Localization in abelian Chern-Simons theory
DEFF Research Database (Denmark)
McLellan, Brendan Donald Kenneth
2013-01-01
Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected, and abelian. The abelian Chern-Simons partition function is derived using the Faddeev-Popov gauge fixing method. The partition function is then formally computed...
Chern-Simons Theory on Supermanifolds
Grassi, Pietro Antonio
2016-01-01
We consider quantum field theories on supermanifolds using integral forms. The latter are used to define a geometric theory of integration and they are essential for a consistent action principle. The construction relies on Picture Changing Operators, analogous to the one introduced in String Theory. As an application, we construct a geometric action principle for N=1 D=3 super-Chern-Simons theory.
Transport in Chern-Simons-Matter Theories
Gur-Ari, Guy; Mahajan, Raghu
2016-01-01
The frequency-dependent longitudinal and Hall conductivities --- $\\sigma_{xx}$ and $\\sigma_{xy}$ --- are dimensionless functions of $\\omega/T$ in 2+1 dimensional CFTs at nonzero temperature. These functions characterize the spectrum of charged excitations of the theory and are basic experimental observables. We compute these conductivities for large $N$ Chern-Simons theory with fermion matter. The computation is exact in the 't Hooft coupling $\\lambda$ at $N = \\infty$. We describe various physical features of the conductivity, including an explicit relation between the weight of the delta function at $\\omega = 0$ in $\\sigma_{xx}$ and the existence of infinitely many higher spin conserved currents in the theory. We also compute the conductivities perturbatively in Chern-Simons theory with scalar matter and show that the resulting functions of $\\omega/T$ agree with the strong coupling fermionic result. This provides a new test of the conjectured 3d bosonization duality. In matching the Hall conductivities we re...
Self-dual Chern-Simons theories
Dunne, Gerald
1995-01-01
Self-dual Chern-Simons theories form a new class of self-dual gauge theories and provide a field theoretical formulation of anyonic excitations in planar (i.e., two-space-dimensional) systems. Much of the recent attention of these theories is due to the surprising and novel ways in which they differ from the standard Maxwell, or Yang-Mills, gauge theories. These Chern-Simons theories are particular to planar systems and have therefore received added research impetus from recent experimental and theoretical breakthroughs in actual planar condensed-matter systems, such as the quantum Hall effect. This book gives a pedagogical introduction to the basic properties of the "self-dual" Chern-Simons theories, concluding with an overview of more advanced results and an extensive bibliography. Such models possess Bogomol'nyi energy bounds, topological charges, vortex solutions, and supersymmetric extensions, features which are familiar from other well-known self-dual systems such as instantons, monopoles, and vortices....
Localization at large N in Chern-Simons-matter theories
Marino, Marcos
2016-01-01
We review some exact results for the matrix models appearing in the localization of Chern-Simons-matter theories, focusing on the structure of non-perturbative effects and onthe M-theory expansion of ABJM theory. We also summarize some of the results obtained for other Chern-Simons-matter theories, as well as recent applications to topological strings.
Resurgence in complex Chern-Simons theory
Gukov, Sergei; Putrov, Pavel
2016-01-01
We study resurgence properties of partition function of SU(2) Chern-Simons theory (WRT invariant) on closed three-manifolds. We check explicitly that in various examples Borel transforms of asymptotic expansions posses expected analytic properties. In examples that we study we observe that contribution of irreducible flat connections to the path integral can be recovered from asymptotic expansions around abelian flat connections. We also discuss connection to Floer instanton moduli spaces, disk instantons in 2d sigma models, and length spectra of "complex geodesics" on the A-polynomial curve.
Perturbative Chern-Simons theory revisited
DEFF Research Database (Denmark)
McLellan, Brendan Donald Kenneth
2013-01-01
We reconsider perturbative Chern-Simons theory on a closed and oriented three-manifold with a choice of contact structure following C. Beasley and E. Witten. Closed three manifolds that admit a Sasakian structure are explicitly computed to first order in perturbation in terms of their Seifert data....... The general problem of extending this work to arbitrary three-manifolds is presented and some initial observations are made. Mathematically, this article is closely related to the work of Rumin and Seshadri and an index type theorem in the contact geometric setting....
Abelian Chern-Simons theory and contact torsion
DEFF Research Database (Denmark)
McLellan, Brendan Donald Kenneth
2013-01-01
Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected and abelian. A shift reduced abelian Chern-Simons partition function is introduced using an alternative formulation of the partition function using formal ideas in ...
Diamagnetic Vortices in Chern Simons Theory
Anber, Mohamed M; Sabancilar, Eray; Shaposhnikov, Mikhail
2015-01-01
We find a new type of topological vortex solution in the $U(1)_Z \\times U(1)_A$ Chern Simons gauge theory in the presence of a $U(1)_A$ magnetic field background. In this theory $U(1)_Z$ is broken spontaneously by the $U(1)_A$ magnetic field. These vortices exhibit long range interactions as they are charged under the unbroken $U(1)_A$. They deplete the $U(1)_A$ magnetic field near their core and also break both $C$ and $P$ symmetries. Understanding the nature of these vortices sheds light on the ground state structure of the superconductivity studied in [1]. We also study the Berezinsky-Kosterlitz-Thouless phase transition in this class of theories and point out that superconductivity can be achieved at high temperatures by increasing the $U(1)_A$ magnetic field.
Kinetic derivation of generalized phase space Chern-Simons theory
Hayata, Tomoya
2016-01-01
We study a kinetic theory in $2d$ phase space when all abelian Berry curvatures are nonzero. We derive the complete form of the Poisson brackets, and calculate transports induced by Berry curvatures. Then we construct the low-energy effective theory to reproduce the transports. Such an effective theory is given by the Chern-Simons theory in $1+2d$ dimensions. Some implications of the Chern-Simons theory are also discussed.
Level/rank Duality and Chern-Simons-Matter Theories
Hsin, Po-Shen
2016-01-01
We discuss in detail level/rank duality in three-dimensional Chern-Simons theories and various related dualities in three-dimensional Chern-Simons-matter theories. We couple the dual Lagrangians to appropriate background fields (including gauge fields, spin$_c$ connections and the metric). The non-trivial maps between the currents and the line operators in the dual theories is accounted for by mixing of these fields. In order for the duality to be valid we must add finite counterterms depending on these background fields. This analysis allows us to resolve a number of puzzles with these dualities, to provide derivations of some of them, and to find new consistency conditions and relations between them. In addition, we find new level/rank dualities of topological Chern-Simons theories and new dualities of Chern-Simons-matter theories, including new boson/boson and fermion/fermion dualities.
Wavefunction of the Universe and Chern-Simons perturbation theory
Energy Technology Data Exchange (ETDEWEB)
Soo Chopin [Department of Physics, National Cheng Kung University Tainan 70101, Taiwan (China)
2002-03-21
The Chern-Simons exact solution of four-dimensional quantum gravity with nonvanishing cosmological constant is presented in metric variables as the partition function of Chern-Simons theory with nontrivial source. The perturbative expansion is given, and the wavefunction is computed to the lowest order of approximation for the Cauchy surface which is topologically a 3-sphere. The state is well-defined even at degenerate and vanishing values of the dreibein. Reality conditions for the Ashtekar variables are also taken into account, and remarkable features of the Chern-Simons state and their relevance to cosmology are pointed out.
Chern-Simons theory in SIM(1) superspace
Energy Technology Data Exchange (ETDEWEB)
Vohanka, Jiri [Masaryk University, Department of Theoretical Physics and Astrophysics, Brno (Czech Republic); Faizal, Mir [University of Waterloo, Department of Physics and Astronomy, Waterloo, ON (Canada)
2015-12-15
In this paper,wewill analyze a three-dimensional supersymmetric Chern-Simons theory in SIM(1) superspace formalism. The breaking of the Lorentz symmetry down to the SIM(1) symmetry breaks half the supersymmetry of the Lorentz invariant theory. So, the supersymmetry of the Lorentz invariant Chern-Simons theory with N = 1 supersymmetry will break down to N = 1/2 supersymmetry, when the Lorentz symmetry is broken down to the SIM(1) symmetry. First, we will write the Chern-Simons action using SIM(1) projections ofN = 1 superfields. However, as the SIM(1) transformations of these projections are very complicated, we will define SIM(1) superfields which transform simply under SIM(1) transformations. We will then express the Chern-Simons action using these SIM(1) superfields. Furthermore, we will analyze the gauge symmetry of this Chern-Simons theory. This is the first time that a Chern-Simons theory with N = 1/2 supersymmetry will be constructed on a manifold without a boundary. (orig.)
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...
Disorder Operators in Chern-Simons-Fermion Theories
Radicevic, Djordje
2015-01-01
Building on the recent progress in solving Chern-Simons-matter theories in the planar limit, we compute the scaling dimensions of a large class of disorder ("monopole") operators in $U(N)_k$ Chern-Simons-fermion theories at all 't Hooft couplings $\\lambda = N/k$. We find that the lowest-dimension operator of this sort has dimension $\\frac23 k^{3/2}$. We comment on the implications of these results to analyzing maps of fermionic disorder operators under 3D bosonization.
Parity anomaly in D=3 Chern-Simons gauge theory
International Nuclear Information System (INIS)
Ultraviolet divergences are calcelled in the effective action of the D=3 Chern-Simons gauge theory but regularization is needed. It is impossible to introduce gauge invariant regularization and conserve the parity of the classical action. As a result, in the limit when regularization is moved the finite contribution to the effective action induced by parity violating regulators remains. 18 refs
A Lie based 4-dimensional higher Chern-Simons theory
Zucchini, Roberto
2015-01-01
We present and study a model of 4-dimensional higher Chern-Simons theory, special Chern-Simons (SCS) theory, instances of which have appeared in the string literature, whose symmetry is encoded in a skeletal semistrict Lie 2-algebra constructed from a compact Lie group with non discrete center. The field content of SCS theory consists of a Lie valued 2-connection coupled to a background closed 3-form. SCS theory enjoys a large gauge and gauge for gauge symmetry organized in an infinite dimensional strict Lie 2-group. The partition function of SCS theory is simply related to that of a topological gauge theory localizing on flat connections with degree 3 second characteristic class determined by the background 3-form. Finally, SCS theory is related to a 3-dimensional special gauge theory whose 2-connection space has a natural symplectic structure with respect to which the 1-gauge transformation action is Hamiltonian, the 2-curvature map acting as moment map.
A Lie based 4-dimensional higher Chern-Simons theory
Zucchini, Roberto
2016-05-01
We present and study a model of 4-dimensional higher Chern-Simons theory, special Chern-Simons (SCS) theory, instances of which have appeared in the string literature, whose symmetry is encoded in a skeletal semistrict Lie 2-algebra constructed from a compact Lie group with non discrete center. The field content of SCS theory consists of a Lie valued 2-connection coupled to a background closed 3-form. SCS theory enjoys a large gauge and gauge for gauge symmetry organized in an infinite dimensional strict Lie 2-group. The partition function of SCS theory is simply related to that of a topological gauge theory localizing on flat connections with degree 3 second characteristic class determined by the background 3-form. Finally, SCS theory is related to a 3-dimensional special gauge theory whose 2-connection space has a natural symplectic structure with respect to which the 1-gauge transformation action is Hamiltonian, the 2-curvature map acting as moment map.
Perturbative and nonperturbative aspects of complex Chern-Simons Theory
Dimofte, Tudor
2016-01-01
We present an elementary review of some aspects of Chern-Simons theory with complex gauge group SL(N,C). We discuss some of the challenges in defining the theory as a full-fledged TQFT, as well as some successes inspired by the 3d-3d correspondence. The 3d-3d correspondence relates partition functions (and other aspects) of complex Chern-Simons theory on a 3-manifold M to supersymmetric partition functions (and other observables) in an associated 3d theory T[M]. Many of these observables may be computed by supersymmetric localization. We present several prominent applications to 3-manifold topology and number theory in light of the 3d-3d correspondence.
Higher Spins from Nambu-Chern-Simons Theory
Arvanitakis, Alex S.
2016-07-01
We propose a new theory of higher spin gravity in three spacetime dimensions. This is defined by what we will call a Nambu-Chern-Simons (NCS) action; this is to a Nambu 3-algebra as an ordinary Chern-Simons (CS) action is to a Lie (2-)algebra. The novelty is that the gauge group of this theory is simple; this stands in contrast to previously understood interacting 3D higher spin theories in the frame-like formalism. We also consider the N = 8 supersymmetric NCS-matter model (BLG theory), where the NCS action originated: Its fully supersymmetric M2 brane configurations are interpreted as Hopf fibrations, the homotopy type of the (infinite) gauge group is calculated and its instantons are classified.
Higher spins from Nambu-Chern-Simons theory
Arvanitakis, Alex S
2015-01-01
We propose a new theory of higher spin gravity in three spacetime dimensions. This is defined by what we will call a Nambu-Chern-Simons (NCS) action; this is to a Nambu 3-algebra as an ordinary Chern-Simons (CS) action is to a Lie (2-)algebra. The novelty is that the gauge group of this theory is \\emph{simple}; this stands in contrast to previously understood interacting 3D higher spin theories in the frame-like formalism. We also consider the $N=8$ supersymmetric NCS-matter model (BLG theory), where the NCS action originated: Its fully supersymmetric M2 brane configurations are interpreted as Hopf fibrations, the homotopy type of the (infinite) gauge group is calculated and its instantons are classified.
Topological entanglement negativity in Chern-Simons theories
Wen, Xueda; Ryu, Shinsei
2016-01-01
We study the topological entanglement negativity between two spatial regions in (2+1)-dimensional Chern-Simons gauge theories by using the replica trick and the surgery method. For a bipartitioned or tripartitioned spatial manifold, we show how the topological entanglement negativity depends on the presence of quasiparticles and the choice of ground states. In particular, for two adjacent non-contractible regions on a tripartitioned torus, the entanglement negativity provides a simple way to distinguish Abelian and non-Abelian theories. Our method applies to a Chern-Simons gauge theory defined on an arbitrary oriented (2+1)-dimensional spacetime manifold. Our results agree with the edge theory approach in a recent work (X. Wen, S. Matsuura and S. Ryu, arXiv:1603.08534).
Topological entanglement negativity in Chern-Simons theories
Wen, Xueda; Chang, Po-Yao; Ryu, Shinsei
2016-09-01
We study the topological entanglement negativity between two spatial regions in (2+1)-dimensional Chern-Simons gauge theories by using the replica trick and the surgery method. For a bipartitioned or tripartitioned spatial manifold, we show how the topological entanglement negativity depends on the presence of quasiparticles and the choice of ground states. In particular, for two adjacent non-contractible regions on a tripartitioned torus, the entanglement negativity provides a simple way to distinguish Abelian and non-Abelian theories. Our method applies to a Chern-Simons gauge theory defined on an arbitrary oriented (2+1)-dimensional spacetime manifold. Our results agree with the edge theory approach in a recent work [35].
Combinatorial quantization of the Hamiltonian Chern-Simons theory II
Alekseev, Anton Yu.; Grosse, Harald; Schomerus, Volker
1996-01-01
This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory advertised in [1]. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of quantum group gauge theory. This allows to discuss flatness of quantum connections so that we can give a mathematically rigorous definition of the algebra of observables A CS of the Chern Simons model. It is a *-algebra of “functions on the quantum moduli space of flat connections” and comes equipped with a positive functional ω (“integration”). We prove that this data does not depend on the particular choices which have been made in the construction. Following ideas of Fock and Rosly [2], the algebra A CS provides a deformation quantization of the algebra of functions on the moduli space along the natural Poisson bracket induced by the Chern Simons action. We evaluate a volume of the quantized moduli space and prove that it coincides with the Verlinde number. This answer is also interpreted as a partition partition function of the lattice Yang-Mills theory corresponding to a quantum gauge group.
Higher-spin Chern-Simons theories in odd dimensions
Energy Technology Data Exchange (ETDEWEB)
Engquist, Johan [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands)], E-mail: j.engquist@phys.uu.nl; Hohm, Olaf [Institute for Theoretical Physics and Spinoza Institute, Utrecht University, 3508 TD Utrecht (Netherlands)], E-mail: o.hohm@phys.uu.nl
2007-12-10
We construct consistent bosonic higher-spin gauge theories in odd dimensions D>3 based on Chern-Simons forms. The gauge groups are infinite-dimensional higher-spin extensions of the anti-de Sitter groups SO(D-1,2). We propose an invariant tensor on these algebras, which is required for the definition of the Chern-Simons action. The latter contains the purely gravitational Chern-Simons theories constructed by Chamseddine, and so the entire theory describes a consistent coupling of higher-spin fields to a particular form of Lovelock gravity. It contains topological as well as non-topological phases. Focusing on D=5 we consider as an example for the latter an AdS{sub 4}xS{sup 1} Kaluza-Klein background. By solving the higher-spin torsion constraints in the case of a spin-3 field, we verify explicitly that the equations of motion reduce in the linearization to the compensator form of the Fronsdal equations on AdS{sub 4}.
Combinatorial quantization of the Hamiltonian Chern-Simons theory, 2
Alekseev, A Yu; Schomerus, V; Grosse, H; Schomerus, V
1994-01-01
This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory advertised in \\cite{AGS}. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of quantum group gauge theory. This allows to discuss flatness of quantum connections so that we can give a mathe- matically rigorous definition of the algebra of observables \\A_{CS} of the Chern Simons model. It is a *-algebra of ``functions on the quantum moduli space of flat connections'' and comes equipped with a positive functional \\omega (``integration''). We prove that this data does not depend on the particular choices which have been made in the construction. Following ideas of Fock and Rosly \\cite{FoRo}, the algebra \\A_{CS} provides a deformation quantization of the algebra of functions on the moduli space along the natural Poisson bracket induced by the Chern Simons action. We evaluate a volume of the quantized moduli space and prove that it coincides with the Verl...
L∞-algebra models and higher Chern-Simons theories
Ritter, Patricia; Sämann, Christian
2016-10-01
We continue our study of zero-dimensional field theories in which the fields take values in a strong homotopy Lie algebra. In the first part, we review in detail how higher Chern-Simons theories arise in the AKSZ-formalism. These theories form a universal starting point for the construction of L∞-algebra models. We then show how to describe superconformal field theories and how to perform dimensional reductions in this context. In the second part, we demonstrate that Nambu-Poisson and multisymplectic manifolds are closely related via their Heisenberg algebras. As a byproduct of our discussion, we find central Lie p-algebra extensions of 𝔰𝔬(p + 2). Finally, we study a number of L∞-algebra models which are physically interesting and which exhibit quantized multisymplectic manifolds as vacuum solutions.
Vortex solutions of PCT-invariant Maxwell-Dirac-Chern-Simons gauge theory
Shin, J
1997-01-01
We construct PCT-invariant Maxwell-Chern-Simons gauge theory coupled to fermions with adding the parity partner to the matter and the gauge field= s, which can give nontopological vortex solutions depending on the sign of t= he Chern-Simons coupling constant.
Framing and localization in Chern-Simons theories with matter
Bianchi, Marco S; Leoni, Matias; Mauri, Andrea; Penati, Silvia; Seminara, Domenico
2016-01-01
Supersymmetric localization provides exact results that should match QFT computations in some regularization scheme. The agreement is particularly subtle in three dimensions where complex answers from localization procedure sometimes arise. We investigate this problem by studying the expectation value of the 1/6 BPS Wilson loop in planar ABJ(M) theory at three loops in perturbation theory. We reproduce the corresponding term in the localization result and argue that it originates entirely from a non-trivial framing of the circular contour. Contrary to pure Chern-Simons theory, we point out that for ABJ(M) the framing phase is a non-trivial function of the couplings and that it potentially receives contributions from vertex-like diagrams. Finally, we briefly discuss the intimate link between the exact framing factor and the Bremsstrahlung function of the 1/2-BPS cusp.
Framing and localization in Chern-Simons theories with matter
Bianchi, Marco S.; Griguolo, Luca; Leoni, Matias; Mauri, Andrea; Penati, Silvia; Seminara, Domenico
2016-06-01
Supersymmetric localization provides exact results that should match QFT computations in some regularization scheme. The agreement is particularly subtle in three dimensions where complex answers from localization procedure sometimes arise. We investigate this problem by studying the expectation value of the 1/6 BPS Wilson loop in planar ABJ(M) theory at three loops in perturbation theory. We reproduce the corresponding term in the localization result and argue that it originates entirely from a non-trivial framing of the circular contour. Contrary to pure Chern-Simons theory, we point out that for ABJ(M) the framing phase is a non-trivial function of the couplings and that it potentially receives contributions from vertex-like diagrams. Finally, we briefly discuss the intimate link between the exact framing factor and the Bremsstrahlung function of the 1/2-BPS cusp.
Quantum modularity and complex Chern-Simons theory
Dimofte, Tudor
2015-01-01
The Quantum Modularity Conjecture of Zagier predicts the existence of a formal power series with arithmetically interesting coefficients that appears in the asymptotics of the Kashaev invariant at each root of unity. Our goal is to construct a power series from a Neumann-Zagier datum (i.e., an ideal triangulation of the knot complement and a geometric solution to the gluing equations) and a complex root of unity $\\zeta$. We prove that the coefficients of our series lie in the trace field of the knot, adjoined a complex root of unity. We conjecture that our series are those that appear in the Quantum Modularity Conjecture and confirm that they match the numerical asymptotics of the Kashaev invariant (at various roots of unity) computed by Zagier and the first author. Our construction is motivated by the analysis of singular limits in Chern-Simons theory with gauge group $SL(2,C)$ at fixed level $k$, where $\\zeta^k=1$.
