaviors, depending on how one treats perturbed motion. Furthermore, any description of perturbed motion can be altered by a gauge transformation. In this paper, I clarify the relationship between two treatments of perturbed motion and the gauge freedom in each. I first show explicitly how one common treatment, called the Gralla-Wald approximation, can be derived from a second, called the self-consistent approximation. I next present a general treatment of smooth gauge transformations in both approximations, in which I emphasise that the approximations' governing equations can be formulated in an invariant manner...
The Gauge Integral Theory in HOL4
Directory of Open Access Journals (Sweden)
Zhiping Shi
2013-01-01
Full Text Available The integral is one of the most important foundations for modeling dynamical systems. The gauge integral is a generalization of the Riemann integral and the Lebesgue integral and applies to a much wider class of functions. In this paper, we formalize the operational properties which contain the linearity, monotonicity, integration by parts, the Cauchy-type integrability criterion, and other important theorems of the gauge integral in higher-order logic 4 (HOL4 and then use them to verify an inverting integrator. The formalized theorem library has been accepted by the HOL4 authority and will appear in HOL4 Kananaskis-9.
Integrating over the Coulomb branch in N=2 gauge theory
Marino, Marcos; Moore, Gregory
1997-01-01
We review the relation of certain integrals over the Coulomb phase of $d=4$, N=2 SO(3) supersymmetric Yang-Mills theory with Donaldson-Witten theory. We describe a new way to write an important contact term in the theory and show how the integrals generalize to higher rank gauge groups.
String organization of field theories duality and gauge invariance
Feng, Y J; Feng, Y J; Lam, C S
1994-01-01
String theories should reduce to ordinary four-dimensional field theories at low energies. Yet the formulation of the two are so different that such a connection, if it exists, is not immediately obvious. With the Schwinger proper-time representation, and the spinor helicity technique, it has been shown that field theories can indeed be written in a string-like manner, thus resulting in simplifications in practical calculations, and providing novel insights into gauge and gravitational theories. This paper continues the study of string organization of field theories by focusing on the question of local duality. It is shown that a single expression for the sum of many diagrams can indeed be written for QED, thereby simulating the duality property in strings. The relation between a single diagram and the dual sum is somewhat analogous to the relation between a old- fashioned perturbation diagram and a Feynman diagram. Dual expressions are particularly significant for gauge theories because they are gauge invari...
Beyond the Standard Model with noncommutative geometry, strolling towards quantum gravity
Martinetti, Pierre
2015-01-01
Noncommutative geometry, in its many incarnations, appears at the crossroad of various researches in theoretical and mathematical physics: from models of quantum space-time (with or without breaking of Lorentz symmetry) to loop gravity and string theory, from early considerations on UV-divergencies in quantum field theory to recent models of gauge theories on noncommutative spacetime, from Connes description of the standard model of elementary particles to recent Pati-Salam like extensions. We list several of these applications, emphasizing also the original point of view brought by noncommutative geometry on the nature of time. This text serves as an introduction to the volume of proceedings of the parallel session "Noncommutative geometry and quantum gravity", as a part of the conference "Conceptual and technical challenges in quantum gravity" organized at the University of Rome "La Sapienza" in September 2014.
Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields
Hadasz, L; Rocek, M; Von Unge, R; Hadasz, Leszek; Lindstrom, Ulf; Rocek, Martin; Unge, Rikard von
2003-01-01
We study one- and two-soliton solutions of noncommutative Chern-Simons theory coupled to a nonrelativistic or a relativistic scalar field. In the nonrelativistic case it is not possible to find the dynamics of the solitons using traditional moduli space techniques. To do better we have found exact time dependent one soliton solutions to the full equations of motion. They represent solitons moving in straight lines with constant velocity. Surprisingly we find that the set of allowed velocities is quantized! The allowed velocities are proportional to the square root of an integer. In the relativistic case we find the metric on the two soliton moduli space and using techinques developed in the nonrelativistic case we also find exact time dependent one-soliton solutions. Again the allowed velocities are quantized, though in a slightly more complicated fashion.