Dynamical Chern-Simons Theory in the Brillouin Zone
Lian, Biao; Vafa, Farzan; Zhang, Shou-Cheng
2016-01-01
Berry connection is conventionally defined as a static gauge field in the Brillouin zone. Here we show that for three-dimensional (3d) time-reversal invariant superconductors, a generalized Berry gauge field behaves as a dynamical fluctuating field of a Chern-Simons gauge theory. The gapless nodal lines in the momentum space play the role of Wilson loop observables, while their linking and knot invariants modify the gravitational theta angle. This angle induces a topological gravitomagnetoelectric effect where a temperature gradient induces a rotational energy flow. We also show how topological strings may be realized in the 6 dimensional phase space, where the physical space defects play the role of topological D-branes.
Superconformal Chern-Simons-matter theories in N =4 superspace
Kuzenko, Sergei M.; Samsonov, Igor B.
2015-11-01
In three dimensions, every known N =4 supermultiplet has an off-shell completion. However, there is no off-shell N =4 formulation for the known extended superconformal Chern-Simons (CS) theories with eight and more supercharges. To achieve a better understanding of this issue, we provide N =4 superfield realizations for the equations of motion which correspond to various N =4 and N =6 superconformal CS theories, including the Gaiotto-Witten theory and the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. These superfield realizations demonstrate that the superconformal CS theories with N ≥4 (except for the Gaiotto-Witten theory) require a reducible long N =4 vector multiplet, from which the standard left and right N =4 vector multiplets are obtained by constraining the field strength to be either self-dual or antiself-dual. Such a long multiplet naturally originates upon reduction of any off-shell N >4 vector multiplet to N =4 superspace. For the long N =4 vector multiplet we develop a prepotential formulation. It makes use of two prepotentials being subject to the constraint which defines the so-called hybrid projective multiplets introduced in the framework of N =4 supergravity-matter systems in arXiv:1101.4013. We also couple N =4 superconformal CS theories to N =4 conformal supergravity.
Supersymmetric Chern-Simons theory in presence of a boundary in the light-like direction
Vohánka, Jiří; Faizal, Mir
2016-03-01
In this paper, we will analyze a three dimensional supersymmetric Chern-Simons theory on a manifold with a boundary. The boundary we will consider in this paper will be defined by n ṡ x = 0, where n is a light-like vector. It will be demonstrated that this boundary is preserved under the action of the SIM (1) subgroup of the Lorentz group. Furthermore, the presence of this boundary will break half of the supersymmetry of the original theory. As the original Chern-Simons theory had N = 1 supersymmetry in absence of a boundary, it will only have N = 1 / 2 supersymmetry in presence of this boundary. We will also observe that the Chern-Simons theory can be made gauge invariant by introducing new degrees of freedom on the boundary. The gauge transformation of these new degrees of freedom will exactly cancel the boundary term obtained from the gauge transformation of the Chern-Simons theory.
Eta-invariants and anomalies in U(1)-Chern-Simons theory
Jeffrey, Lisa
2010-01-01
This paper studies U(1)-Chern-Simons theory and its relation to a construction of Chris Beasley and Edward Witten. The natural geometric setup here is that of a three-manifold with a Seifert structure. Based on a suggestion of Edward Witten we are led to study the stationary phase approximation of the path integral for U(1)-Chern-Simons theory after one of the three components of the gauge field is decoupled. This gives an alternative formulation of the partition function for U(1)-Chern-Simons theory that is conjecturally equivalent to the usual U(1)-Chern-Simons theory. The goal of this paper is to establish this conjectural equivalence rigorously through appropriate regularization techniques. This approach leads to some rather surprising results and opens the door to studying hypoelliptic operators and their associated eta invariants in a new light.
Wave function of the Universe and Chern-Simons Perturbation Theory
Soo, C P
2002-01-01
The Chern-Simons exact solution of four-dimensional quantum gravity with nonvanishing cosmological constant is presented in metric variable as the partition function of a Chern-Simons theory with nontrivial source. The perturbative expansion is given, and the wave function is computed to the lowest order of approximation for the Cauchy surface which is topologically a 3-sphere. The state is well-defined even at degenerate and vanishing values of the dreibein. Reality conditions for the Ashtekar variables are also taken into account; and remarkable features of the Chern-Simons state and their relevance to cosmology are pointed out.
Embedded graph invariants in Chern-Simons theory
International Nuclear Information System (INIS)
Chern-Simons gauge theory, since its inception as a topological quantum field theory, has proved to be a rich source of understanding for knot invariants. In this work the theory is used to explore the definition of the expectation value of a network of Wilson lines -- an embedded graph invariant. Using a generalization of the variational method, lowest-order results for invariants for graphs of arbitrary valence and general vertex tangent space structure are derived. Gauge invariant operators are introduced. Higher order results are found. The method used here provides a Vassiliev-type definition of graph invariants which depend on both the embedding of the graph and the group structure of the gauge theory. It is found that one need not frame individual vertices. However, without a global projection of the graph there is an ambiguity in the relation of the decomposition of distinct vertices. It is suggested that framing may be seen as arising from this ambiguity -- as a way of relating frames at distinct vertices
Matrix Model of Chern-Simons Matter Theories Beyond The Spherical Limit
Yokoyama, Shuichi
2016-01-01
A general class of matrix models which arises as partition function in U(N) Chern-Simons matter theories on three sphere is investigated. Employing the standard technique of the 1/N expansion we solve the system beyond the planar limit. We confirm that the subleading correction in the free energy correctly reproduces the one obtained by expanding the past exact result in the case of pure Chern-Simons theory.
Maxwell-Chern-Simons theory for curved spacetime backgrounds
International Nuclear Information System (INIS)
We consider a modified version of four-dimensional electrodynamics, which has a photonic Chern-Simons-like term with spacelike background vector in the action. Light propagation in curved spacetime backgrounds is discussed using the geometrical-optics approximation. The corresponding light path is modified, which allows for new effects. In a Schwarzschild background, for example, there now exist stable bounded orbits of light rays and the two polarization modes of light rays in unbounded orbits can have different gravitational redshifts
A Higher-Spin Chern-Simons Theory of Anyons
Boulanger, Nicolas; Valenzuela, Mauricio
2013-01-01
We propose Chern-Simons models of fractional-spin fields interacting with ordinary tensorial higher-spin fields and internal color gauge fields. For integer and half-integer values of the fractional spins, the model reduces to finite sets of fields modulo infinite-dimensional ideals. We present the model on-shell using Fock-space representations of the underlying deformed-oscillator algebra.
On supersymmetric Chern-Simons-type theories in five dimensions
Energy Technology Data Exchange (ETDEWEB)
Kuzenko, Sergei M.; Novak, Joseph [School of Physics M013, The University of Western Australia,35 Stirling Highway, Crawley W.A. 6009 (Australia)
2014-02-24
We present a closed-form expression for the supersymmetric non-Abelian Chern-Simons action in conventional five-dimensional N=1 superspace. Our construction makes use of the superform formalism to generate supersymmetric invariants. Similar ideas are applied to construct supersymmetric actions for off-shell supermultiplets with an intrinsic central charge. In particular, the large tensor supermultiplet is described in superspace for the first time.
Black hole entropy and SU(2) Chern-Simons theory
Engle, Jonathan; Noui, Karim; Perez, Alejandro
2009-01-01
Black holes in equilibrium can be defined locally in terms of the so-called isolated horizon boundary condition given on a null surface representing the event horizon. We show that this boundary condition can be treated in a manifestly SU(2) invariant manner. Upon quantization, state counting is expressed in terms of the dimension of Chern-Simons Hilbert spaces on a sphere with marked points. Moreover, the counting can be mapped to counting the number of SU(2) intertwiners compatible with the...
On the Chern-Simons State in General Relativity and Modified Gravity Theories
International Nuclear Information System (INIS)
The Chern-Simons state is one solution to quantum constraints of gravity in the context of general relativity (GR) theory if we use Ashtekar's variables and if one orders the constraints with the triads to the left. Six years ago Krasnov introduced a certain class of modified gravity theories by replacing the cosmological constant by a cosmological function of the curvature. If this function is a constant we come back to GR. In this note we review how the Chern-Simons state is one solution to the constraints of GR and we state the problem to face if we wish a generalized Chern-Simons state for the modified Krasnov's theories
3D gravity with torsion as a Chern-Simons gauge theory
Blagojevic, M; Vasilic, M.
2003-01-01
We show that topological 3D gravity with torsion can be formulated as a Chern-Simons gauge theory, provided a specific parameter, known as the effective cosmological constant, is negative. In that case, the boundary dynamics of the theory corresponding to anti-de Sitter boundary conditions is described by a conformal field theory with two different central charges.
Chern-Simons theory for frustrated quantum magnets
Kumar, Krishna; Fradkin, Eduardo
2013-03-01
We study the problem of frustrated quantum magnets by mapping models with Heisenberg spins, which are hard-core bosons, onto a problem of fermions coupled to a Chern-Simons gauge field. Similar methods have been used successfully in the case of unfrustrated systems like the square lattice. However, in the case of frustrated systems there always exists some arbitrariness in defining the problem. At the mean-field level these issues can be over looked but the effects of fluctuations, which are generally strong in these systems, are expected to alter the mean-field physics. We discuss the difficulties involved in setting up this problem on a triangular or kagome lattice and some approaches to tackle these issues. We study the effects of fluctuations in these systems and the possibility of spin-liquid type phases.
Black hole entropy and SU(2) Chern-Simons theory.
Engle, Jonathan; Noui, Karim; Perez, Alejandro
2010-07-16
Black holes (BH's) in equilibrium can be defined locally in terms of the so-called isolated horizon boundary condition given on a null surface representing the event horizon. We show that this boundary condition can be treated in a manifestly SU(2) invariant manner. Upon quantization, state counting is expressed in terms of the dimension of Chern-Simons Hilbert spaces on a sphere with punctures. Remarkably, when considering an ensemble of fixed horizon area a(H), the counting can be mapped to simply counting the number of SU(2) intertwiners compatible with the spins labeling the punctures. The resulting BH entropy is proportional to a(H) with logarithmic corrections ΔS=-3/2 loga(H). Our treatment from first principles settles previous controversies concerning the counting of states. PMID:20867755
Light-like polygonal Wilson loops in 3d Chern-Simons and ABJM theory
Henn, Johannes M.; Plefka, Jan; Wiegandt, Konstantin
2010-01-01
We study light-like polygonal Wilson loops in three-dimensional Chern-Simons and ABJM theory to two-loop order. For both theories we demonstrate that the one-loop contribution to these correlators cancels. For pure Chern-Simons, we find that specific UV divergences arise from diagrams involving two cusps, implying the loss of finiteness and topological invariance at two-loop order. Studying those UV divergences we derive anomalous conformal Ward identities for n-cusped Wilson loops which rest...
Path-integral measure for Chern-Simons theory within the stochastic quantization approach
International Nuclear Information System (INIS)
We discuss how the dependence of the path-integral measure on the metric affects the generating functional for the d=3 Chern-Simons theory. Using the stochastic quantization, we show that the choice of an invariant measure preserves the topological character of the theory. (author). 18 refs
Chern-Simons Invariants on Hyperbolic Manifolds and Topological Quantum Field Theories
Bonora, Loriano; Goncalves, Antonio E
2016-01-01
We derive formulas for the classical Chern-Simons invariant of irreducible $SU(n)$-flat connections on negatively curved locally symmetric three-manifolds. We determine the condition for which the theory remains consistent (with basic physical principles). We show that a connection between holomorphic values of Selberg-type functions at point zero, associated with R-torsion of the flat bundle, and twisted Dirac operators acting on negatively curved manifolds, can be interpreted by means of the Chern-Simons invariant. On the basis of Labastida-Marino-Ooguri-Vafa conjecture we analyze a representation of the Chern-Simons quantum partition function (as a generating series of quantum group invariants) in the form of an infinite product weighted by S-functions and Selberg-type functions. We consider the case of links and a knot and use the Rogers approach to discover certain symmetry and modular form identities.
Chern-Simons Supersymmetric Branes
Mora, P
2001-01-01
In this paper we continue the study of the model proposed in the previous paper hep-th/0002077. The model consist of a system of extended objects of diverse dimensionalities, with or without boundaries, with actions of the Chern-Simons form for a supergroup. We also discuss possible connections with Superstring/M-theory.
Nonrelativistic Chern-Simons theories and three-dimensional Hořava-Lifshitz gravity
Hartong, Jelle; Lei, Yang; Obers, Niels A.
2016-09-01
We show that certain three-dimensional Hořava-Lifshitz gravity theories can be written as Chern-Simons gauge theories on various nonrelativistic algebras. The algebras are specific extensions of the Bargmann, Newton-Hooke and Schrödinger algebras each of which has the Galilean algebra as a subalgebra. To show this we employ the fact that Hořava-Lifshitz gravity corresponds to dynamical Newton-Cartan geometry. In particular, the extended Bargmann (Newton-Hooke) Chern-Simons theory corresponds to projectable Hořava-Lifshitz gravity with a local U (1 ) gauge symmetry without (with) a cosmological constant. Moreover we identify an extended Schrödinger algebra containing three extra generators that are central with respect to the subalgebra of Galilean boosts, momenta and rotations, for which the Chern-Simons theory gives rise to a novel version of nonprojectable conformal Hořava-Lifshitz gravity that we refer to as Chern-Simons Schrödinger gravity. This theory has a z =2 Lifshitz geometry as a vacuum solution and thus provides a new framework to study Lifshitz holography.
Probing Wilson loops in N = 4 Chern-Simons-matter theories at weak coupling
Griguolo, Luca; Leoni, Matias; Mauri, Andrea; Penati, Silvia; Seminara, Domenico
2016-02-01
For three-dimensional N = 4 super-Chern-Simons-matter theories associated to necklace quivers U (N0) × U (N1) × ⋯ U (N 2 r - 1), we study at quantum level the two kinds of 1/2 BPS Wilson loop operators recently introduced http://arxiv.org/abs/1507
Canonical quantization of the WZW model with defects and Chern-Simons theory
DEFF Research Database (Denmark)
Sarkissian, Gor
2010-01-01
We perform canonical quantization of the WZW model with defects and permutation branes. We establish symplectomorphism between phase space of WZW model with $N$ defects on cylinder and phase space of Chern-Simons theory on annulus times $R$ with $N$ Wilson lines, and between phase space of WZW...
Asymptotic completeness and the three-dimensional gauge theory having the Chern-Simon term
International Nuclear Information System (INIS)
The three-dimensional Abelian gauge theory having the Chern-Simon term is studied. When matter current is absent, the gauge field in covariant gauge is explicitly expressed in terms of asymptotic fields. It is shown that the mechanism of mass generation can be understood as a kind of the Higgs mechanism
Quaternion based generalization of Chern-Simons theories in arbitrary dimensions
D'Adda, Alessandro; Shimode, Naoki; Tsukioka, Takuya
2016-01-01
A generalization of Chern-Simons gauge theory is formulated in any dimension and arbitrary gauge group where gauge fields and gauge parameters are differential forms of any degree. The quaternion algebra structure of this formulation is shown to be equivalent to a three Z(2)-gradings structure, thus clarifying the quaternion role in a previous formulation.
Eigenvalue distributions in matrix models for Chern-Simons-matter theories
International Nuclear Information System (INIS)
The eigenvalue distribution is investigated for matrix models related via the localization to Chern-Simons-matter theories. An integral representation of the planar resolvent is used to derive the positions of the branch points of the planar resolvent in the large 't Hooft coupling limit. Various known exact results on eigenvalue distributions and the expectation value of Wilson loops are reproduced.
SL(2,C) Chern-Simons Theory and Quantum Gravity with a Cosmological Constant
Haggard, Hal; Han, Muxin; Kaminski, Wojciech; Riello, Aldo
2015-04-01
We show a relation between 4-dimensional quantum gravity with a cosmological constant and SL(2,C) Chern-Simons theory in 3-dimensions with knotted graph defects. In particular, we study the expectation value of a non-planar Wilson graph operator in SL(2,C) Chern-Simons theory on S3. We analyze its asymptotic behavior in the double-scaling limit in which both the representation labels and the Chern-Simons coupling are taken to be large, but with fixed ratio. We find that a class of flat connections in the graph complement manifold are in correspondence with the geometries of constant curvature 4-simplices. We show that the asymptotic behavior of the amplitude contains an oscillatory part proportional to the Regge action for the single 4-simplex in the presence of a cosmological constant. In particular, the cosmological term contains the full-fledged curved volume of the 4-simplex. Interestingly, the volume term stems from the asymptotics of the Chern-Simons action. Another peculiarity of our approach is that the sign of the curvature of the reconstructed geometry, and hence of the cosmological constant in the Regge action, is not fixed a priori, but rather emerges semiclassically and dynamically from the solution of the equations of motion. This work was supported by the U.S. National Science Foundation, the European Marie Curie actions, and the Perimeter Institute.
Inner Structure of Statistical Gauge Potential in Chern-Simons-Ginzburg-Landau Theory
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Based on the decomposition theory of the U(1) gauge potential, the inner structure of the statistical gauge potential in the Chern-Simons-Ginzburg-Landau (CSGL) theory is studied. We give a new creation mechanism of the statistical gauge potential. Furthermore, making use of the φ-mapping topological current theory, we obtain the precise topological expression of the statistical magnetic field, which takes the topological information of the vortices.
Analytic Torsion, 3d Mirror Symmetry And Supergroup Chern-Simons Theories
Mikhaylov, Victor
2015-01-01
We consider topological field theories that compute the Reidemeister-Milnor-Turaev torsion in three dimensions. These are the psl(1|1) and the U(1|1) Chern-Simons theories, coupled to a background complex flat gauge field. We use the 3d mirror symmetry to derive the Meng-Taubes theorem, which relates the torsion and the Seiberg-Witten invariants, for a three-manifold with arbitrary first Betti number. We also present the Hamiltonian quantization of our theories, find the modular transformations of states, and various properties of loop operators. Our results for the U(1|1) theory are in general consistent with the results, found for the GL(1|1) WZW model. We also make some comments on more general supergroup Chern-Simons theories.
Quantum Spectral Curve of the N =6 Supersymmetric Chern-Simons Theory
Cavaglià, Andrea; Fioravanti, Davide; Gromov, Nikolay; Tateo, Roberto
2014-07-01
Recently, it was shown that the spectrum of anomalous dimensions and other important observables in planar N=4 supersymmetric Yang-Mills theory are encoded into a simple nonlinear Riemann-Hilbert problem: the Pμ system or quantum spectral curve. In this Letter, we extend this formulation to the N =6 supersymmetric Chern-Simons theory introduced by Aharony, Bergman, Jafferis, and Maldacena. This may be an important step towards the exact determination of the interpolating function h(λ) characterizing the integrability of this model. We also discuss a surprising relation between the quantum spectral curves for the N=4 supersymmetric Yang-Mills theory and the N=6 supersymmetric Chern-Simons theory considered here.
Holographic Chern-Simons Defects
Fujita, Mitsutoshi; Meyer, Rene; Sugimoto, Shigeki
2016-01-01
We study SU(N) Yang-Mills-Chern-Simons theory in the presence of defects that shift the Chern-Simons level from a holographic point of view by embedding the system in string theory. The model is a D3-D7 system in Type IIB string theory, whose gravity dual is given by the AdS soliton background with probe D7-branes attaching to the AdS boundary along the defects. We holographically renormalize the free energy of the defect system with sources, from which we obtain the correlation functions for certain operators naturally associated to these defects. We find interesting phase transitions when the separation of the defects as well as the temperature are varied. We also discuss some implications for the Fractional Quantum Hall Effect and for two-dimensional QCD.
Holographic Chern-Simons defects
Fujita, Mitsutoshi; Melby-Thompson, Charles M.; Meyer, René; Sugimoto, Shigeki
2016-06-01
We study SU( N ) Yang-Mills-Chern-Simons theory in the presence of defects that shift the Chern-Simons level from a holographic point of view by embedding the system in string theory. The model is a D3-D7 system in Type IIB string theory, whose gravity dual is given by the AdS soliton background with probe D7 branes attaching to the AdS boundary along the defects. We holographically renormalize the free energy of the defect system with sources, from which we obtain the correlation functions for certain operators naturally associated to these defects. We find interesting phase transitions when the separation of the defects as well as the temperature are varied. We also discuss some implications for the Fractional Quantum Hall Effect and for 2-dimensional QCD.
BPS operators from the Wilson loop in the 3-dimensional supersymmetric Chern-Simons theory
Fujita, Mitsutoshi
2009-01-01
We consider the small deformation of the pointlike Wilson loop in the 3-dimensional N=6 superconformal Chern-Simons theory. By Taylor expansion of the pointlike Wilson loop in powers of the loop variables, we obtain the BPS operators that correspond to the excited string states of the dual IIA string theory on the pp wave background. The BPS conditions of the Wilson loop constrain both the loop variables and the forms of the operators obtained in the Taylor expansion.
Split Chern-Simons theory in the BV-BFV formalism
Cattaneo, Alberto; Wernli, Konstantin
2015-01-01
The goal of this note is to give a brief overview of the BV-BFV formalism developed by the first two authors and Reshetikhin in [arXiv:1201.0290], [arXiv:1507.01221] in order to perform perturbative quantisation of Lagrangian field theories on manifolds with boundary, and present a special case of Chern-Simons theory as a new example.
Kauffman, Louis H.
This paper is an exposition of the relationship between Witten's Chern-Simons functional integral and the theory of Vassiliev invariants of knots and links in three-dimensional space. We conceptualize the functional integral in terms of equivalence classes of functionals of gauge fields and we do not use measure theory. This approach makes it possible to discuss the mathematics intrinsic to the functional integral rigorously and without functional integration. Applications to loop quantum gravity are discussed.
Noncommutative Chern-Simons theory and exotic geometry emerging from the lowest Landau level
Luo, Xi; Wu, Yong-Shi; Yu, Yue
2016-06-01
We relate the collective dynamic internal geometric degrees of freedom to the gauge fluctuations in ν =1 /m (m odd ) fractional quantum Hall effects. In this way, in the lowest Landau level, a highly nontrivial quantum geometry in two-dimensional guiding center space emerges from these internal geometric modes. Using the Dirac bracket method, we find that this quantum geometric field theory is a topological noncommutative Chern-Simons theory. Topological indices, such as the guiding center angular momentum (also called the shift) and the guiding center spin, which characterize the fractional quantum Hall (FQH) states besides the filling factor, are naturally defined. A noncommutative K-matrix Chern-Simons theory is proposed as a generalization to a large class of Abelian FQH topological orders.
Non-Abelian T-duality, G 2-structure rotation and holographic duals of = 1 Chern-Simons theories
Macpherson, Niall T.
2013-11-01
A new dynamic SU(3)-structure solution in type-IIA is found by T-dualising a deformation of the Maldacena-Nastase solution along an SU(2) isometry. It is argued that this is dual to a quiver gauge theory with multiple Chern-Simons levels. A clear way of defining Chern-Simons levels in terms of Page charges is presented, which is also used to define a Chern-Simons term for the G 2-structure analogue of Klebanov-Strassler, providing evidence of a cascade in both the ranks and levels of the dual quiver.
Light States in Chern-Simons Theory Coupled to Fundamental Matter
Banerjee, Shamik; Maltz, Jonathan; Shenker, Stephen H
2012-01-01
Motivated by developments in vectorlike holography, we study SU(N) Chern-Simons theory coupled to matter fields in the fundamental representation on various spatial manifolds. On the spatial torus T^2, we find light states at small `t Hooft coupling \\lambda=N/k, where k is the Chern-Simons level, taken to be large. In the free scalar theory the gaps are of order \\sqrt {\\lambda}/N and in the critical scalar theory and the free fermion theory they are of order \\lambda/N. The entropy of these states grows like N Log(k). We briefly consider spatial surfaces of higher genus. Based on results from pure Chern-Simons theory, it appears that there are light states with entropy that grows even faster, like N^2 Log(k). This is consistent with the log of the partition function on the three sphere S^3, which also behaves like N^2 Log(k). These light states require bulk dynamics beyond standard Vasiliev higher spin gravity to explain them.
Non-Relativistic Chern-Simons Theories and Three-Dimensional Horava-Lifshitz Gravity
Hartong, Jelle; Obers, Niels A
2016-01-01
We show that certain three-dimensional Horava-Lifshitz gravity theories can be written as Chern-Simons gauge theories on various non-relativistic algebras. The algebras are specific extensions of the Bargmann, Newton-Hooke and Schroedinger algebra each of which has the Galilean algebra as a subalgebra. To show this we employ the fact that Horava-Lifshitz gravity corresponds to dynamical Newton-Cartan geometry. In particular, the extended Bargmann (Newton-Hooke) Chern-Simons theory corresponds to projectable Horava-Lifshitz gravity with a local U(1) gauge symmetry without (with) a cosmological constant. Moreover we identify an extended Schroedinger algebra containing 3 extra generators that are central with respect to the subalgebra of Galilean boosts, momenta and rotations, for which the Chern-Simons theory gives rise to a novel version of non-projectable conformal Horava-Lifshitz gravity that we refer to as Schroedinger gravity. This theory has a z=2 Lifshitz geometry as a vacuum solution and thus provides a...
Torsion as a Gauge Field in a Lorentz-Chern-Simons Theory
del Pino, Simón
2016-01-01
We explore a model of gravity that arises from the consideration of the Chern-Simons form in 2+1 dimensions for a spin connection with a contorsion described by a scalar and a vector field. The effective Lagrangian presents a local Weyl symmetry allowing us to gauge the scalar field to a constant value. From a gauge field theory perspective, it is shown that the vector part of the torsion (related to its trace) is a gauge field for the Weyl group, which allows the interpretation of the torsion as an electromagnetic field. In the gauge of constant scalar field we obtain Chiral Gravity coupled to a Chern-Simons-Proca theory for the vector field, that at the level of equations of motion is equivalent to Topologically Massive Electrodynamics minimally coupled to Chiral Gravity. Electrodynamics and gravity appear here unified as geometrical features of a Riemann-Cartan manifold.
Supersymmetry, quantum gauge anomalies and generalized Chern-Simons terms in chiral gauge theory
Energy Technology Data Exchange (ETDEWEB)
Schmidt, Torsten
2009-05-13
The purpose of this thesis is to investigate the interplay of anomaly cancellation and generalized Chern-Simons terms in four-dimensional chiral gauge theory. We start with a detailed discussion of generalized Chern-Simons terms with the canellation of anomalies via the Green-Schwarz mechanism. With this at hand, we investigate the situation in general N=1 supersymmetric field theories with generalized Chern-Simons terms. Two simple consistency conditions are shown to encode strong constraints on the allowed anomalies for different types of gauge groups. In one major part of this thesis we are going to display to what extent one has to modify the existing formalism in order to allow for the cancellation of quantum gauge anomalies via the Green-Schwarz mechanism. At the end of this thesis we comment on a puzzle in the literature on supersymmetric field theories with massive tensor fields. The potential contains a term that does not arise from eliminating an auxiliary field. We clarify the origin of this term and display the relation to standard D-term potential. In an appendix it is explicitly shown how these low energy effective actions might be connected to the formulation of four-dimensional gauge theories discussed at earlier stages of this thesis. (orig.)
Refined BPS invariants, Chern-Simons theory, and the quantum dilogarithm
Dimofte, Tudor Dan
In this thesis, we consider two main subjects: the refined BPS invariants of Calabi-Yau threefolds, and three-dimensional Chern-Simons theory with complex gauge group. We study the wall-crossing behavior of refined BPS invariants using a variety of techniques, including a four-dimensional supergravity analysis, statistical-mechanical melting crystal models, and relations to new mathematical invariants. We conjecture an equivalence between refined invariants and the motivic Donaldson-Thomas invariants of Kontsevich and Soibelman. We then consider perturbative Chern-Simons theory with complex gauge group, combining traditional and novel approaches to the theory (including a new state integral model) to obtain exact results for perturbative partition functions. We thus obtain a new class of topological invariants, which are not of finite type, defined in the background of genuinely nonabelian flat connections. The two main topics, BPS invariants and Chern-Simons theory, are connected at both a formal and (we believe) deeper conceptual level by the striking central role that the quantum dilogarithm function plays in each.
Supersymmetry, quantum gauge anomalies and generalized Chern-Simons terms in chiral gauge theory
International Nuclear Information System (INIS)
The purpose of this thesis is to investigate the interplay of anomaly cancellation and generalized Chern-Simons terms in four-dimensional chiral gauge theory. We start with a detailed discussion of generalized Chern-Simons terms with the canellation of anomalies via the Green-Schwarz mechanism. With this at hand, we investigate the situation in general N=1 supersymmetric field theories with generalized Chern-Simons terms. Two simple consistency conditions are shown to encode strong constraints on the allowed anomalies for different types of gauge groups. In one major part of this thesis we are going to display to what extent one has to modify the existing formalism in order to allow for the cancellation of quantum gauge anomalies via the Green-Schwarz mechanism. At the end of this thesis we comment on a puzzle in the literature on supersymmetric field theories with massive tensor fields. The potential contains a term that does not arise from eliminating an auxiliary field. We clarify the origin of this term and display the relation to standard D-term potential. In an appendix it is explicitly shown how these low energy effective actions might be connected to the formulation of four-dimensional gauge theories discussed at earlier stages of this thesis. (orig.)
Chern-Simons Theory with Complex Gauge Group on Seifert Fibred 3-Manifolds
Blau, Matthias
2016-01-01
We consider Chern-Simons theory with complex gauge group and present a complete non-perturbative evaluation of the path integral (the partition function and certain expectation values of Wilson loops) on Seifert fibred 3-Manifolds. We use the method of Abelianisation. In certain cases the path integral can be seen to factorize neatly into holomorphic and anti-holomorphic parts. We obtain closed formulae of this factorization for the expectation values of torus knots.
Noncommutative Maxwell-Chern-Simons theory (I): One-loop dispersion relation analysis
Ghasemkhani, M.; Bufalo, R.
2015-01-01
In this paper, we study the three-dimensional noncommutative Maxwell-Chern-Simons theory. In the present analysis, a complete account for the gauge field two-point function renormalizability is presented and physical significant quantities are carefully established. The respective form factor expressions from the gauge field self-energy are computed at one-loop order. More importantly, an analysis of the gauge field dispersion relation, in search of possible noncommutative anomalies and infra...
Noncommutative Maxwell-Chern-Simons theory (I): One-loop dispersion relation analysis
Ghasemkhani, M
2015-01-01
In this paper we study the three-dimensional noncommutative Maxwell-Chern-Simons theory. In the present analysis, a complete account for the gauge field two-point function renormalizability is presented and physical significant quantities are carefully established. We compute the respective form factor expressions from the gauge field self-energy at one-loop order. Moreover, a detailed discussion on the gauge field dispersion relation is presented for three particular cases, with particular interest in the highly noncommutative limit.
Monopole operators in N=4 Chern-Simons theories and wrapped M2-branes
Imamura, Yosuke
2009-01-01
Monopole operators in Abelian N=4 Chern-Simons theories described by circular quiver diagrams are investigated. The magnetic charges of non-diagonal U(1) gauge symmetries form the SU(p)xSU(q) root lattice where p and q are numbers of untwisted and twisted hypermultiplets, respectively. For monopole operators corresponding to the roots, we propose a correspondence between the monopole operators and states of a wrapped M2-brane in the dual geometry.
Asymptotically flat, stable black hole solutions in Einstein-Yang-Mills-Chern-Simons theory.
Brihaye, Yves; Radu, Eugen; Tchrakian, D H
2011-02-18
We construct finite mass, asymptotically flat black hole solutions in d=5 Einstein-Yang-Mills-Chern-Simons theory. Our results indicate the existence of a second order phase transition between Reissner-Nordström solutions and the non-Abelian black holes which generically are thermodynamically preferred. Some of the non-Abelian configurations are also stable under linear, spherically symmetric perturbations. PMID:21405506
F-theorem, duality and SUSY breaking in one-adjoint Chern-Simons-Matter theories
Morita, Takeshi
2011-01-01
We extend previous work on N=2 Chern-Simons theories coupled to a single adjoint chiral superfield using localization techniques and the F-maximization principle. We provide tests of a series of proposed 3D Seiberg dualities and a new class of tests of the conjectured F-theorem. In addition, a proposal is made for a modification of the F-maximization principle that takes into account the effects of decoupling fields. Finally, we formulate and provide evidence for a new general non-perturbative constraint on spontaneous supersymmetry breaking in three dimensions based on Q-deformed S^3 partition functions computed via localization. An explicit illustration based on the known analytic solution of the Chern-Simons matrix model is presented.
Chern-Simons theory for Heisenberg spins on the Kagome Lattice
Kumar, Krishna; Sun, Kai; Fradkin, Eduardo
2015-03-01
We study the problem of Heisenberg spins on the frustrated Kagome lattice using a 2D Jordan-Wigner transformation that maps the spins (hard-core bosons) onto a system of (interacting) fermions coupled to a Chern-Simons gauge field. This mapping requires us to define a discretized version of the Chern-Simons term on the lattice. Using a recently developed result on how to define Chern-Simons theories on a class of planar lattices, we can consistently study spin models beyond the mean-field level and include the effects of fluctuations, which are generally strong in frustrated systems. Here, we apply these results to study magnetization plateau type states on the Kagome lattice in the regime of XY anisotropy. We find that the 1/3 and 2/3 magnetization plateaus are chiral spin liquid states equivalent to a primary Laughlin fractional quantum Hall state of bosons with (spin) Hall conductivity 1/2 1/4 π and semionic excitations. The 5/9 plateau is a chiral spin liquid equivalent to the first Jain descendant. We also consider the spin-1/2 Heisenberg model on the Kagome lattice with a chirality-breaking term on the triangular plaquettes. This situation also leads to a primary Laughlin bosonic fractional quantum Hall type state with filling fraction 1 / 2 .
Blázquez-Salcedo, Jose Luis; Navarro-Lérida, Francisco; Radu, Eugen
2016-01-01
We consider rotating black hole solutions in five-dimensional Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant and a generic value of the Chern-Simons coupling constant $\\lambda$. Using both analytical and numerical techniques, we focus on cohomogeneity-1 configurations, with two equal-magnitude angular momenta, which approach at infinity a globally AdS background. We find that the generic solutions share a number of basic properties with the known Cvetic, L\\"u and Pope black holes which have $\\lambda=1$. New features occur as well, for example, when the Chern-Simons coupling constant exceeds a critical value, the solutions are no longer uniquely determined by their global charges. Moreover, the black holes possess radial excitations which can be labelled by the node number of the magnetic gauge potential function. Solutions with small values of $\\lambda$ possess other distinct features. For instance, the extremal black holes there form two disconnected branches, while not all near-h...
Instability of Chern-Simons Theory with Fermions at Large N
Zhang, Chen
2016-01-01
We study the (in)stability around the dynamical gap solution of the $U(N)$ Chern-Simons gauge theory with fundamental fermions (massless or massive) coupled in $D=3$ at large $N$. Explicit analyses on both the Auxiliary-Field (AF) and the Cornwall-Jackiw-Tomboulis (CJT) effective potentials are given. In both approaches we manage to analytically identify the saddle-point instability around the gap solution. We also give a comparison with the QCD-like theories. This study can help understanding the scale symmetry breaking picture of this theory.
Evolution of Nielsen-Olesen's String from Chern-Simons Field Theory
Institute of Scientific and Technical Information of China (English)
DUAN Yi-Shi; SHI Xu-Guang
2007-01-01
We study the topology of Nielsen-Olesen's local field theory of single dual string. Based on the Chern-Simons field theory in three dimensons, we find many strings that can form world sheets in four dimensions. These strings have important relation to the zero point of the complex scalar field. These world sheets of strings can be expressed by the topological invariant number, Hopf index, and Brower degree. Nambu-Goto's action is obtained from the Nielsen's action definitely by using o-mapping theory.
Large N phase transitions in supersymmetric Chern-Simons theory with massive matter
International Nuclear Information System (INIS)
We study three-dimensional N=2U(N) Chern-Simons theory on S3 coupled to 2Nf chiral multiplets deformed by mass terms. The partition function localizes to a matrix integral, which can be exactly computed in the large N limit. In a specific decompactification limit, the theory exhibits quantum (third-order) phase transitions at finite critical values of the coupling. The theory presents three phases when 0
BPS operators from the Wilson loop in the 3-dimensional supersymmetric Chern-Simons theory
Fujita, Mitsutoshi
2009-01-01
We consider the small deformation of the point-like Wilson loop in the 3-dimensional $\\mathcal{N}=6$ superconformal Chern-Simons theory. By Taylor expansion of the point-like Wilson loop in powers of the loop variables, we obtain the BPS operators that correspond to the excited string states of the dual IIA string theory on the pp wave background. The BPS conditions of the Wilson loop constrain both the loop variables and the forms of the operators obtained in the Taylor expansion.
Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories
Marino, Marcos
2011-01-01
In these lectures I give a pedagogical presentation of some of the recent progress in supersymmetric Chern-Simons-matter theories, coming from the use of localization and matrix model techniques. The goal is to provide a simple derivation of the exact interpolating function for the free energy of ABJM theory on the three-sphere, which implies in particular the N^{3/2} behavior at strong coupling. I explain in detail part of the background needed to understand this derivation, like holographic renormalization, localization of path integrals, and large N techniques in matrix models
Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
Moriyama, Sanefumi
2014-01-01
We study the partition function of three-dimensional ${\\mathcal N}=4$ superconformal Chern-Simons theories of the circular quiver type, which is a natural generalization of the ABJM theory, the worldvolume theory of M2-branes. In the ABJM case, it was known that the perturbative part of the partition function is summed up to the Airy function $e^{A}C^{-1/3}\\mathrm{Ai}[C^{-1/3}(N-B)]$ with coefficients $C$, $B$ and $A$ and for the non-perturbative part the divergences coming from the coefficients of worldsheet instantons and membrane instantons cancel among themselves. We find that many of the interesting properties in the ABJM theory are extended to the general superconformal Chern-Simons theories. Especially, we find an explicit expression of $B$ for general ${\\mathcal N}=4$ theories, a conjectural formula of $A$ for a special class, and cancellation in the non-perturbative coefficients for the next-to-simplest theory aside from the ABJM theory.
An alternative S-matrix for N = 6 Chern-Simons theory?
International Nuclear Information System (INIS)
We have recently proposed an S-matrix for the planar limit of the N = 6 superconformal Chern-Simons theory of Aharony, Bergman, Jafferis and Maldacena which leads to the all-loop Bethe ansatz equations conjectured by Gromov and Vieira. An unusual feature of this proposal is that the scattering of A and B particles is reflectionless. We consider here an alternative S-matrix, for which A-B scattering is not reflectionless. We argue that this S-matrix does not lead to the Bethe ansatz equations which are consistent with perturbative computations.
Finite size giant magnons in the string dual of N = 6 superconformal Chern-Simons theory
International Nuclear Information System (INIS)
We find the exact solution for a finite size Giant Magnon in the SU(2) x SU(2) sector of the string dual of the N = 6 superconformal Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena. The finite size Giant Magnon solution consists of two magnons, one in each SU(2). In the infinite size limit this solution corresponds to the Giant Magnon solution of arXiv:0806.4959. The magnon dispersion relation exhibits finite-size exponential corrections with respect to the infinite size limit solution.
Chern-Simons-Higgs theory with visible and hidden sectors and its N = 2 SUSY extension
Arias, Paola; Ireson, Edwin; Schaposnik, Fidel A.; Tallarita, Gianni
2015-10-01
We study vortex solutions in Abelian Chern-Simons-Higgs theories with visible and hidden sectors. We first consider the case in which the two sectors are connected through a BF-like gauge mixing term with no explicit interaction between the two scalars. Since first order Bogomolny equations do not exist in this case, we derive the second order field equations. We then proceed to an N = 2 supersymmetric extension including a Higgs portal mixing among the visible and hidden charged scalars. As expected, Bogomolny equations do exist in this case and we study their string-like solutions numerically.
Transgression forms as source for topological gravity and Chern-Simons-Higgs theories
Valdivia, Omar
2014-01-01
Two main gauge invariant off-shell models are studied in this Thesis. I) Poincare-invariant topological gravity in even dimensions is formulated as a transgression field theory whose gauge connections are associated to linear and nonlinear realizations of the Poincare group ISO(d-1,1). The resulting theory is a gauged Wess-Zumino-Witten model whereby the transition functions relating gauge fields belong to the coset ISO(d-1,1)/SO(d-1,1). The supersymmetric extension leads to topological supergravity in two dimensions starting from a transgression field theory for the super-Poincare group in three dimensions. The construction is extended to a three-dimensional Chern-Simons theory of gravity invariant under the Maxwell algebra, where the corresponding Maxwell gauged Wess-Zumino-Witten model is obtained. II) dimensional reduction of Chern-Simons theories with arbitrary gauge group in a formalism based on equivariant principal bundles is considered. For the classical gauge groups the relations between equivariant...
Mutual Chern-Simons theory and its applications in condensed matter physics
Institute of Scientific and Technical Information of China (English)
KOU Su-peng; WENG Zheng-yu; WEN Xiao-gang
2007-01-01
In this paper, the mutual Chern-Simons (MCS) theory is introduced as a new kind of topological gauge theory in 2+1 dimensions. We use the MCS theory in gapped phase as an effective low energy theory to describe the Z2 topological order of the Kitaev-Wen model. Our results show that the MCS theory can catch the key properties for the Z2 topological order. On the other hand, we use the MCS theory as an effective model to deal with the doped Mott insulator. Based on the phase string theory, the t-J model reduces to a MCS theory for spinons and holons. The related physics in high Tc cuprates is discussed.