Unification of gravity and quantum field theory from extended noncommutative geometry
Yu, Hefu; Ma, Bo-Qiang
2017-02-01
We make biframe and quaternion extensions on the noncommutative geometry, and construct the biframe spacetime for the unification of gravity and quantum field theory (QFT). The extended geometry distinguishes between the ordinary spacetime based on the frame bundle and an extra non-coordinate spacetime based on the biframe bundle constructed by our extensions. The ordinary spacetime frame is globally flat and plays the role as the spacetime frame in which the fields of the Standard Model are defined. The non-coordinate frame is locally flat and is the gravity spacetime frame. The field defined in both frames of such “flat” biframe spacetime can be quantized and plays the role as the gravity field which couples with all the fields to connect the gravity effect with the Standard Model. Thus, we provide a geometric paradigm in which gravity and QFT can be unified.
Algebraic approach to quantum field theory on a class of noncommutative curved spacetimes
Ohl, Thorsten
2009-01-01
In this article we construct the quantum field theory of a free real scalar field on a class of noncommutative manifolds, obtained via deformation quantization using triangular Drinfel'd twists. We construct deformed quadratic action functionals and compute the corresponding equation of motion operators. The Green's operators and the fundamental solution of the deformed equation of motion are obtained in terms of formal power series. It is shown that, using the deformed fundamental solution, we can define the Weyl algebra of field observables, which in general depends on the spacetime deformation parameter. This dependence is absent in the special case of Killing deformations, which include in particular the Moyal-Weyl deformation of the Minkowski spacetime.
Quantum Critical Behaviour of Semi-Simple Gauge Theories
DEFF Research Database (Denmark)
Esbensen, Jacob Kamuk; Ryttov, Thomas A.; Sannino, Francesco
2016-01-01
We study the perturbative phase diagram of semi-simple fermionic gauge theories resembling the Standard Model. We investigate an $SU(N)$ gauge theory with $M$ Dirac flavors where we gauge first an $SU(M)_L$ and then an $SU(2)_L \\subset SU(M)_L$ of the original global symmetry $SU(M)_L\\times SU......(M)_R \\times U(1) $ of the theory. To avoid gauge anomalies we add lepton-like particles. At the two-loops level an intriguing phase diagram appears. We uncover phases in which one, two or three fixed points exist and discuss the associated flows of the coupling constants. We discover a phase featuring...
Hamiltonian Poincaré gauge theory of gravitation
Tiemblo, A
1996-01-01
We develop a Hamiltonian formalism suitable to be applied to gauge theories in the presence of Gravitation, and to Gravity itself when considered as a gauge theory. It is based on a nonlinear realization of the Poincar\\'e group, taken as the local spacetime group of the gravitational gauge theory, with SO(3) as the classification subgroup. The Wigner--like rotation induced by the nonlinear approach singularizes out the role of time and allows to deal with ordinary SO(3) vectors. We apply the general results to the Einstein--Cartan action. We study the constraints and we obtain Einstein's classical equations in the extremely simple form of time evolution equations of the coframe. As a consequence of our approach, we identify the gauge--theoretical origin of the Ashtekar variables.
Multigrid methods for propagators in lattice gauge theories
Kalkreuter, T
1994-01-01
Multigrid methods were invented for the solution of discretized partial differential equations in ordered systems. The slowness of traditional algorithms is overcome by updates on various length scales. In this article we discuss generalizations of multigrid methods for disordered systems, in particular for propagators in lattice gauge theories. A discretized nonabelian gauge theory can be formulated as a system of statistical mechanics where the gauge field degrees of freedom are SU(N) matrices on the links of the lattice. These SU(N) matrices appear as random coefficients in Dirac equations. We aim at finding an efficient method by which one can solve Dirac equations without critical slowing down. If this could be achieved, Monte Carlo simulations of Quantum Chromodynamics (the theory of the strong interaction) would be accelerated considerably. In principle, however, the methods discussed can be used in arbitrary space-time dimension and for arbitrary gauge group. Moreover, there are applications in multig...
Hydrodynamics of strongly coupled gauge theories from gravity
Energy Technology Data Exchange (ETDEWEB)
Benincasa, P. [Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7 (Canada)
2007-09-15
In this talk we review some recent developments in the analysis of gauge theories from a holographic perspective. We focus on the transport properties of strongly coupled gauge theories. In particular, we discuss the results for two specific non-conformal models: the N=2* supersymmetric SU(N{sub c}) Yang-Mills theory and the Sakai-Sugimoto model. Finally, we discuss the hydrodynamic picture for the N=4SU(N{sub c}) SYM theory when the leading correction in the inverse 't Hooft coupling is taken into account.