Duality, Quantum Vortices and Anyons in Maxwell-Chern-Simons-Higgs Theories
Marino, E C
1993-01-01
The order-disorder duality structure is exploited in order to obtain a quantum description of anyons and vortices in: a) the Maxwell theory; b) the Abelian Higgs Model; c) the Maxwell-Chern-Simons theory; d) the Maxwell-Chern-Simons-Higgs theory. A careful construction of a charge bearing order operator($\\sigma$) and a magnetic flux bearing disorder operator (vortex operator) ($\\mu$) is performed, paying attention to the necessary requirements for locality. An anyon operator is obtained as the product $\\varphi=\\sigma\\mu$. A detailed and comprehensive study of the euclidean correlation functions of $\\sigma$, $\\mu$ and $\\varphi$ is carried on in the four theories above. The exact correlation functions are obtained in cases $\\underline{a}$ and $\\underline{c}$. The large distance behavior of them is obtained in cases $\\underline{b}$ and $\\underline{d}$. The study of these correlation functions allows one to draw conclusions about the condensation of charge and magnetic flux, establishing thereby an analogy with t...
String Theory Origin of Dyonic N=8 Supergravity and Its Chern-Simons Duals.
Guarino, Adolfo; Jafferis, Daniel L; Varela, Oscar
2015-08-28
We clarify the higher-dimensional origin of a class of dyonic gaugings of D=4 N=8 supergravity recently discovered, when the gauge group is chosen to be ISO(7). This dyonically gauged maximal supergravity arises from consistent truncation of massive IIA supergravity on S^6, and its magnetic coupling constant descends directly from the Romans mass. The critical points of the supergravity uplift to new four-dimensional anti-de Sitter space (AdS4) massive type IIA vacua. We identify the corresponding three-dimensional conformal field theory (CFT3) duals as super-Chern-Simons-matter theories with simple gauge group SU(N) and level k given by the Romans mass. In particular, we find a critical point that uplifts to the first explicit N=2 AdS4 massive IIA background. We compute its free energy and that of the candidate dual Chern-Simons theory by localization to a solvable matrix model, and find perfect agreement. This provides the first AdS4/CFT3 precision match in massive type IIA string theory. PMID:26371639
String Theory Origin of Dyonic N=8 Supergravity and Its Chern-Simons Duals.
Guarino, Adolfo; Jafferis, Daniel L; Varela, Oscar
2015-08-28
We clarify the higher-dimensional origin of a class of dyonic gaugings of D=4 N=8 supergravity recently discovered, when the gauge group is chosen to be ISO(7). This dyonically gauged maximal supergravity arises from consistent truncation of massive IIA supergravity on S^6, and its magnetic coupling constant descends directly from the Romans mass. The critical points of the supergravity uplift to new four-dimensional anti-de Sitter space (AdS4) massive type IIA vacua. We identify the corresponding three-dimensional conformal field theory (CFT3) duals as super-Chern-Simons-matter theories with simple gauge group SU(N) and level k given by the Romans mass. In particular, we find a critical point that uplifts to the first explicit N=2 AdS4 massive IIA background. We compute its free energy and that of the candidate dual Chern-Simons theory by localization to a solvable matrix model, and find perfect agreement. This provides the first AdS4/CFT3 precision match in massive type IIA string theory.
From Doubled Chern-Simons-Maxwell Lattice Gauge Theory to Extensions of the Toric Code
Olesen, T Z; Wiese, U -J
2015-01-01
We regularize compact and non-compact Abelian Chern-Simons-Maxwell theories on a spatial lattice using the Hamiltonian formulation. We consider a doubled theory with gauge fields living on a lattice and its dual lattice. The Hilbert space of the theory is a product of local Hilbert spaces, each associated with a link and the corresponding dual link. The two electric field operators associated with the link-pair do not commute. In the non-compact case with gauge group $\\mathbb{R}$, each local Hilbert space is analogous to the one of a charged "particle" moving in the link-pair group space $\\mathbb{R}^2$ in a constant "magnetic" background field. In the compact case, the link-pair group space is a torus $U(1)^2$ threaded by $k$ units of quantized "magnetic" flux, with $k$ being the level of the Chern-Simons theory. The holonomies of the torus $U(1)^2$ give rise to two self-adjoint extension parameters, which form two non-dynamical background lattice gauge fields that explicitly break the manifest gauge symmetry...
Chern-Simons theory with finite gauge group
Freed, Daniel S.; Quinn, Frank
1993-10-01
We construct in detail a 2+1 dimensional gauge field theory with finite gauge group. In this case the path integral reduces to a finite sum, so there are no analytic problems with the quantization. The theory was originally introduced by Dijkgraaf and Witten without details. The point of working it out carefully is to focus on the algebraic structure, and particularly the construction of quantum Hilbert spaces on closed surfaces by cutting and pasting. This includes the “Verlinde formula”. The careful development may serve as a model for dealing with similar issues in more complicated cases.
The Quantum Hall Effect in Supersymmetric Chern-Simons Theories
Tong, David
2015-01-01
In d=2+1 dimensions, there exist gauge theories which are supersymmetric but non-relativistic. We solve the simplest U(1) gauge theory in this class and show that the low-energy physics is that of the fractional quantum Hall effect, with ground states given by the Laughlin wavefunctions. We do this by quantising the vortices and relating them to the quantum Hall matrix model. We further construct coherent state representations of the excitations of vortices. These are quasi-holes. By an explicit computation of the Berry phase, without resorting to a plasma analogy, we show that these excitations have fractional charge and spin.
Chern-Simons theory with finite gauge group
International Nuclear Information System (INIS)
We construct in detail a 2+1 dimensional gauge field theory with finite gauge group. In this case the path integral reduces to a finite sum, so there are no analytic problems with the quantization. The theory was originally introduced by Dijkgraaf and Witten without details. The point of working it out carefully is to focus on the algebraic structure, and particularly the construction of quantum Hilbert spaces on closed surfaces by cutting and pasting. This includes the 'Verlinde formula'. The careful development may serve as a model for dealing with similar issues in more complicated cases. (orig.)
Heavy operators in superconformal Chern-Simons theory
de Mello Koch, Robert; Kreyfelt, Rocky; Smith, Stephanie
2014-12-01
We study the anomalous dimensions for scalar operators in Aharony-Bergman-Jafferis-Maldacena theory in the S U (2 ) sector. The operators we consider have a classical dimension that grows as N in the large N limit. Consequently, the large N limit is not captured by summing planar diagrams—nonplanar contributions have to be included. We find that the mixing matrix at two-loop order is diagonalized using a double coset ansatz, reducing it to the Hamiltonian of a set of decoupled oscillators. The spectrum of anomalous dimensions, when interpreted in the dual gravity theory, shows that the energy of the fluctuations of the corresponding giant graviton is dependent on the size of the giant. The first subleading corrections to the large N limit are also considered. These subleading corrections to the dilatation operator do not commute with the leading terms, indicating that integrability may not survive beyond the large N limit.
Transgressions and Holographic Conformal Anomalies for Chern-Simons Gravities
Mora, Pablo
2010-01-01
I present two calculations of the holographic Weyl anomalies induced by Chern-Simons gravity theories alternative to the ones presented in the literature. The calculations presented here rest on the extension from Chern-Simons to Transgression forms as lagrangians, motivated by gauge invariance, which automatically yields the boundary terms suitable to regularize the theory. The procedure followed here sheds light in the structure of Chern-Simons gravities and their regularization.
Construction of novel BPS Wilson loops in three-dimensional quiver Chern-Simons-matter theories
Ouyang, Hao; Zhang, Jia-ju
2015-01-01
In this paper, we construct novel Drukker-Trancanelli (DT) type BPS Wilson loops along infinite straight lines in $\\mathcal N=2,3$ quiver super Chern-Simons-matter (CSM) theories, Aharony-Bergman-Jafferis-Maldacena (ABJM) theory, and $\\mathcal N=4$ orbifold ABJM theory. There are several free complex parameters in the DT type BPS Wilson loops, and for Wilson loops in ABJM theory and $\\mathcal N=4$ orbifold ABJM theory there are supersymmetry enhancements at special values of the parameters. We check that the differences of the DT type and Gaiotto-Yin (GY) type Wilson loops are $Q$-exact with $Q$ being some supercharges preserved by both the DT type and GY type Wilson loops. The results would be useful to calculate vacuum expectation values of the Wilson loops in matrix models if they are still BPS quantum mechanically.
3d N = 1 Chern-Simons-matter theory and localization
Tsimpis, Dimitrios; Zhu, Yaodong
2016-10-01
We consider the most general, classically-conformal, three-dimensional N = 1 Chern-Simons-matter theory with global symmetry Sp (2) and gauge group U (N) × U (N). We show that the Lagrangian in the on-shell formulation of the theory admits one more free parameter as compared to the theory formulated in off-shell N = 1 superspace. The theory on T3 can be formally localized. We partially carry out the localization procedure for the theory on T3 with periodic boundary conditions. In particular we show that restricting to the saddle points with vanishing gauge connection gives a trivial contribution to the partition function, i.e. the bosonic and fermionic contributions exactly cancel each other.
Induced spin from the ISO(2,1) gauge theory with the gravitational Chern-Simons term
Cho, J H; Cho, Jin Ho
1994-01-01
In the context of ISO(2,1) gauge theory, we consider (2+1)-dimensional gravity with the gravitational Chern-Simons term (CST). This formulation allows the `exact' solution for the system coupled to a massive point particle (which is not the case in the conventional Chern-Simons gravity). The solution exhibits locally trivial structure even with the CST, although still shows globally nontrivialness such as the conical space and the helical time structure. Since the solution is exact, we can say the CST induces spin even for noncritical case of \\s+\\al m\
Coordinate dependence of Chern-Simons theory on noncommutative AdS3
International Nuclear Information System (INIS)
We investigate the coordinate dependence of noncommutative theory by studying the solutions of noncommutative U(1, 1) x U(1, 1) Chern-Simons theory on AdS3 in polar and rectangular coordinates. We assume that only the space coordinates are noncommuting. When the two coordinate systems are equivalent only up to first order in the noncommutativity parameter θ, we investigate the effect of this non-exact equivalence between the two coordinate systems for two cases, a conical solution and a BTZ black hole solution in noncommutative AdS3, by using the Seiberg-Witten map. In each case, the noncommutative solutions in the two coordinate systems obtained from the same corresponding commutative solution turn out to be different even to the first order in θ.
Coordinate dependence of Chern-Simons theory on noncommutative AdS{sub 3}
Energy Technology Data Exchange (ETDEWEB)
EE, Changyoung; Lee, Daeho [Sejong University, Seoul (Korea, Republic of); Lee, Youngone [Daejin University, Pocheon (Korea, Republic of)
2010-02-15
We investigate the coordinate dependence of noncommutative theory by studying the solutions of noncommutative U(1, 1) x U(1, 1) Chern-Simons theory on AdS{sub 3} in polar and rectangular coordinates. We assume that only the space coordinates are noncommuting. When the two coordinate systems are equivalent only up to first order in the noncommutativity parameter {theta}, we investigate the effect of this non-exact equivalence between the two coordinate systems for two cases, a conical solution and a BTZ black hole solution in noncommutative AdS{sub 3}, by using the Seiberg-Witten map. In each case, the noncommutative solutions in the two coordinate systems obtained from the same corresponding commutative solution turn out to be different even to the first order in {theta}.
Vortices and domain walls in a Chern-Simons theory with magnetic moment interactions
International Nuclear Information System (INIS)
We study the structure and properties of vortices in a recently proposed Abelian Maxwell-Chern-Simons model in 2+1 dimensions. The model which is described by a gauge field interacting with a complex scalar field includes two parity- and time-violating terms: the Chern-Simons and the anomalous magnetic terms. Self-dual relativistic vortices are discussed in detail. We also find one-dimensional soliton solutions of the domain wall type. The vortices are correctly described by the domain wall solutions in the large flux limit. copyright 1997 The American Physical Society
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.
The quantum 1/2 BPS Wilson loop in N=4 Chern-Simons-matter theories
Bianchi, Marco S.; Griguolo, Luca; Leoni, Matias; Mauri, Andrea; Penati, Silvia; Seminara, Domenico
2016-09-01
In three dimensional N=4 Chern-Simons-matter theories two independent fermionic Wilson loop operators can be defined, which preserve half of the supersymmetry charges and are cohomologically equivalent at classical level. We compute their three-loop expectation value in a convenient color sector and prove that the degeneracy is uplifted by quantum corrections. We expand the matrix model prediction in the same regime and by comparison we conclude that the quantum 1/2 BPS Wilson loop is the average of the two operators. We provide an all-loop argument to support this claim at any order. As a by-product, we identify the localization result at three loops as a correction to the framing factor induced by matter interactions. Finally, we comment on the quantum properties of the non-1/2 BPS Wilson loop operator defined as the difference of the two fermionic ones.
Non-minimal Maxwell-Chern-Simons theory and the composite Fermion model
Paschoal, Ricardo C.; Helayël-Neto, José A.
2003-01-01
The magnetic field redefinition in Jain's composite fermion model for the fractional quantum Hall effect is shown to be effectively described by a mean-field approximation of a model containing a Maxwell-Chern-Simons gauge field non-minimally coupled to matter. Also an explicit non-relativistic limit of the non-minimal (2+1)D Dirac equation is derived.
Hamiltonian analysis of Einstein-Chern-Simons gravity
Avilés, L.; Salgado, P.
2016-06-01
In this work we consider the construction of the Hamiltonian action for the transgressions field theory. The subspace separation method for Chern-Simons Hamiltonian is built and used to find the Hamiltonian for five-dimensional Einstein-Chern-Simons gravity. It is then shown that the Hamiltonian for Einstein gravity arises in the limit where the scale parameter l approaches zero.
Boundary Dynamics of Higher Dimensional Chern-Simons Gravity
Gegenberg, J.; Kunstatter, G.
2000-01-01
We review the relevance to the black hole entropy problem of boundary dynamics in Chern-Simons gravity. We then describe a recent derivation of the action induced on the four dimensional boundary in a five dimensional Chern-Simons gravity theory with gauge invariant, anti-deSitter boundary conditions.
The Hilbert space of the Chern-Simons theory on a cylinder: a loop quantum gravity approach
Energy Technology Data Exchange (ETDEWEB)
Constantinidis, Clisthenis P; Piguet, Olivier [Departamento de Fisica, Universidade Federal do Espirito Santo (UFES), Vitoria, ES (Brazil); Luchini, Gabriel, E-mail: cpconstantinidis@pq.cnpq.b, E-mail: opiguet@pq.cnpq.b, E-mail: gabriel.luchini@usp.b [Instituto de Fisica de Sao Carlos (IFSC), Universidade de Sao Paulo (USP), Sao Carlos, SP (Brazil)
2010-03-21
As a laboratory for loop quantum gravity, we consider the canonical quantization of the three-dimensional Chern-Simons theory on a noncompact space with the topology of a cylinder. Working within the loop quantization formalism, we define at the quantum level the constraints appearing in the canonical approach and completely solve them, thus constructing a gauge and diffeomorphism invariant physical Hilbert space for the theory. This space turns out to be infinite dimensional, but separable.
D2-brane Chern-Simons theories: F -maximization = a-maximization
Fluder, Martin; Sparks, James
2016-01-01
We study a system of N D2-branes probing a generic Calabi-Yau three-fold singularity in the presence of a non-zero quantized Romans mass n. We argue that the low-energy effective c N=2 Chern-Simons quiver gauge theory flows to a superconformal fixed point in the IR, and construct the dual AdS4 solution in massive IIA supergravity. We compute the free energy F of the gauge theory on S 3 using localization. In the large N limit we find F = c ( nN )1/3 a 2/3, where c is a universal constant and a is the a-function of the "parent" four-dimensional N=1 theory on N D3-branes probing the same Calabi-Yau singularity. It follows that maximizing F over the space of admissible R-symmetries is equivalent to maximizing a for this class of theories. Moreover, we show that the gauge theory result precisely matches the holographic free energy of the supergravity solution, and provide a similar matching of the VEV of a BPS Wilson loop operator.
D2-brane Chern-Simons theories: F-maximization = a-maximization
Fluder, Martin
2015-01-01
We study a system of N D2-branes probing a generic Calabi-Yau three-fold singularity in the presence of a non-zero quantized Romans mass n. We argue that the low-energy effective N = 2 Chern-Simons quiver gauge theory flows to a superconformal fixed point in the IR, and construct the dual AdS_4 solution in massive IIA supergravity. We compute the free energy F of the gauge theory on S^3 using localization. In the large N limit we find F = c(nN)^{1/3}a^{2/3}, where c is a universal constant and a is the a-function of the "parent" four-dimensional N = 1 theory on N D3-branes probing the same Calabi-Yau singularity. It follows that maximizing F over the space of admissible R-symmetries is equivalent to maximizing a for this class of theories. Moreover, we show that the gauge theory result precisely matches the holographic free energy of the supergravity solution, and provide a similar matching of the VEV of a BPS Wilson loop operator.
Construction and classification of novel BPS Wilson loops in quiver Chern-Simons-matter theories
Ouyang, Hao; Wu, Jun-Bao; Zhang, Jia-ju
2016-09-01
In this paper we construct and classify novel Drukker-Trancanelli (DT) type BPS Wilson loops along infinite straight lines and circles in N = 2 , 3 quiver superconformal Chern-Simons-matter theories, Aharony-Bergman-Jafferis-Maldacena (ABJM) theory, and N = 4 orbifold ABJM theory. Generally we have four classes of Wilson loops, and all of them preserve the same supersymmetries as the BPS Gaiotto-Yin (GY) type Wilson loops. There are several free complex parameters in the DT type BPS Wilson loops, and for two classes of Wilson loops in ABJM theory and N = 4 orbifold ABJM theory there are supersymmetry enhancements at special values of the parameters. We check that the differences of the DT type and GY type Wilson loops are Q-exact with Q being some supercharges preserved by both the DT type and GY type Wilson loops. The results would be useful to calculate vacuum expectation values of the DT type Wilson loops in matrix models if they are still BPS quantum mechanically.
Chern-Simons theory on spherical Seifert manifolds, topological strings and integrable systems
Borot, Gaetan
2015-01-01
We consider the Gopakumar-Ooguri-Vafa correspondence, relating U(N) Chern-Simons theory at large N to topological strings, in the context of spherical Seifert 3-manifolds. These are quotients $S^\\Gamma=S^3/\\Gamma$ of the three-sphere by the free action of a finite isometry group. Guided by string theory dualities, we propose a large N dual description in terms of both A- and B-twisted topological strings on (in general non-toric) local Calabi-Yau threefolds. The target space of the B-model theory is obtained from the spectral curve of Toda-type integrable systems constructed on the double Bruhat cells of the simply-laced group identified by the ADE label of $\\Gamma$. Its mirror A-model theory is realized as the local Gromov-Witten theory of suitable ALE fibrations on $CP^1$ generalizing the results known for lens spaces. We propose an explicit construction of the family of target manifolds relevant for the correspondence, which we verify through a large N analysis of the matrix model that expresses the contri...
Doubled Lattice Chern-Simons-Yang-Mills Theories with Discrete Gauge Group
Caspar, Stephan; Olesen, Therkel Z; Vlasii, Nadiia D; Wiese, Uwe-Jens
2016-01-01
We construct doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group $G$ in the Hamiltonian formulation. Here, these theories are considered on a square spatial lattice and the fundamental degrees of freedom are defined on pairs of links from the direct lattice and its dual, respectively. This provides a natural lattice construction for topologically-massive gauge theories, which are invariant under parity and time-reversal symmetry. After defining the building blocks of the doubled theories, paying special attention to the realization of gauge transformations on quantum states, we examine the dynamics in the group space of a single cross, which is spanned by a single link and its dual. The dynamics is governed by the single-cross electric Hamiltonian and admits a simple quantum mechanical analogy to the problem of a charged particle moving on a discrete space affected by an abstract electromagnetic potential. Such a particle might accumulate a phase shift equivalent to an Aharonov-Bohm pha...
Doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group
Caspar, S.; Mesterházy, D.; Olesen, T. Z.; Vlasii, N. D.; Wiese, U.-J.
2016-11-01
We construct doubled lattice Chern-Simons-Yang-Mills theories with discrete gauge group G in the Hamiltonian formulation. Here, these theories are considered on a square spatial lattice and the fundamental degrees of freedom are defined on pairs of links from the direct lattice and its dual, respectively. This provides a natural lattice construction for topologically-massive gauge theories, which are invariant under parity and time-reversal symmetry. After defining the building blocks of the doubled theories, paying special attention to the realization of gauge transformations on quantum states, we examine the dynamics in the group space of a single cross, which is spanned by a single link and its dual. The dynamics is governed by the single-cross electric Hamiltonian and admits a simple quantum mechanical analogy to the problem of a charged particle moving on a discrete space affected by an abstract electromagnetic potential. Such a particle might accumulate a phase shift equivalent to an Aharonov-Bohm phase, which is manifested in the doubled theory in terms of a nontrivial ground-state degeneracy on a single cross. We discuss several examples of these doubled theories with different gauge groups including the cyclic group Z(k) ⊂ U(1) , the symmetric group S3 ⊂ O(2) , the binary dihedral (or quaternion) group D¯2 ⊂ SU(2) , and the finite group Δ(27) ⊂ SU(3) . In each case the spectrum of the single-cross electric Hamiltonian is determined exactly. We examine the nature of the low-lying excited states in the full Hilbert space, and emphasize the role of the center symmetry for the confinement of charges. Whether the investigated doubled models admit a non-Abelian topological state which allows for fault-tolerant quantum computation will be addressed in a future publication.
Quantum Computation and Non-Abelian Statistics in Chern-Simons-Higgs Theory
Brozeguini, J C
2013-01-01
We naturally obtain the NOT and CNOT logic gates, which are key pieces of quantum computing algorithms, in the framework of the non-Abelian Chern-Simons-Higgs theory in two spatial dimensions. For that, we consider the anyonic quantum vortex topological excitations occurring in this system and show that self-adjoint (Majorana-like) combinations of these vortices and anti-vortices have in general non-Abelian statistics. The associated unitary monodromy braiding matrices become the required logic gates in the special case when the vortex spin is $s=1/4$. We explicitly construct the vortex field operators, show that they carry both magnetic flux and charge and obtain their euclidean correlation functions by using the method of quantization of topological excitations, which is based on the order-disorder duality. These correlators are in general multivalued, the number of sheets being determined by the vortex spin. This, by its turn, is proportional to the vacuum expectation value of the Higgs field and therefore...
Maxwell-Chern-Simons Casimir Effect
Milton, K A
1992-01-01
In odd-dimensional spaces, gauge invariance permits a Chern-Simons mass term for the gauge fields in addition to the usual Maxwell-Yang-Mills kinetic energy term. We study the Casimir effect in such a (2+1)-dimensional Abelian theory. For the case of parallel conducting lines the result is the same as for a scalar field. For the case of circular boundary conditions the results are completely different, with even the sign of the effect being opposite for Maxwell-Chern-Simons fields and scalar fields. We further examine the effect of finite temperature. The Casimir stress is found to be attractive at both low and high temperature. Possibilities of observing this effect in the laboratory are discussed.
Ruiz Ruiz, Fernando; Martin, C. P.; Giavarini, G.
1993-01-01
We show that the renormalized vacuum expectation value of the Wilson loop for topologically massive abelian gauge theory in $\\RR^3$ can be defined so that its large-mass limit be the renormalized vacuum expectation value of the Wilson loop for abelian Chern-Simons theory also in $\\RR^3$.
International Nuclear Information System (INIS)
We show that the renormalized vacuum expectation value of the Wilson loop for topologically massive abelian gauge theory in bbfR3 can be defined so that its large-mass limit be the renormalized vaccum expectation value of the Wilson loop for abelian Chern-Simons theory also in bbfR3. (orig.)
The Chern-Simons Number as a Dynamical Variable
Tye, S -H Henry
2016-01-01
In the standard electroweak theory that describes nature, the Chern-Simons number associated with the vacua as well as the unstable sphaleron solutions play a crucial role in the baryon number violating processes. We recall why the Chern-Simons number should be generalized from a set of discrete values to a dynamical (quantum) variable. Via the construction of an appropriate Hopf invariant and the winding number, we discuss how the geometric information in the gauge fields is also captured in the Higgs field. We then discuss the choice of the Hopf variable in relation to the Chern-Simons variable.
Rey, Soo-Jong; Suyama, Takao; Yamaguchi, Satoshi
2008-01-01
We study Wilson loop operators in three-dimensional, N=6 superconformal Chern-Simons theory dual to IIA superstring theory on AdS4 x CP3. Novelty of Wilson loop operators in this theory is that, for a given contour, there are two linear combinations of Wilson loop transforming oppositely under time-reversal transformation. We show that one combination is holographically dual to IIA fundamental string, while orthogonal combination is set to zero. We gather supporting evidences from detailed co...
Ouyang, Hao; Zhang, Jia-ju
2015-01-01
We show that generic three-dimensional $\\mathcal N=2$ quiver Chern-Simons-matter theories admit Bogomol'nyi-Prasad-Sommerfield (BPS) Drukker-Trancanelli (DT) type Wilson loops. In Aharnoy-Bergman-Jafferis-Maldacena theory, we find that the generic BPS DT type Wilson loops preserve the same number of supersymmetries as Gaiotto-Yin type Wilson loops. There are several free parameters for the generic BPS DT type Wilson loops in the construction, and supersymmetry enhancement for Wilson loops only happens for special values of the parameters.
Spontaneous Breaking of Scale Invariance in U(N) Chern-Simons Gauge Theories in Three Dimensions
Energy Technology Data Exchange (ETDEWEB)
Bardeen, William A. [Fermilab
2015-09-24
I explore the existence of a massive phase in a conformally invariant U(N) Chern-Simons gauge theories in D = 3 with matter fields in the fundamental representation. These models have attracted recent attention as being dual, in the conformal phase, to theories of higher spin gravity on AdS 4. Using the 0t Hooft large N expansion, exact solutions are obtained for scalar current correlators in the massive phase where the conformal symmetry is spontaneously broken. A massless dilaton appears as a composite state, and its properties are discussed. Solutions exist for matters field that are either bosons or fermions.
Spontaneous Breaking of Scale Invariance in U(N) Chern-Simons Gauge Theories in Three Dimensions
Energy Technology Data Exchange (ETDEWEB)
Bardeen, William [Fermilab
2014-10-24
I explore the existence of a massive phase in a conformally invariant U(N) Chern-Simons gauge theories in D = 3 with matter fields in the fundamental representation. These models have attracted recent attention as being dual, in the conformal phase, to theories of higher spin gravity on AdS 4. Using the 1t Hooft large N expansion, exact solutions are obtained for scalar current correlators in the massive phase where the conformal symmetry is spontaneously broken. A massless dilaton appears as a composite state, and its properties are discussed. Solutions exist for matters field that are either bosons or fermions.
N=6 super Chern-Simons theory S-matrix and all-loop Bethe ansatz equations
Ahn, Changrim
2008-01-01
We propose the exact S-matrix for the planar limit of the N=6 super Chern-Simons theory recently proposed by Aharony, Bergman, Jafferis, and Maldacena for the AdS_4/CFT_3 correspondence. Assuming SU(2|2) symmetry, factorizability and certain crossing-unitarity relations, we find the S-matrix including the dressing phase. We use this S-matrix to formulate the asymptotic Bethe ansatz. Our result for the Bethe-Yang equations and corresponding Bethe ansatz equations confirms the all-loop Bethe ansatz equations recently conjectured by Gromov and Vieira.
Chern-Simons-Higgs Theory with Visible and Hidden Sectors and its ${\\cal N}=2$ SUSY Extension
Arias, Paola; Schaposnik, Fidel A; Tallarita, Gianni
2015-01-01
We study vortex solutions in Abelian Chern-Simons-Higgs theories with visible and hidden sectors. We first consider the case in which the two sectors are connected through a BF-like gauge mixing term with no explicit interaction between the the two scalars. Since first order Bogomolny equations do not exist in this case, we derive the second order field equations. We then proceed to an ${\\cal N}=2$ supersymmetric extension including a Higgs portal mixing among the visible and hidden charged scalars. As expected, Bogomolnyi equations do exist in this case and we study their string-like solutions numerically.
Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles
Caporaso, N; Griguolo, L; Pasquetti, S; Seminara, D; Szabó, R J
2006-01-01
We study the relations between two-dimensional Yang-Mills theory on the torus, topological string theory on a Calabi-Yau threefold whose local geometry is the sum of two line bundles over the torus, and Chern-Simons theory on torus bundles. The chiral partition function of the Yang-Mills gauge theory in the large N limit is shown to coincide with the topological string amplitude computed by topological vertex techniques. We use Yang-Mills theory as an efficient tool for the computation of Gromov-Witten invariants and derive explicitly their relation with Hurwitz numbers of the torus. We calculate the Gopakumar-Vafa invariants, whose integrality gives a non-trivial confirmation of the conjectured nonperturbative relation between two-dimensional Yang-Mills theory and topological string theory. We also demonstrate how the gauge theory leads to a simple combinatorial solution for the Donaldson-Thomas theory of the Calabi-Yau background. We match the instanton representation of Yang-Mills theory on the torus with ...
Setare, M R
2016-01-01
In the first order formalism of gravity theories, may be exist some theories which are not Lorentz-difeomorphism covariant so for such theories a method for which one can calculate conserved charges of Lorentz-difeomorphism covariant theories are useless. In this letter we introduce the total variation of a quantity due to an infinitesimal Lorentz-diffeomorphism transformation. Then using this concept, in order to obtain the conserved charges in Lorentz-diffeomorphism non-covariant theories, we extend the Tachikawa's method \\cite{3} so that it includes Lorentz gauge transformation in addition to diffeomorphism. We apply this method on the Chern-Simons-like theories of gravity and we find out a general formula for the entropy of black holes in those theories. Eventually, we consider some examples and calculate entropy of the BTZ black hole in the context of this examples.
Setare, M. R.; Adami, H.
2016-01-01
In the first order formalism of gravity theories, there are some theories which are not Lorentz-diffeomorphism covariant. In the framework of such theories we cannot apply the method of conserved charge calculation used in Lorentz-diffeomorphism covariant theories. In this paper we firstly introduce the total variation of a quantity due to an infinitesimal Lorentz-diffeomorphism transformation. Secondly, in order to obtain the conserved charges of Lorentz-diffeomorphism non-covariant theories, we extend the Tachikawa method [1]. This extension includes not only Lorentz gauge transformation but also the diffeomorphism. We apply this method to the Chern-Simons-like theories of gravity (CSLTG) and obtain a general formula for the entropy of black holes in those theories. Finally, some examples on CSLTG are provided and the entropy of the BTZ black hole is calculated in the context of the examples.
Institute of Scientific and Technical Information of China (English)
DUAN Yi-Shi; LIU Xin; FU Li-Bin
2003-01-01
In this paper, the decomposition of SU(2) gauge potential in terms of Pauli spinor is studied. Using thisdecomposition, the spinor structures of Chern-Simons form and the Chern density are obtained. Furthermore, the knotquantum number of non-Abelian gauge theory can be expressed by the Chern-Simons spinor structure, and the secondChern number is characterized by the Hopf indices and the Brouwer degrees of φ-mapping.
Institute of Scientific and Technical Information of China (English)
DUANYi-Shi; LIUXin; FULi-Bin
2003-01-01
In this paper, the decomposition of SU(2) gauge potential in terms of Pauli spinor is studied. Using this decomposition, the spinor structures of Chern Simons form and the Chern density are obtained. Furthermore, the knot quantum number of non-Abelian gauge theory can be expressed by the Chern-Simons spinor structure, and the second Chern number is characterized by the Hopf indices and the Brouwer degrees of Φ-mapping.
Chern Simons Bosonization along RG Flows
Minwalla, Shiraz
2015-01-01
It has previously been conjectured that the theory of free fundamental scalars minimally coupled to a Chern Simons gauge field is dual to the theory of critical fundamental fermions minimally coupled to a level rank dual Chern Simons gauge field. In this paper we study RG flows away from these two fixed points by turning on relevant operators. In the t' Hooft large N limit we compute the thermal partition along each of these flows and find a map of parameters under which the two partition functions agree exactly with each other all the way from the UV to the IR. We conjecture that the bosonic and fermionic RG flows are dual to each other under this map of parameters. Our flows can be tuned to end at the gauged critical scalar theory and gauged free fermionic theories respectively. Assuming the validity of our conjecture, this tuned trajectory may be viewed as RG flow from the gauged theory of free bosons to the gauged theory of free fermions.
The moduli spaces of $3d$ ${\\cal N} \\ge 2$ Chern-Simons gauge theories and their Hilbert series
Cremonesi, Stefano; Zaffaroni, Alberto
2016-01-01
We present a formula for the Hilbert series that counts gauge invariant chiral operators in a large class of 3d ${\\cal N} \\ge 2$ Yang-Mills-Chern-Simons theories. The formula counts 't Hooft monopole operators dressed by gauge invariants of a residual gauge theory of massless fields in the monopole background. We provide a general formula for the case of abelian theories, where nonperturbative corrections are absent, and consider a few examples of nonabelian theories where nonperturbative corrections are well understood. We also analyze in detail nonabelian ABJ(M) theories as well as worldvolume theories of M2-branes probing Calabi-Yau fourfold and hyperK\\"ahler twofold singularities with ${\\cal N} = 2$ and ${\\cal N} = 3$ supersymmetry.
Multiple Chern-Simons fields on a torus
Wesolowski, D J; Ho, C L
1994-01-01
Intertwined multiple Chern-Simons gauge fields induce matrix statistics among particles. We analyse this theory on a torus, focusing on the vacuum structure and the Hilbert space. The theory can be mimicked, although not completely, by an effective theory with one Chern-Simons gauge field. The correspondence between the Wilson line integrals, vacuum degeneracy and wave functions for these two theories are discussed. Further, it is obtained in both of these cases that the two total momenta and Hamiltonian commute only in the physical Hilbert space.
Chern-Simons terms and cocycles in physics and mathematics
Energy Technology Data Exchange (ETDEWEB)
Jackiw, R.
1984-12-01
Contemporary topological research in Yang-Mills theory is reviewed, emphasizing the Chern-Simons terms and their relatives. Three applications of the Chern-Simons terms in physical theory are described: to help understanding gauge theories in even dimensional space-time; gauge field dynamics in odd dimensional space-time; and mathematically coherent description of even-dimensional gauge theories with chiral fermions that are apparently inconsistent due to chiral anomalies. Discussion of these applications is preceded by explanation of the mathematical preliminaries and examples in simple quantum mechanical settings. 24 refs. (LEW)
Inbasekar, Karthik; Mazumdar, Subhajit; Minwalla, Shiraz; Umesh, V; Yokoyama, Shuichi
2015-01-01
We study the most general renormalizable ${\\cal N}=1$ $U(N)$ Chern-Simons gauge theory coupled to a single (generically massive) fundamental matter multiplet. At leading order in the 't Hooft large $N$ limit we present computations and conjectures for the $2 \\times 2$ $S$ matrix in these theories; our results apply at all orders in the 't Hooft coupling and the matter self interaction. Our $S$ matrices are in perfect agreement with the recently conjectured strong weak coupling self duality of this class of theories. The consistency of our results with unitarity requires a modification of the usual rules of crossing symmetry in precisely the manner anticipated in arXiv:1404.6373, lending substantial support to the conjectures of that paper. In a certain range of coupling constants our $S$ matrices have a pole whose mass vanishes on a self dual codimension one surface in the space of couplings.
The SU(2)xSU(2) sector in the string dual of N=6 superconformal Chern-Simons theory
International Nuclear Information System (INIS)
We examine the string dual of the recently constructed N=6 superconformal Chern-Simons theory of Aharony, Bergman, Jafferis and Maldacena (ABJM theory). We focus in particular on the SU(2)xSU(2) sector. We find a sigma-model limit in which the resulting sigma-model is two Landau-Lifshitz models added together. We consider a Penrose limit for which we can approach the SU(2)xSU(2) sector. Finally, we find a new Giant Magnon solution in the SU(2)xSU(2) sector corresponding to one magnon in each SU(2). We put these results together to find the full magnon dispersion relation and we compare this to recently found results for ABJM theory at weak coupling
The SU(2)xSU(2) sector in the string dual of N=6 superconformal Chern-Simons theory
Energy Technology Data Exchange (ETDEWEB)
Grignani, Gianluca [Dipartimento di Fisica, Universita di Perugia, I.N.F.N. Sezione di Perugia, Via Pascoli, I-06123 Perugia (Italy)], E-mail: grignani@pg.infn.it; Harmark, Troels [Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen O (Denmark)], E-mail: harmark@nbi.dk; Orselli, Marta [Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen O (Denmark)], E-mail: orselli@nbi.dk
2009-03-21
We examine the string dual of the recently constructed N=6 superconformal Chern-Simons theory of Aharony, Bergman, Jafferis and Maldacena (ABJM theory). We focus in particular on the SU(2)xSU(2) sector. We find a sigma-model limit in which the resulting sigma-model is two Landau-Lifshitz models added together. We consider a Penrose limit for which we can approach the SU(2)xSU(2) sector. Finally, we find a new Giant Magnon solution in the SU(2)xSU(2) sector corresponding to one magnon in each SU(2). We put these results together to find the full magnon dispersion relation and we compare this to recently found results for ABJM theory at weak coupling.
Wen, Xueda; Matsuura, Shunji; Ryu, Shinsei
2016-06-01
We develop an approach based on edge theories to calculate the entanglement entropy and related quantities in (2+1)-dimensional topologically ordered phases. Our approach is complementary to, e.g., the existing methods using replica trick and Witten's method of surgery, and applies to a generic spatial manifold of genus g , which can be bipartitioned in an arbitrary way. The effects of fusion and braiding of Wilson lines can be also straightforwardly studied within our framework. By considering a generic superposition of states with different Wilson line configurations, through an interference effect, we can detect, by the entanglement entropy, the topological data of Chern-Simons theories, e.g., the R symbols, monodromy, and topological spins of quasiparticles. Furthermore, by using our method, we calculate other entanglement/correlation measures such as the mutual information and the entanglement negativity. In particular, it is found that the entanglement negativity of two adjacent noncontractible regions on a torus provides a simple way to distinguish Abelian and non-Abelian topological orders.
Chern-Simons modified gravity and closed timelike curves
Porfírio, P. J.; Fonseca-Neto, J. B.; Nascimento, J. R.; Petrov, A. Yu.; Ricardo, J.; Santos, A. F.
2016-08-01
We verify the consistency of the Gödel-type solutions within the four-dimensional Chern-Simons modified gravity with the nondynamical Chern-Simons coefficient for different forms of matter including dust, fluid, scalar field, and electromagnetic field and discuss the related causality issues. We show that, unlike general relativity, a vacuum solution is possible in our theory. Another essentially new result of our theory having no analogue in general relativity consists in the existence of the hyperbolic causal solutions for a physically well-motivated matter.
The quantum 1/2 BPS Wilson loop in ${\\cal N}=4$ Chern-Simons-matter theories
Bianchi, Marco S; Leoni, Matias; Mauri, Andrea; Penati, Silvia; Seminara, Domenico
2016-01-01
In three dimensional ${\\cal N}=4$ Chern-Simons-matter theories two independent fermionic Wilson loop operators can be defined, which preserve half of the supersymmetry charges and are cohomologically equivalent at classical level. We compute their three-loop expectation value in a convenient color sector and prove that the degeneracy is uplifted by quantum corrections. We expand the matrix model prediction in the same regime and by comparison we conclude that the quantum 1/2 BPS Wilson loop is the average of the two operators. We provide an all-loop argument to support this claim at any order. As a by-product, we identify the localization result at three loops as a correction to the framing factor induced by matter interactions. Finally, we comment on the quantum properties of the non-1/2 BPS Wilson loop operator defined as the difference of the two fermionic ones.
Chern-Simons from Dirichlet 2-brane instantons
O'Loughlin, M H
1996-01-01
In the vicinity of points in Calabi-Yau moduli space where there are degenerating three-cycles the low energy effective action of type IIA string theory will contain significant contributions arising from membrane instantons that wrap around these three-cycles. We show that the world-volume description of these instantons is Chern-Simons theory.
Even-dimensional topological gravity from Chern-Simons gravity
Merino, N.; Perez, Alfredo; Salgado, P.(Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción, Chile)
2009-01-01
It is shown that the topological action for gravity in 2n-dimensions can be obtained from the 2n+1-dimensional Chern-Simons gravity genuinely invariant under the Poincare group. The 2n-dimensional topological gravity is described by the dynamics of the boundary of a 2n+1-dimensional Chern-Simons gravity theory with suitable boundary conditions. The field $\\phi^{a}$, which is necessary to construct this type of topological gravity in even dimensions, is identified with the coset field associat...
Non-Abelian Chern-Simons Quantum Mechanics
Lee, Taejin; Oh, Phillial
1993-01-01
We propose a classical model for the non-Abelian Chern-Simons theory coupled to $N$ point-like sources and quantize the system using the BRST technique. The resulting quantum mechanics provides a unified framework for fractional spin, braid statistics and Knizhnik-Zamolodchikov equation.
Rey, Soo-Jong; Yamaguchi, Satoshi
2009-01-01
We investigate Wilson loop operators in three-dimensional, N=6 superconformal Chern-Simons theory dual to IIA superstring theory on AdS4 x CP3. A novelty of the Wilson loop operators is that, for a given Wilson loop contour, there are even and odd varieties under generalized spacetime parity. We assert that parity-even BPS Wilson loop is special and that it is holographic dual to IIA fundamental string piercing D2-branes, rather than ending on it. We show that parity-even BPS Wilson loop exhibits remarkable features that are strikingly parallel to the BPS Wilson loop in N=4 super Yang-Mills theory in four dimensions. We compute vacuum expectation value of the parity-even BPS Wilson loops in planar perturbation theory up to three-loop order. From this, we propose that circular Wilson loop is computable exactly by a zero-dimensional Gaussian matrix model whose variance is specified by a specific transcendental function. We expect the function interpolates smoothly between weak and strong coupling regime, thus o...
Karndumri, Parinya
2016-08-01
We study various supersymmetric renormalization group (RG) flows of N =3 Chern-Simons-Matter theory in three dimensions by using four-dimensional N =3 gauged supergravity coupled to eight vector multiplets with S O (3 )×S U (3 ) gauge group. The AdS4 critical point preserving the full S O (3 )×S U (3 ) provides a gravity dual of N =3 superconformal field theory with flavor symmetry S U (3 ). We study the scalar potential and identify a new supersymmetric AdS4 critical point preserving the full N =3 supersymmetry and unbroken S O (3 )×U (1 ) symmetry. An analytic RG flow solution interpolating between S O (3 )×S U (3 ) and S O (3 )×U (1 ) critical points is explicitly given. We then investigate possible RG flows from these AdS4 critical points to nonconformal field theories in the IR. All of the singularities appearing in the IR turn out to be physically acceptable. Furthermore, we look for supersymmetric solutions of the form AdS2×Σ2 with Σ2 being a two-sphere or a two-dimensional hyperbolic space and find a number of AdS2 geometries preserving four supercharges with S O (2 )×S O (2 )×S O (2 ) and S O (2 )×S O (2 ) symmetries.
Setare, M R
2016-01-01
In this paper we study the near horizon symmetry algebra of the non-extremal black hole solutions of the Chern-Simons-like theories of gravity, which are stationary but are not necessarily spherically symmetric. We define the extended off-shell ADT current which is an extension of the generalized ADT current. We use the extended off-shell ADT current to define quasi-local conserved charges such that they are conserved for Killing vectors and asymptotically Killing vectors which depend on dynamical fields of the considered theory. We apply this formalism to the Generalized Minimal Massive Gravity( GMMG) and obtain conserved charges of a spacetime which describes near horizon geometry of non-extremal black holes. Eventually, we find the algebra of conserved charges in Fourier modes. It is interesting that, similar to the Einstein gravity in the presence of negative cosmological constant, for the GMMG model also we obtain the Heisenberg algebra as the near horizon symmetry algebra of the black flower solutions. ...
Gaete, Patricio
2016-01-01
By using the gauge-invariant but path-dependent, variables formalism, we consider a recently proposed topologically massive $U{\\left( 1 \\right)_{\\cal W}} \\times U{(1)_{\\cal Y}}$ Chern-Simons-Higgs theory in $2+1$ dimensions. In particular, we inspect the impact of a Chern-Simons mixing term between two Abelian gauge fields on physical observables. We pursue our investigation by analysing the model in two different situations. In the first case, where we integrate out the massive excitation and consider an effective model for the massless field, we show that the interaction energy contains a linear term leading to the confinement of static charge probes along with a screening contribution. The second situation, where the massless field can be exactly integrated over with its constraint duly taken into account, the interesting feature is that the resulting effective model describes a purely screening phase, without any trace of a confining regime.
Gauge fixing and classical dynamical r-matrices in ISO(2,1)-Chern-Simons theory
Meusburger, Catherine
2012-01-01
We apply Dirac's gauge fixing procedure to Chern-Simons theory with gauge group ISO(2,1) on manifolds RxS, where S is a punctured oriented surface of general genus. For all gauge fixing conditions that satisfy certain structural requirements, this yields an explicit description of the Poisson structure on the moduli space of flat ISO(2,1)-connections on S via the resulting Dirac bracket. The Dirac bracket is determined by classical dynamical r-matrices for ISO(2,1). We show that the Poisson structures and classical dynamical r-matrices arising from different gauge fixing conditions are related by dynamical ISO(2,1)-valued transformations that generalise the usual gauge transformations of classical dynamical r-matrices. By means of these transformations, it is possible to classify all Poisson structures and classical dynamical r-matrices obtained from such gauge fixings. Generically these Poisson structures combine classical dynamical r-matrices for non-conjugate Cartan subalgebras of ISO(2,1).
Chern-Simons expectation values and quantum horizons from loop quantum gravity and the Duflo map.
Sahlmann, Hanno; Thiemann, Thomas
2012-03-16
We report on a new approach to the calculation of Chern-Simons theory expectation values, using the mathematical underpinnings of loop quantum gravity, as well as the Duflo map, a quantization map for functions on Lie algebras. These new developments can be used in the quantum theory for certain types of black hole horizons, and they may offer new insights for loop quantum gravity, Chern-Simons theory and the theory of quantum groups. PMID:22540458
Institute of Scientific and Technical Information of China (English)
DUAN Yi-Shi; REN Ji-Rong; LI Ran
2007-01-01
In this paper, spinor and vector decompositions of SU(2) gauge potential are presented and their equivalence is constructed using a simply proposal. We also obtain the action of Faddeev nonlinear O(3) sigma model from the SU(2)massive gauge field theory, which is proposed according to the gauge invariant principle. At last, the knot structure in SU(2) Chern-Simons filed theory is discussed in terms of the φ-mapping topological current theory. The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of φ-mapping.
Chern-Simons: Fano and Calabi-Yau
Hanany, Amihay
2009-01-01
We present the complete classification of smooth toric Fano threefolds, known to the algebraic geometry literature, and perform some preliminary analyses in the context of brane-tilings and Chern-Simons theory on M2-branes probing Calabi-Yau fourfold singularities. We emphasise that these 18 spaces should be as intensely studied as their well-known counter-parts: the del Pezzo surfaces.
Chern-Simons Invariants of Torus Knots and Links
Stevan, Sébastien
2010-01-01
We compute the vacuum expectation values of torus knot operators in Chern-Simons theory, and we obtain explicit formulae for all classical gauge groups and for arbitrary representations. We reproduce a known formula for the HOMFLY invariants of torus links and we obtain an analogous formula for Kauffman invariants. We also derive a formula for cable knots. We use our results to test a recently proposed conjecture that relates HOMFLY and Kauffman invariants.
Setare, M. R.; Adami, H.
2016-08-01
The Chern-Simons-like theories of gravity (CSLTG) are formulated at first order formalism. In this formalism, the derivation of the entropy of a black hole on bifurcation surface, as a quasi-local conserved charge is problematic. In this paper we overcome these problems by considering the concept of total variation and the Lorentz-Lie derivative. We firstly find an expression for the ADT conserved current in the context of the CSLTG which is based on the concept of the Killing vector fields. Then, we generalize it to be conserved for all diffeomorphism generators. Thus, we can extract an off-shell conserved charge for any vector field which generates a diffeomorphism. The formalism presented here is based on the concept of quasi-local conserved charges which are off-shell. The charges can be calculated on any codimension two space-like surface surrounding a black hole and the results are independent of the chosen surface. By using the off-shell quasi-local conserved charge, we investigate the Virasoro algebra and find a formula to calculate the central extension term. We apply the formalism to the BTZ black hole solution in the context of the Einstein gravity and the Generalized massive gravity, then we find the eigenvalues of their Virasoro generators as well as the corresponding central charges. Eventually, we calculate the entropy of the BTZ black hole by the Cardy formula and we show that the result exactly matches the one obtained by the concept of the off-shell conserved charges.
Chern-Simons-Schwinger model of confinement in $QCD$
Aurilia, Antonio; Spallucci, Euro
2015-01-01
It has been shown that the mechanism of formation of glue-bags in the strong coupling limit of Yang-Mills theory can be understood in terms of the dynamics of a higher-rank abelian gauge field, namely, the 3-form dual to the Chern-Simons topological current. Building on this result, we show that the field theoretical interpretation of the Chern-Simons term, as opposed to its topological interpretation, also leads to the analytic form of the confinement potential that arises in the large distance limit of $QCD$. In fact, for a $(3+1)$-dimensional generalization of the Schwinger model, we explicitly compute the interaction energy. This generalization is due to the presence of the topological gauge field $A_{\\mu\
Enhancement of hidden symmetries and Chern-Simons couplings
Henneaux, Marc; Lekeu, Victor
2015-01-01
We study the role of Chern--Simons couplings for the appearance of enhanced symmetries of Cremmer--Julia type in various theories. It is shown explicitly that for generic values of the Chern--Simons coupling there is only a parabolic Lie subgroup of symmetries after reduction to three space-time dimensions but that this parabolic Lie group gets enhanced to the full and larger Cremmer--Julia Lie group of hidden symmetries if the coupling takes a specific value. This is heralded by an enhanced isotropy group of the metric on the scalar manifold. Examples of this phenomenon are discussed as well as the relation to supersymmetry. Our results are also connected with rigidity theorems of Borel-like algebras.
Chern-Simons Supergravity in D=3 and Maxwell superalgebras
Concha, P K; Rodríguez, E K; Salgado, P
2015-01-01
We present the construction of the $D=3$ Chern-Simons supergravity action from the Maxwell superalgebra $s\\mathcal{M}$, which can be obtained from the anti-De Sitter superalgebra by combining the abelian semigroup expansion procedure and the In\\"{o}n\\"{u}-Wigner contraction. \\ The Chern-Simons supergravity action from a generalized Maxwell superalgebra is also introduced.
International Nuclear Information System (INIS)
Vortex-like and string-like solutions of 2+1 Dim. SU(2) YM theory with the Chern-Simons term are discussed. Two ansatze are constructed which yield respectively analytic Bessel function solutions and elliptic function solutions. The Bessel function solutions are vortex-like and tend to the same vacuum state as the Ginzburg-Landau vortex solution at large ρ. The Jacobi elliptic function solutions are string-like, have finite energy and magnetic flux concentrated along a line in the x1 - x2 plane. (author). 18 refs
Accelerated FRW solutions in Chern-Simons gravity
Energy Technology Data Exchange (ETDEWEB)
Cataldo, Mauricio [Universidad del Bio-Bio, Departamento de Fisica, Concepcion (Chile); Crisostomo, Juan; Gomez, Fernando; Salgado, Patricio [Universidad de Concepcion, Departamento de Fisica, Concepcion (Chile); Campo, Sergio del [Pontificia Universidad Catolica de Valparaiso, Instituto de Fisica, Valparaiso (Chile); Quinzacara, Cristian C. [Universidad de Concepcion, Departamento de Fisica, Concepcion (Chile); Universidad San Sebastian, Facultad de Ingenieria y Tecnologia, Concepcion (Chile)
2014-10-15
We consider a five-dimensional Einstein-Chern-Simons action which is composed of a gravitational sector and a sector of matter where the gravitational sector is given by a Chern-Simons gravity action instead of the Einstein-Hilbert action and where the matter sector is given by the so-called perfect fluid. It is shown that (i) the Einstein-Chern-Simons (EChS) field equations subject to suitable conditions can be written in a similar way to the Einstein-Maxwell field equations; (ii) these equations have solutions that describe an accelerated expansion for the three possible cosmological models of the universe, namely, spherical expansion, flat expansion, and hyperbolic expansion when α a parameter of the theory, is greater than zero. This result allows us to conjecture that these solutions are compatible with the era of dark energy and that the energy-momentum tensor for the field h{sup a}, a bosonic gauge field from the Chern-Simons gravity action, corresponds to a form of positive cosmological constant. It is also shown that the EChS field equations have solutions compatible with the era of matter: (i) In the case of an open universe, the solutions correspond to an accelerated expansion (α > 0) with a minimum scale factor at initial time that, when time goes to infinity, the scale factor behaves as a hyperbolic sine function. (ii) In the case of a flat universe, the solutions describe an accelerated expansion whose scale factor behaves as an exponential function of time. (iii) In the case of a closed universe there is found only one solution for a universe in expansion, which behaves as a hyperbolic cosine function of time. (orig.)
Chern-Simons diffusion rate across different phase transitions
Rougemont, Romulo; Finazzo, Stefano Ivo
2016-05-01
We investigate how the dimensionless ratio given by the Chern-Simons diffusion rate ΓCS divided by the product of the entropy density s and temperature T behaves across different kinds of phase transitions in the class of bottom-up nonconformal Einstein-dilaton holographic models originally proposed by Gubser and Nellore. By tuning the dilaton potential, one is able to holographically mimic a first order, a second order, or a crossover transition. In a first order phase transition, ΓCS/s T jumps at the critical temperature (as previously found in the holographic literature), while in a second order phase transition it develops an infinite slope. On the other hand, in a crossover, ΓCS/s T behaves smoothly, although displaying a fast variation around the pseudo-critical temperature. In all the cases, ΓCS/s T increases with decreasing T . The behavior of the Chern-Simons diffusion rate across different phase transitions is expected to play a relevant role for the chiral magnetic effect around the QCD critical end point, which is a second order phase transition point connecting a crossover band to a line of first order phase transition. Our findings in the present work add to the literature the first predictions for the Chern-Simons diffusion rate across second order and crossover transitions in strongly coupled nonconformal, non-Abelian gauge theories.
Chern-Simons production during preheating in hybrid inflation models
García-Bellido, J; González-Arroyo, A; Garcia-Bellido, Juan; Perez, Margarita Garcia; Gonzalez-Arroyo, Antonio
2004-01-01
We study the onset of symmetry breaking after hybrid inflation in a model having the field content of the SU(2) gauge-scalar sector of the standard model, coupled to a singlet inflaton. This process is studied in (3+1)-dimensions in a fully non-perturbative way with the help of lattice techniques within the classical approximation. We focus on the role played by gauge fields and, in particular, on the generation of Chern-Simons number. Our results are shown to be insensitive to the various cut-offs introduced in our numerical approach. The spectra preserves a large hierarchy between long and short-wavelength modes during the whole period of symmetry breaking and Chern-Simons generation, confirming that the dynamics is driven by the low momentum sector of the theory. We establish that the Chern-Simons production mechanism is associated with local sphaleron-like structures. The corresponding sphaleron rates are of order 10^{-5} m^{-4}, which, within certain scenarios of electroweak baryogenesis and a (not unnat...
Supersymmetric Wilson Loops in N=6 Super Chern-Simons-matter theory
Chen, Bin; Wu, Jun-Bao
2008-01-01
We study supersymmetric Wilson loop operators in ABJM theory from both sides of the AdS_4/CFT_3 correspondence. We first construct some supersymmetric Wilson loops. The perturbative computations are performed in the field theory side at the first two orders. A fundamental string solution ending on a circular loop is also studied.
The Topological Inner Structure of Chern-Simons Tensor Current and the World-Sheet of Strings
Institute of Scientific and Technical Information of China (English)
DUAN Yi-Shi; YANG Jie
2005-01-01
@@ Using the decomposition theory of U(1) gauge potential and φ-mapping topological current theory, we investigate the topological inner structure of Chern-Simons tensor current. It is proven that the U(1) Chern-Simons tensor current in four-dimensional manifold is just the topological current of creating the string world-sheets.
Exact Slope and Interpolating Functions in N=6 Supersymmetric Chern-Simons Theory
Gromov, Nikolay; Sizov, Grigory
2014-09-01
Using the quantum spectral curve approach we compute, exactly, an observable (called slope function) in the planar Aharony-Bergman-Jafferis-Maldacena theory in terms of an unknown interpolating function h(λ) which plays the role of the coupling in any integrability based calculation in this theory. We verified our results with known weak coupling expansion in the gauge theory and with the results of semiclassical string calculations. Quite surprisingly at strong coupling the result is given by an explicit rational function of h(λ) to all orders. By comparing the structure of our result with that of an exact localization based calculation for a similar observable in Marino and Putrov [J. High Energy Phys. 06 (2010) 011], we conjecture an exact expression for h(λ).
Exact slope and interpolating functions in N=6 supersymmetric Chern-Simons theory.
Gromov, Nikolay; Sizov, Grigory
2014-09-19
Using the quantum spectral curve approach we compute, exactly, an observable (called slope function) in the planar Aharony-Bergman-Jafferis-Maldacena theory in terms of an unknown interpolating function h(λ) which plays the role of the coupling in any integrability based calculation in this theory. We verified our results with known weak coupling expansion in the gauge theory and with the results of semiclassical string calculations. Quite surprisingly at strong coupling the result is given by an explicit rational function of h(λ) to all orders. By comparing the structure of our result with that of an exact localization based calculation for a similar observable in Marino and Putrov [J. High Energy Phys. 06 (2010) 011], we conjecture an exact expression for h(λ).
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.
Dynamical Mass Generation and Confinement in Maxwell-Chern-Simons Planar Quantum Electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Sanchez Madrigal, S; Raya, A [Instituto de Fisica y Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, Edificio C-3, Ciudad Universitaria, Morelia, Michoacan 58040 (Mexico); Hofmann, C P, E-mail: saul@ifm.umicri.mx, E-mail: christoph@ucol.mx, E-mail: raya@ifm.umich.mx [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima, Colima 28045 (Mexico)
2011-04-01
We study the non-perturbative phenomena of Dynamical Mass Generation and Confinement by truncating at the non-perturbative level the Schwinger-Dyson equations in Maxwell-Chern-Simons planar quantum electrodynamics. We obtain numerical solutions for the fermion propagator in Landau gauge within the so-called rainbow approximation. A comparison with the ordinary theory without the Chern-Simons term is presented.
Schnitzer, Howard J
2016-01-01
R\\'enyi and entanglement entropies are constructed for 2d q-deformed topological Yang-Mills theories with gauge group $U(N)$, as well as the dual 3d Chern-Simons (CS) theory on Seifert manifolds. When $q=\\exp[2\\pi i/(N+K)]$, and $K$ is odd, the topological R\\'enyi entropy and Wilson line observables of the CS theory can be expressed in terms of the modular transformation matrices of the WZW theory, $\\rm{\\hat{U}(N)}_{K,N(K+N)}$. If both $K$ and $N$ are odd, there is a level-rank duality of the 2d qYM theory and of the associated CS theory, as well as that of the R\\'enyi and entanglement entropies, and Wilson line observables.
A Dilogarithmic Formula for the Cheeger-Chern-Simons Class
DEFF Research Database (Denmark)
Dupont, Johan Louis; Zickert, C.K.
2005-01-01
We present a simplification of Neumann's formula in [8] for the universal Cheeger-Chern-Simons class of the second Chern polynomial. Our approach is completely algebraic, and the final formula can be applied directly on a homology class in the bar complex.......We present a simplification of Neumann's formula in [8] for the universal Cheeger-Chern-Simons class of the second Chern polynomial. Our approach is completely algebraic, and the final formula can be applied directly on a homology class in the bar complex....
Chern-Simons Particles with Nonstandard Gravitational Interaction
Lukierski, J.; Stichel, P. C.; Zakrzewski, W. J.
2000-01-01
The model of nonrelativistic particles coupled to nonstandard (2+1)-gravity [1] is extended to include Abelian or non-Abelian charges coupled to Chern-Simons gauge fields. Equivalently, the model may be viewed as describing the (Abelian or non-Abelian) anyonic dynamics of Chern-Simons particles coupled, in a reparametrization invariant way, to a translational Chern-Simons action. The quantum two-body problem is described by a nonstandard Schr\\"{o}dinger equation with a noninteger angular mome...
Optical properties of Chern-Simons systems
Huerta, Luis
2016-05-01
Chern-Simons (CS) systems interacting with electromagnetic radiation are described by a term f FɅF added to the Maxwell action. In (3+1)D, this CS term is a boundary term affecting the system behaviour in its borders. We study the consequences of the above in the properties of electromagnetic radiation, in particular, by considering the interplay between magneto-electric properties and topology. Apart from a modified Kerr polarization rotation, compared to that found for the particular case of topological insulators, we also found two Brewster angles, for s and p polarization of reflected radiation, respectively. Energy distribution between reflected and transmitted radiation is also studied in terms of the magneto-electric properties and topological condition of the system.
SIM(1)-VSR Maxwell-Chern-Simons electrodynamics
Bufalo, R.
2016-06-01
In this paper we propose a very special relativity (VSR)-inspired generalization of the Maxwell-Chern-Simons (MCS) electrodynamics. This proposal is based upon the construction of a proper study of the SIM (1)-VSR gauge-symmetry. It is shown that the VSR nonlocal effects present a significant and healthy departure from the usual MCS theory. The classical dynamics is analysed in full detail, by studying the solution for the electric field and static energy for this configuration. Afterwards, the interaction energy between opposite charges is derived and we show that the VSR effects play an important part in obtaining a (novel) finite expression for the static potential.
Massive gravitational waves in Chern-Simons modified gravity
Myung, Yun Soo; Moon, Taeyoon(Institute of Basic Science and Department of Computer Simulation, Inje University, Gimhae, 621-749, Korea)
2014-01-01
We consider the nondynamical Chern-Simons (nCS) modified gravity, which is regarded as a parity-odd theory of massive gravity in four dimensions. We first find polarization modes of gravitational waves for $\\theta=x/\\mu$ in nCS modified gravity by using the Newman-Penrose formalism where the null complex tetrad is necessary to specify gravitational waves. We show that in the Newman-Penrose formalism, the number of polarization modes is one in addition to an unspecified $\\Psi_4$, implying thre...
SIM$(1)$--VSR Maxwell-Chern-Simons electrodynamics
Bufalo, R
2016-01-01
In this paper we propose a very special relativity (VSR)-inspired generalization of the Maxwell-Chern-Simons (MCS) electrodynamics. This proposal is based upon the construction of a proper study of the SIM$(1)$--VSR gauge-symmetry. It is shown that the VSR nonlocal effects present a significant and health departure from the usual MCS theory. The classical dynamics is analysed in full detail, by studying the solution for the electric field and static energy for this configuration. Afterwards, the interaction energy between opposite charges are derived and we show that the VSR effects play an important part in obtaining a (novel) finite expression for the static potential.
Topological aspect of Chern-Simons p-branes
Institute of Scientific and Technical Information of China (English)
Duan Yi-Shi; Zhao Li; Liu Yu-Xiao; Ren Ji-Rong
2007-01-01
By generalizing the topological current of Abelian Chern Simons (CS) vortices, we present a topological tensor current of CS p-branes based on the φ-mapping topological current theory. It is revealed that CS p-branes are located at the isolated zeros of the vector field φ(x), and the topological structure of CS p-branes is characterized by the winding number of the φ-mappings. Furthermore, the Nambu-Goto action and the equation of motion for multi CS p-branes are obtained.
Self-Dual Chern-Simons Vortices in Higgs Field
Institute of Scientific and Technical Information of China (English)
DUAN Yi-Shi; ZHONG Wo-Jun; SI Tie-Yan
2005-01-01
@@ By decomposing the Bogomol'nyi self-dual equation in the Abelian Chern-Simons Higgs model, we find a selfdual topological term that was ignored all the time in the Bogomol'nyi self-duality equation due to the improper decomposition of the complex Higgs field. We also present a new self-dual equation that includes the topological term. It is shown that the self-dual vortex just arises from the symmetric phase of the Higgs field φ = 0. Using our φ-mapping theory, the inner topological structure of the vortex and double vortex is given.
Giambelli Identity in Super Chern-Simons Matrix Model
Matsuno, Satsuki
2016-01-01
A classical identity due to Giambelli in representation theory states that the character in any representation is expressed as a determinant whose components are characters in the hook representation constructed from all the combinations of the arm and leg lengths of the original representation. Previously it was shown that the identity persists in taking, for each character, the matrix integration in the super Chern-Simons matrix model in the grand canonical ensemble. We prove here that this Giambelli compatibility still holds in the deformation of the fractional-brane background.
On the Boundary Dynamics of Chern-Simons Gravity
Arcioni, Giovanni; Blau, Matthias; O'Loughlin, Martin
2002-01-01
We study Chern-Simons theory with a complex G_C or a real G x G gauge group on a manifold with boundary - this includes Lorentzian and Euclidean (anti-) de Sitter (E/A)dS gravity for G=SU(2) or G=SL(2,R). We show that there is a canonical choice of boundary conditions that leads to an unambiguous, fully covariant and gauge invariant, off-shell derivation of the boundary action - a G_C/G or G WZW model, coupled in a gauge invariant way to the boundary value of the gauge field. In particular, f...
Bosonization of $QED_3$ with an induced Chern - Simons term
Kovner, A
1994-01-01
We extend the bosonization of $2+1$ - dimensional QED with one fermionic flavor performed previously to the case of QED with an induced Chern - Simons term. The coefficient of this term is quantized: $e^2n/8\\pi$, $n\\in {\\bf Z}$. The fermion operators are constructed in terms of the bosonic fields $A_i$ and $E_i$. The construction is similar to that in the $n=0$ case. The resulting bosonic theory is Lorentz invariant in the continuum limit and has Maxwell's equations as its equations of motion. The algebra of bilinears exhibits nontrivial operatorial mixing with lower dimensional operators, which is absent for $n=0$.
Extremal Black Holes in Dynamical Chern-Simons Gravity
McNees, Robert; Yunes, Nicolás
2015-01-01
Rapidly rotating black hole solutions in theories beyond general relativity play a key role in experimental gravity, as they allow us to compute observables in extreme spacetimes that deviate from the predictions of general relativity (GR). Such solutions are often difficult to find in beyond-GR theories due to the inclusion of additional fields that couple to the metric non-linearly and non-minimally. In this paper, we consider rotating black hole solutions in one such theory, dynamical Chern-Simons gravity, where the Einstein-Hilbert action is modified by the introduction of a dynamical scalar field that couples to the metric through the Pontryagin density. We treat dynamical Chern-Simons gravity as an effective field theory and thus work in the decoupling limit, where corrections are treated as small perturbations from general relativity. We perturb about the maximally-rotating Kerr solution, the so-called extremal limit, and develop mathematical insight into the analysis techniques needed to construct sol...
Dynamics of magnetic fields in Maxwell, Yang-Mills and Chern-Simons theories on the torus
International Nuclear Information System (INIS)
The problem of uniform magnetic fields passing perpendicularly through a 2-torus, Abelian and Non-Abelian, is considered. Focus is on dynamical effects of non-integrable phases on the torus at non zero B and from magnetic fields themselves in the vacuum. The spectrum is computed and is shown to be always independent of the non-integrable phases on the torus. It is concluded that a Chern-Simons term will always be induced by radiative corrections to fermions on the torus when B ≠ 0. The special case of an electromagnetically uncharged anyon gas in noted and shown to be a system whose spectrum can depend on the non-integrable phases in the two torus directions, subject to a consistency requirement. In three and four dimensions, dynamical symmetry breaking of non-Abelian fields and associated condensate formation is possible by radiative corrections. The classification on non-Abelian magnetic fields in terms of ''flux integers'' is discussed, and a method for obtaining such integers for an arbitrary gauge algebra is presented. This provides a rigorous generalisation of Hooft's su (2) classification. 72 refs., 5 figs
Gauge Symmetries and Holographic Anomalies of Chern-Simons and Transgression AdS Gravity
Mora, Pablo
2014-01-01
We review the issue of gauge and gravitational anomalies with backgrounds, maybe offering a new outlook on some aspects of these questions. We compute the holographic anomalies of hypothetical theories dual, in the sense of the AdS-CFT correspondence, to Chern-Simons AdS gravities. Those anomalies are either gauge anomalies associated to the AdS gauge group of the theory or diffeomorphism anomalies, with each kind related to the other. As a result of using suitable action principles por Chern-Simons AdS gravities, coming from Transgression forms, we obtain finite results without the need for further regularization. Our results are of potential interest for Lovelock gravity theories, as it has been shown that the boundary terms dictated by the transgressions for Chern-Simons gravities are also suitable to regularize Lovelock theories. The Wess-Zumino consistency condition ensures that anomalies of the generic form computed here should appear for these and other theories.
Self-Dual Vortices in Chern-Simons Hydrodynamics
Pashaev, O K; Pashaev, Oktay K.; Lee, and Jyh-Hao
2001-01-01
The classical theory of non-relativistic charged particle interacting with U(1) gauge field is reformulated as the Schr\\"odinger wave equation modified by the de-Broglie-Bohm quantum potential nonlinearity. For, (1 - $\\hbar^2$) deformed strength of quantum potential the model is gauge equivalent to the standard Schr\\"odinger equation with Planck constant $\\hbar$, while for the strength (1 + $\\hbar^2$), to the pair of diffusion-anti-diffusion equations. Specifying the gauge field as Abelian Chern-Simons (CS) one in 2+1 dimensions interacting with the Nonlinear Schr\\"odinger field (the Jackiw-Pi model), we represent the theory as a planar Madelung fluid, where the Chern-Simons Gauss law has simple physical meaning of creation the local vorticity for the fluid flow. For the static flow, when velocity of the center-of-mass motion (the classical velocity) is equal to the quantum one (generated by quantum potential velocity of the internal motion), the fluid admits N-vortex solution. Applying the Auberson-Sabatier ...
Seiberg duality for Chern-Simons quivers and D-brane mutations
Closset, Cyril
2012-01-01
Chern-Simons quivers for M2-branes at Calabi-Yau singularities are best understood as the low energy theory of D2-branes on a dual type IIA background. We show how the D2-brane point of view naturally leads to three dimensional Seiberg dualities for Chern-Simons quivers with chiral matter content: They arise from a change of brane basis (or mutation), in complete analogy with the better known Seiberg dualities for D3-brane quivers. This perspective reproduces the known rules for Seiberg dualities in Chern-Simons-Yang-Mills theories with unitary gauge groups. We provide explicit examples of dual theories for the quiver dual to the Y^{p,q}(CP^2) geometries. We also comment on the string theory derivation of CS quivers dual to massive type IIA geometries.
Dense Chern-Simons Matter with Fermions at Large N
Geracie, Michael; Son, Dam T
2015-01-01
In this paper we investigate properties of Chern-Simons theory coupled to massive fermions in the large N limit. We demonstrate that at low temperatures the system is in a Fermi liquid state whose features can be systematically compared to the standard phenomenological theory of Landau Fermi liquids. This includes matching microscopically derived Landau parameters with thermodynamic predictions of Landau Fermi liquid theory. We also calculate the exact conductivity and viscosity tensors at zero temperature and finite chemical potential. In particular we point out that the Hall conductivity of an interacting system is not entirely accounted for by the Berry flux through the Fermi sphere. Furthermore, investigation of the thermodynamics in the non-relativistic limit reveals novel phenomena at strong coupling. As the 't Hooft coupling approaches 1, the system exhibits an extended intermediate temperature regime in which the thermodynamics is described by neither the quantum Fermi liquid theory nor the classical ...
A note on large N thermal free energy in supersymmetric Chern-Simons vector models
Energy Technology Data Exchange (ETDEWEB)
Yokoyama, Shuichi [Department of Theoretical Physics, Tata Institute of Fundamental Research,Homi Bhabha Road, Mumbai 400005 (India)
2014-01-27
We compute the exact effective action for N=3U(N){sub k} and N=4,6U(N){sub k}×U(N′){sub −k} Chern-Simons theories with minimal matter content in the ’t Hooft vector model limit under which N and k go to infinity holding N/k,N′ fixed. We also extend this calculation to N=4,6 mass deformed case. We show that those large N effective actions except mass-deformed N=6 case precisely reduce to that of N=2U(N){sub k} Chern-Simons theory with one fundamental chiral field up to overall multiple factor. By using this result we argue the thermal free energy and self-duality of the N=3,4,6 Chern-Simons theories including the N=4 mass term reduce to those of the N=2 case under the limit.
A note on large N thermal free energy in supersymmetric Chern-Simons vector models
International Nuclear Information System (INIS)
We compute the exact effective action for N=3U(N)k and N=4,6U(N)k×U(N′)−k Chern-Simons theories with minimal matter content in the ’t Hooft vector model limit under which N and k go to infinity holding N/k,N′ fixed. We also extend this calculation to N=4,6 mass deformed case. We show that those large N effective actions except mass-deformed N=6 case precisely reduce to that of N=2U(N)k Chern-Simons theory with one fundamental chiral field up to overall multiple factor. By using this result we argue the thermal free energy and self-duality of the N=3,4,6 Chern-Simons theories including the N=4 mass term reduce to those of the N=2 case under the limit
Hassaine, Mokhtar
2016-01-01
This book grew out of a set of lecture notes on gravitational Chern–Simons (CS) theories developed over the past decade for several schools and different audiences including graduate students and researchers.CS theories are gauge-invariant theories that can include gravity consistently. They are only defined in odd dimensions and represent a very special class of theories in the Lovelock family. Lovelock gravitation theories are the natural extensions of General Relativity for dimensions greater than four that yield second-order field equations for the metric. These theories also admit local supersymmetric extensions where supersymmetry is an off-shell symmetry of the action, as in a standard gauge theory.Apart from the arguments of mathematical elegance and beauty, the gravitational CS actions are exceptionally endowed with physical attributes that suggest the viability of a quantum interpretation. CS theories are gauge-invariant, scale-invariant and background independent; they have no dimensional couplin...
Chern-Simons modified gravity and closed time-like curves
Porfirio, P J; Nascimento, J R; Petrov, A Yu; Ricardo, J; Santos, A F
2016-01-01
We verify the consistency of the G\\"odel-type solutions within the four-dimensional Chern-Simons modified gravity with the non-dynamical Chern-Simons coefficient, for different forms of matter including dust, fluid, scalar field and electromagnetic field, and the related causality issues. Unlike the general relativity, the vacuum solution turns out to be possible in our theory. Another essentially new result of our theory having no analogue in the general relativity consists in the existence of the hyperbolic causal solutions for the physically well-motivated matter.
Chern-Simons topological Lagrangians in odd dimensions and their Kaluza-Klein reduction
International Nuclear Information System (INIS)
Clarifying the behavior of generic Chern-Simons secondary invariants under infinitesimal variation and finite gauge transformation, it is proved that they are eligible to be a candidate term in the Lagrangian in odd dimensions (2k-1 for gauge theories and 4k-1 for gravity). The coefficients in front of these terms may be quantized because of topological reasons. As a possible application, the dimensional reduction of such actions in Kaluza-Klein theory is discussed. The difficulty in defining the Chern-Simons action for topologically nontrivial field configurations is pointed out and resolved
On the boundary dynamics of Chern-Simons gravity
International Nuclear Information System (INIS)
We study Chern-Simons theory with a complex GC or a real GxG gauge group on a manifold with boundary - this includes lorentzian and euclidean (anti-) de Sitter (E/A)dS gravity for G=SU(2) or G=SL(2,R). We show that there is a canonical choice of boundary conditions that leads to an unambiguous, fully covariant and gauge invariant, off-shell derivation of the boundary action - a GC/G or G WZW model, coupled in a gauge invariant way to the boundary value of the gauge field. In particular, for (E/A)dS gravity, the boundary action is a WZW model with target space (E/A)dS3, reminiscent of a worldsheet for worldsheet mechanism. We discuss in some detail the properties of the boundary theories that arise and we confront our results with various related constructions in the literature. (author)
On the Boundary Dynamics of Chern-Simons Gravity
Arcioni, G; O'Loughlin, M H; Arcioni, Giovanni; Blau, Matthias; Loughlin, Martin O'
2003-01-01
We study Chern-Simons theory with a complex G_C or a real G x G gauge group on a manifold with boundary - this includes Lorentzian and Euclidean (anti-) de Sitter (E/A)dS gravity for G=SU(2) or G=SL(2,R). We show that there is a canonical choice of boundary conditions that leads to an unambiguous, fully covariant and gauge invariant, off-shell derivation of the boundary action - a G_C/G or G WZW model, coupled in a gauge invariant way to the boundary value of the gauge field. In particular, for (E/A)dS gravity, the boundary action is a WZW model with target space (E/A)dS_3, reminiscent of a worldsheet for worldsheet mechanism. We discuss in some detail the properties of the boundary theories that arise and we confront our results with various related constructions in the literature.
Chern-Simons Particles with Nonstandard Gravitational Interaction
Lukierski, J; Zakrzewski, W J
2001-01-01
The model of nonrelativistic particles coupled to nonstandard (2+1)-gravity [1] is extended to include Abelian or non-Abelian charges coupled to Chern-Simons gauge fields. Equivalently, the model may be viewed as describing the (Abelian or non-Abelian) anyonic dynamics of Chern-Simons particles coupled, in a reparametrization invariant way, to a translational Chern-Simons action. The quantum two-body problem is described by a nonstandard Schr\\"{o}dinger equation with a noninteger angular momentum depending on energy as well as particle charges. Some numerical results describing the modification of the energy levels by these charges in the confined regime are presented. The modification involves a shift as well as splitting of the levels.
Chern-Simons particles with nonstandard gravitational interaction
Energy Technology Data Exchange (ETDEWEB)
Lukierski, J. [Wroclaw Univ. (Poland). Inst. of Theoretical Physics; Dept. de Fisica Teorica, Universidad de Valencia, Burjasot (Spain); Stichel, P.C.; Zakrzewski, W.J. [Dept. of Mathematical Sciences, Univ. of Durham (United Kingdom); Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)
2001-05-01
The model of nonrelativistic particles coupled to nonstandard (2+1)-gravity is extended to include Abelian or non-Abelian charges coupled to Chern-Simons gauge fields. Equivalently, the model may be viewed as describing the (Abelian or non-Abelian) anyonic dynamics of Chern-Simons particles coupled, in a reparameterization invariant way, to a translational Chern-Simons action. The quantum 2-body problem is described by a nonstandard Schroedinger equation with a noninteger angular momentum depending on energy as well as particle charges. Some numerical results describing the modification of the energy levels by these charges in the confined regime are presented. The modification involves a shift as well as splitting of the levels. (orig.)
Chern-Simons particles with nonstandard gravitational interaction
International Nuclear Information System (INIS)
The model of nonrelativistic particles coupled to nonstandard (2+1)-gravity is extended to include Abelian or non-Abelian charges coupled to Chern-Simons gauge fields. Equivalently, the model may be viewed as describing the (Abelian or non-Abelian) anyonic dynamics of Chern-Simons particles coupled, in a reparameterization invariant way, to a translational Chern-Simons action. The quantum 2-body problem is described by a nonstandard Schroedinger equation with a noninteger angular momentum depending on energy as well as particle charges. Some numerical results describing the modification of the energy levels by these charges in the confined regime are presented. The modification involves a shift as well as splitting of the levels. (orig.)
2D Gravity on $AdS_2$ with Chern-Simons Corrections
Alishahiha, Mohsen; Mosaffa, Amir E
2009-01-01
We study 2D Maxwell-dilaton gravity with higher order corrections given by the Chern-Simons term. The model admits three distinctive $AdS_2$ vacuum solutions. By making use of the entropy function formalism we find the entropy of the solutions which is corrected due to the presence of the Chern-Simons term. We observe that the form of the correction depends not only on the coefficient of the Chern-Simons term, but also on the sign of the electric charge; pointing toward the chiral nature of the dual CFT. Using the asymptotic symmetry of the theory as well as requiring a consistent picture we can find the central charge and the level of U(1) current. Upon uplifting the solutions to three dimensions we get purely geometric solutions which will be either $AdS_3$ or warped $AdS_3$ with an identification.
Maxwell-Chern-Simons Hydrodynamics for the Chiral Magnetic Effect
Ozonder, Sener
2010-01-01
The rate of vacuum changing topological solutions of the gluon field, sphalerons, is estimated to be large at the typical temperatures of heavy-ion collisions, particularly at the Relativistic Heavy Ion Collider. Such windings in the gluon field are expected to produce parity-odd bubbles, which cause separation of positively and negatively charged quarks along the axis of the external magnetic field. This Chiral Magnetic Effect can be mimicked by Chern-Simons modified electromagnetism. Here we present a model of relativistic hydrodynamics including the effects of axial anomalies via the Chern-Simons term.
AdS Chern-Simons Gravity induces Conformal Gravity
Aros, Rodrigo
2013-01-01
The leitmotif of this paper is the question of whether four- and higher even-dimensional Conformal Gravities do have a Chern-Simons pedigree. We show that Weyl gravity can be obtained as dimensional reduction of a five-dimensional Chern-Simons action for a suitable (gauged-fixed, tractor-like) five-dimensional AdS connection. The gauge-fixing and dimensional reduction program admits a readily generalization to higher dimensions for the case of certain conformal gravities obtained by contractions of the Weyl tensor.
Resolution of Chern--Simons--Higgs Vortex Equations
Han, Xiaosen; Yang, Yisong
2015-01-01
It is well known that the presence of multiple constraints of non-Abelian relativisitic Chern--Simons--Higgs vortex equations makes it difficult to develop an existence theory when the underlying Cartan matrix $K$ of the equations is that of a general simple Lie algebra and the strongest result in the literature so far is when the Cartan subalgebra is of dimension 2. In this paper we overcome this difficulty by implicitly resolving the multiple constraints using a degree-theorem argument, utilizing a key positivity property of the inverse of the Cartan matrix deduced in an earlier work of Lusztig and Tits, which enables a process that converts the equality constraints to inequality constraints in the variational formalism. Thus this work establishes a general existence theorem which settles a long-standing open problem in the field regarding the general solvability of the equations.
Massive gravitational waves in Chern-Simons modified gravity
Energy Technology Data Exchange (ETDEWEB)
Myung, Yun Soo; Moon, Taeyoon, E-mail: ysmyung@inje.ac.kr, E-mail: tymoon@inje.ac.kr [Institute of Basic Science and Department of Computer Simulation, Inje University, Gimhae 621-749 (Korea, Republic of)
2014-10-01
We consider the nondynamical Chern-Simons (nCS) modified gravity, which is regarded as a parity-odd theory of massive gravity in four dimensions. We first find polarization modes of gravitational waves for θ=x/μ in nCS modified gravity by using the Newman-Penrose formalism where the null complex tetrad is necessary to specify gravitational waves. We show that in the Newman–Penrose formalism, the number of polarization modes is one in addition to an unspecified Ψ{sub 4}, implying three degrees of freedom for θ=x/μ. This compares with two for a canonical embedding of θ=t/μ. Also, if one introduces the Ricci tensor formalism to describe a massive graviton arising from the nCS modified gravity, one finds one massive mode after making second-order wave equations, which is compared to five found from the parity-even Einstein–Weyl gravity.
A note on large N thermal free energy in supersymmetric Chern-Simons vector models
Shuichi Yokoyama
2014-01-01
We compute the exact effective action for $ \\mathcal{N} $ = 3 U( N ) k and $ \\mathcal{N} $ = 4, 6 U( N ) k × U( N ′) − k Chern-Simons theories with minimal matter content in the ’t Hooft vector model limit under which N and k go to infinity holding N/k,N ′ fixed. We also extend this calculation to $ \\mathcal{N} $ = 4, 6 mass deformed case. We show that those large N effective actions except mass-deformed $ \\mathcal{N} $ = 6 case precisely reduce to that of $ \\mathcal{N} $ = 2 U( N ) k Chern-S...
Lorentz and PCT Violating Chern-Simons Term in the Derivative Expansion of QED
Chung, J M; Oh, Phillial
1999-01-01
We calculate by the method of dimensional regularization and derivative expansion the one-loop effective action for a Dirac fermion with a Lorentz-violating and PCT-odd kinetic term in the background of a gauge field. We show that this term induces a Chern-Simons modification to Maxwell theory. Some related issues are also discussed.
Duality between Noncommutative Yang-Mills-Chern-Simons and Non-Abelian Self-Dual Models
Cantcheff, M B; Minces, Pablo
2003-01-01
By introducing an appropriate parent action and considering a perturbative approach, we establish, up to fourth order terms in the field and for the full range of the coupling constant, the equivalence between the noncommutative Yang-Mills-Chern-Simons theory and the noncommutative, non-Abelian Self-Dual model.
A first-class approach of higher derivative Maxwell-Chern-Simons-Proca model
Energy Technology Data Exchange (ETDEWEB)
Sararu, Silviu-Constantin [University of Craiova, Department of Physics, Craiova (Romania)
2015-11-15
The equivalence between a higher derivative extension of Maxwell-Chern-Simons-Proca model and some gauge invariant theories from the point of view of the Hamiltonian path integral quantization in the framework of the gauge-unfixing approach is investigated. The Hamiltonian path integrals of the first-class systems take manifestly Lorentz-covariant forms. (orig.)
Parametrized Post-Newtonian Expansion of Chern-Simons Gravity
Alexander, Stephon
2007-01-01
We investigate the weak-field, post-Newtonian expansion to the solution of the field equations in Chern-Simons gravity with a perfect fluid source. In particular, we study the mapping of this solution to the parameterized post-Newtonian formalism to 1 PN order in the metric. We find that the PPN parameters of Chern-Simons gravity are identical to those of general relativity, with the exception of the inclusion of a new term that is proportional to the Chern-Simons coupling parameter and the curl of the PPN vector potentials. We also find that the new term is naturally enhanced by the non-linearity of spacetime and we provide a physical interpretation for it. By mapping this correction to the gravito-electro-magnetic framework, we study the corrections that this new term introduces to the acceleration of point particles and the frame-dragging effect in gyroscopic precession. We find that the Chern-Simons correction to these classical predictions could be used by current and future experiments to place bounds o...
Euler Chern Simons Gravity from Lovelock Born Infeld Gravity
Izaurieta, Fernando; Rodriguez, Eduardo; Salgado, Patricio
2004-01-01
In the context of a gauge theoretical formulation, higher dimensional gravity invariant under the AdS group is dimensionally reduced to Euler-Chern-Simons gravity. The dimensional reduction procedure of Grignani-Nardelli [Phys. Lett. B 300, 38 (1993)] is generalized so as to permit reducing D-dimensional Lanczos Lovelock gravity to d=D-1 dimensions.
Stellar equilibrium in Einstein-Chern-Simons gravity
Quinzacara, Cristian
2016-01-01
We consider a spherically symmetric internal solution within the context of Einstein-Chern-Simons gravity and derive a generalized five-dimensional Tolman-Oppenheimer-Volkoff (TOV) equation. It is shown that the generalized TOV equation leads, in a certain limit, to the standard five-dimensional TOV equation
Institute of Scientific and Technical Information of China (English)
张龙; 翁征宇
2015-01-01
The fermion sign plays a dominant role in Fermi liquid theory. However, in Mott insulators, the strong Coulomb interaction suppresses the charge fluctuations and eliminates the fermion signs due to electron permutation. In this article, we first review the phase string theory of the Hubbard model for a bipartite lattice, which unifies the Fermi liquid at weak coupling and the antiferromagnetic Mott insulator at strong coupling. We first derive the exact sign structure of the Hubbard model for an arbitrary Coulomb interaction U . In small U limit, the conventional fermion sign is restored, while at large U limit, it leads to the phase string sign structure of the t-J model. For half filling, we construct an electron fractionalization representation, in which chargons and spinons are coupled to each other via emergent mutual Chern-Simons gauge fields. The corresponding ground state ansatz and low energy effective theory capture the ground state phase diagram of the Hubbard model qualitatively. For weak coupling regime, the Fermi liquid quasiparticle is formed by the bound state of a chargon and a spinon, and the long range phase coherence is determined by the background spin correlation. The Mott transition can be realized either by forming the chargon gap or by condensing the background spinons.
Action Principles for Transgression and Chern-Simons AdS Gravities
Mora, Pablo
2014-01-01
Chern-Simons gravities are theories with a lagrangian given by a Chern-Simons form constructed from a space-time gauge group. In previous investigations we showed that, for some special field configurations that are solutions of the field equations, the extension from Chern-Simons to Transgression forms as lagrangians, motivated by gauge invariance, automatically yields the boundary terms required to regularize the theory, giving finite conserved charges and black hole thermodynamics. Further work by other researchers showed that one of the action functionals considered in the above mentioned work yields a well defined action principle in the metric (zero torsion) case and for asymptotically Anti de Sitter (AdS) space-times. In the present work we consider several action functionals for Chern-Simons AdS gravity constructed from Transgression forms, and show the action principles to be well defined and the Noether charges and Euclidean action to be finite for field configurations satisfying only that the gauge...
The Chern-Simons invariant as the natural time variable for classical and quantum cosmology
Smolin, L; Smolin, Lee; Soo, Chopin
1995-01-01
We propose that the Chern-Simons invariant of the Ashtekar-Sen connection is the natural internal time coordinate for classical and quantum cosmology. The reasons for this are a number of interesting properties of this functional, which we describe here. 1)It is a function on the gauge and diffeomorphism invariant configuration space, whose gradient is orthogonal to the two physical degrees of freedom, in the metric defined by the Ashtekar formulation of general relativity. 2)The imaginary part of the Chern-Simons form reduces in the limit of small cosmological constant, \\Lambda, and solutions close to DeSitter spacetime, to the York extrinsic time coordinate. 3)Small matter-field excitations of the Chern-Simons state satisfy, by virtue of the quantum constraints, a functional Schroedinger equation in which the matter fields evolve on a DeSitter background in the Chern-Simons time. We then n propose this is the natural vacuum state of the theory for \\Lambda \
Spherical Symmetric Gravitational Collapse in Chern-Simon Modified Gravity
Amir, Muhammad Jamil
2014-01-01
This paper is devoted to investigate the gravitational perfect fluid collapse in the framework of Chern-Simon modified gravity. For this purpose, we assume the spherically symmetric metric as an interior region and the Schwarzchild spacetime is considered as an exterior region of the star. The Israel junction conditions are used to match the interior and exterior spacetimes. For the sake of simplicity, we take the external field $\\Theta$ as a function of time parameter $t$ and obtain the solution of the field equations of Chern-Simon modified gravity. Junction conditions have been used to calculate the gravitational mass. We discuss the apparent horizons and their physical consequences. It is mentioning here that our results will reduce to those of general relativity, available in literature, if the external field is taken to be constant.
Gauged Baby Skyrme Model with Chern-Simons term
Samoilenka, A
2016-01-01
The properties of the multisoliton solutions of the (2+1)-dimensional Maxwell-Chern-Simons-Skyrme model are investigated numerically. Coupling to the Chern-Simons term allows for existence of the electrically charge solitons which may also carry magnetic fluxes. Two particular choices of the potential term is considered: (i) the weakly bounded potential and (ii) the double vacuum potential. In the absence of the gauge interaction in the former case the individual constituents of the multisoliton configuration are well separated, while in the latter case the rotational invariance of the configuration remains unbroken. It is shown that coupling of the planar multi-Skyrmions to the electric and magnetic field strongly affects the pattern of interaction between the constituents. We analyze the dependency of the structure of the solutions, the energies, angular momenta, electric and magnetic fields of the configurations on the gauge coupling constant $g$, and the electric potential. It is found that, generically, ...
Chern-Simons Couplings and Inequivalent Vector-Tensor Multiplets
Claus, P; Faux, M; Termonia, P
1996-01-01
The off-shell vector-tensor multiplet is considered in an arbitrary background of N=2 vector supermultiplets. We establish the existence of two inequivalent versions, characterized by different Chern-Simons couplings. In one version the vector field of the vector-tensor multiplet is contained quadratically in the Chern-Simons term, which implies nonlinear terms in the supersymmetry transformations and equations of motion. In the second version, which requires a background of at least two abelian vector supermultiplets, the supersymmetry transformations remain at most linear in the vector-tensor components. This version is of the type known to arise from reduction of tensor supermultiplets in six dimensions. Our work applies to any number of vector-tensor multiplets.
Two gravitationally Chern-Simons terms are too many
Aragone, C; Khoudeir, A; Arias, Pio J.
1993-01-01
It is shown that topological massive gravity augmented by the triadic gravitational Chern-Simons first order term is a curved a pure spin-2 action. This model contains two massive spin-2 excitations. However, since its light-front energy is not semidefinite positive, this double CS-action does not have any physical relevance.In other words, topological massive gravity cannot be spontaneously broken down by the presence of the triadic CS term.
Higgs- and Skyrme-Chern-Simons densities in all dimensions
Tchrakian, D H
2015-01-01
Two types of new Chern-Simons (CS) densities, both defined in all odd and even dimensions, are proposed. These new CS densities feature a scalar field interacting with a scalar. In one case this is a Higgs scalar while in the other it is a Skyrme scalar. The motivation is to study the effects of adding these new CS terms to a Lagrangian which supports static soliton solutions prior to their introduction.
Translational Chern--Simons Action and New Planar Particle Dynamics
Lukierski, J.; Stichel, P. C.; Zakrzewski, W. J.
2000-01-01
We consider a nonstandard $D=2+1$ gravity described by a translational Chern--Simons action, and couple it to the nonrelativistic point particles. We fix the asymptotic coordinate transformations in such a way that the space part of the metric becomes asymptotically Euclidean. The residual symmetries are (local in time) translations and rigid rotations. The phase space Hamiltonian $H$ describing two-body interactions satisfies a nonlinear equation $H={\\cal H}(\\vec{x},\\vec{p};H)$ what implies,...
Standard general relativity from Chern-Simons gravity
International Nuclear Information System (INIS)
Chern-Simons models for gravity are interesting because they provide a truly gauge-invariant action principle in the fiber-bundle sense. So far, their main drawback has largely been its perceived remoteness from standard General Relativity, based on the presence of higher powers of the curvature in the Lagrangian (except, remarkably, for three-dimensional spacetime). Here we report on a simple model that suggests a mechanism by which standard General Relativity in five-dimensional spacetime may indeed emerge at a special critical point in the space of couplings, where additional degrees of freedom and corresponding 'anomalous' Gauss-Bonnet constraints drop out from the Chern-Simons action. To achieve this goal, both the Lie algebra g and the symmetric g-invariant tensor that define the Chern-Simons Lagrangian are constructed by means of the Lie algebra S-expansion method with a suitable finite Abelian semigroup S. The results are generalized to arbitrary odd dimensions, and the possible extension to the case of eleven-dimensional supergravity is briefly discussed.
Fractional angular momentum in noncommutative generalized Chern-Simons quantum mechanics
Zhang, Xi-Lun; Sun, Yong-Li; Wang, Qing; Long, Zheng-Wen; Jing, Jian
2016-07-01
The noncommutative generalized Chern-Simons quantum mechanics, i.e., the Chern-Simons quantum mechanics on the noncommutative plane in the presence of Aharonov-Bohm magnetic vector potentials, is studied in this paper. We focus our attention on the canonical orbital angular momentum and show that there are two different approaches to produce the fractional angular momentum in the noncommutative generalized Chern-Simons quantum mechanics.
Scattering Amplitude and Bosonization Duality in General Chern-Simons Vector Models
Yokoyama, Shuichi
2016-01-01
We present exact large N calculus of four point function in general Chern-Simons bosonic and fermionic vector models. Applying the LSZ formula to the four point function we determine two body scattering amplitudes in these theories combined with a special care for a non-analytic term to achieve unitarity in the singlet channel. We show that the S-matrix enjoys the bosonization duality, usual crossing relation and admits non-relativistic reduction to Aharonov-Bohm scattering. We also argue that the S-matrix develops a pole in a certain range of coupling constants, which disappears in the range where the theory reduces to Chern-Simons theory with free fermions.
Chern-Simons dilaton black holes in 2+1 dimensions
Moussa, Karim Ait; Guennoune, Hakim
2015-01-01
We construct rotating magnetic solutions to the three-dimensional Einstein-Maxwell-Chern-Simons-dilaton theory with a Liouville potential. These include a class of black hole solutions which generalize the warped AdS black holes. The regular black holes belong to two disjoint sectors. The first sector includes black holes which have a positive mass and are co-rotating, while the black holes of the second sector have a negative mass and are counter-rotating. We also show that a particular, non-black hole, subfamily of our three-dimensional solutions may be uplifted to new regular non-asymptotically flat solutions of five-dimensional Einstein-Maxwell-Chern-Simons theory.
Notes on Planar Resolvents of Chern-Simons-matter Matrix Models
Suyama, Takao
2016-01-01
We revisit planar resolvents of matrix models corresponding to ${\\cal N}\\ge3$ Chern-Simons-matter theories with the gauge groups of the form ${\\rm U}(N_1)\\times{\\rm U}(N_2)$ coupled to any number of bi-fundamental hypermultiplets. We find that the derivative of a suitably defined planar resolvent can be written explicitly. From this resolvent, we derive the explicit formula for (a linear combination of) the vevs of BPS Wilson loops.
Knot Invariants and M-Theory I: Hitchin Equations, Chern-Simons Actions, and the Surface Operators
Dasgupta, Keshav; Ramadevi, P; Tatar, Radu
2016-01-01
Recently Witten introduced a type IIB brane construction with certain boundary conditions to study knot invariants and Khovanov homology. The essential ingredients used in his work are the topologically twisted N = 4 Yang-Mills theory, localization equations and surface operators. In this paper we extend his construction in two possible ways. On one hand we show that a slight modification of Witten's brane construction could lead, using certain well defined duality transformations, to the model used by Ooguri-Vafa to study knot invariants using gravity duals. On the other hand, we argue that both these constructions, of Witten and of Ooguri-Vafa, lead to two different seven-dimensional manifolds in M-theory from where the topological theories may appear from certain twisting of the G-flux action. The non-abelian nature of the topological action may also be studied if we take the wrapped M2-brane states in the theory. We discuss explicit constructions of the seven-dimensional manifolds in M-theory, and show th...
Wilson lines and Chern-Simons flux in explicit heterotic Calabi-Yau compactifications
Apruzzi, Fabio; Parameswaran, Susha; Zagermann, Marco
2014-01-01
We study to what extent Wilson lines in heterotic Calabi-Yau compactifications lead to non-trivial H-flux via Chern-Simons terms. Wilson lines are basic ingredients for Standard Model constructions but their induced H-flux may affect the consistency of the leading order background geometry and of the two-dimensional worldsheet theory. Moreover H-flux in heterotic compactifications would play an important role for moduli stabilization and could strongly constrain the supersymmetry breaking scale. We show how to compute H-flux and the corresponding superpotential, given an explicit complete intersection Calabi-Yau compactification and choice of Wilson lines. We do so by classifying special Lagrangian submanifolds in the Calabi-Yau, understanding how the Wilson lines project onto these submanifolds, and computing their Chern-Simons invariants. We illustrate our procedure with the quintic hypersurface as well as the split-bicubic, which can provide a potentially realistic three generation model.
Charged Rotating AdS Black Holes with Chern-Simons coupling
Mir, Mozhgan
2016-01-01
We obtain a perturbative solution for rotating charged black holes in 5-dimensional Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant. We start from a small undeformed Kerr-AdS solution and use the electric charge as a perturbative parameter to build up black holes with equal-magnitude angular momenta up to forth order. These black hole solutions are described by three parameters, the charge, horizon radius and horizon angular velocity. We determine the physical quantities of these black holes and study their dependence on the parameters of black holes and arbitrary Chern-Simons coefficient. In particular, for values of CS coupling constant beyond its supergravity amount, due to a rotational instability, counterrotating black holes arise. Also the rotating solutions appear to have vanishing angular momenta and do not manifest uniquely by their global charges.
Self-Dual Chern-Simons Solitons in (2+1)-Dimensional Einstein Gravity
Cangemi, D; Cangemi, Daniel; Lee, Choonkyu
1992-01-01
We consider here a generalization of the Abelian Higgs model in curved space, by adding a Chern--Simons term. The static equations are self-dual provided we choose a suitable potential. The solutions give a self-dual Maxwell--Chern--Simons soliton that possesses a mass and a spin.
Perturbative evaluation of circular 1/2 BPS Wilson loops in N = 6 Super Chern-Simons theories
Griguolo, Luca; Poggi, Matteo; Seminara, Domenico
2013-01-01
We present a complete two-loop analysis of the quantum expectation value for circular BPS Wilson loops in ABJ(M) theories. We examine in details the 1/2 BPS case, that requires non-trivial fermionic couplings with the contour, finding perfect agreement with the exact matrix model answer at zero framing. The result is obtained through a careful application of DRED regularization scheme, combined with a judicious rearrangement of the relevant perturbative contributions that reduces the computation to simple integrals. We carefully analyze the contribution of fermions that is crucial for the consistency with the localization procedure and point out the arising of pivotal evanescent terms, discussing their meaning in relation to Ward identities.
New Chern-Simons densities in both odd and even dimensions
Radu, Eugen; Tchrakian, Tigran
2011-01-01
After reviewing briefly the dimensional reduction of Chern--Pontryagin densities, we define new Chern--Simons densities expressed in terms of Yang-Mills and Higgs fields. These are defined in all dimensions, including in even dimensional spacetimes. They are constructed by subjecting the dimensionally reduced Chern--Pontryagin densites to further descent by two steps.
Dirichlet boundary-value problem for Chern-Simons modified gravity
International Nuclear Information System (INIS)
Chern-Simons modified gravity comprises the Einstein-Hilbert action and a higher-derivative interaction containing the Chern-Pontryagin density. We derive the analog of the Gibbons-Hawking-York boundary term required to render the Dirichlet boundary-value problem well defined. It turns out to be a boundary Chern-Simons action for the extrinsic curvature. We address applications to black hole thermodynamics.
Complex Chern-Simons and Gribov
Amaral, M M; Ventura, O S; Vilar, L C Q
2016-01-01
We explore a contact point between two distinct approaches to the confinment problem. We show that BLG-ABJM like theories generate gauge propagators with just the complex pole structure prescribed by the Gribov scenario for confinemnt. This structure, known as i-particles in Gribov-Zwanziger theories, effectively allows the definition of composite operators with a positive K\\"{a}ll\\'{e}n-Lehmann spectral representation for their two-point functions . Then, these operators satisfy the criteria to describe glue-ball condensates. We calculate the (first order) contribution to the two-point function of the gauge invariant condensate in an ABJM environment, showing its interpretation as a physical particle along K\\"{a}ll\\'{e}n-Lehmann. In the meantime, we argue for the necessity of absorbing Witten's work on holomorphic complex theories in order to settle the physical interpretation of this non-perturbative scenario.
Chern--Simons--Yang--Mills system in presence of Gribov horizon with fundamental Higgs matter
Gomez, Arturo J; Sorella, Silvio P
2015-01-01
In this work we study the behaviour of Yang--Mills--Chern--Simons theory coupled to a Higgs field in the fundamental representation by taking into account the effects of the presence of the Gribov horizon. By analyzing the infrared structure of the gauge field propagator, both confined and de-confined regions can be detected. The confined region corresponds to the appearance of complex poles in the propagators, while the de-confined one to the presence of real poles. One can move from one region to another by changing the parameters of the theory.
Bound states in the (2+1)D scalar electrodynamics with Chern-Simons term
International Nuclear Information System (INIS)
This work studies the existence of bound states for the 3-dimensions scalar electrodynamics, with the Chern-Simons. Quantum field theory is used for calculation of the Mfi scattering matrices, in the non-relativistic approximation. The field propagators responsible for the interaction in the scattering processes have been calculated, and scattering matrices have been constructed. After obtaining the scattering matrix, the cross section in the quantum field theory has been compared with the quantum mechanic cross section in the Born approximation, allowing to obtain the form of the potential responsible for the interactions in the scattering processes. The possibility of bound states are analyzed by using the Schroedinger equation
Gravitational waves from quasicircular black-hole binaries in dynamical Chern-Simons gravity.
Yagi, Kent; Yunes, Nicolás; Tanaka, Takahiro
2012-12-21
Dynamical Chern-Simons gravity cannot be strongly constrained with current experiments because it reduces to general relativity in the weak-field limit. This theory, however, introduces modifications in the nonlinear, dynamical regime, and thus it could be greatly constrained with gravitational waves from the late inspiral of black-hole binaries. We complete the first self-consistent calculation of such gravitational waves in this theory. For favorable spin orientations, advanced ground-based detectors may improve existing solar system constraints by 6 orders of magnitude. PMID:23368447
Membrane paradigm of black holes in Chern-Simons modified gravity
Zhao, Tian-Yi; Wang, Towe
2016-06-01
The membrane paradigm of black hole is studied in the Chern-Simons modified gravity. Derived with the action principle a la Parikh-Wilczek, the stress tensor of membrane manifests a rich structure arising from the Chern-Simons term. The membrane stress tensor, if related to the bulk stress tensor in a special form, obeys the low-dimensional fluid continuity equation and the Navier-Stokes equation. This paradigm is applied to spherically symmetric static geometries, and in particular, the Schwarzschild black hole, which is a solution of a large class of dynamical Chern-Simons gravity.
Membrane paradigm of black holes in Chern-Simons modified gravity
Zhao, Tian-Yi
2015-01-01
The membrane paradigm of black hole is studied in the Chern-Simons modified gravity. Derived with the action principle a la Parikh-Wilczek, the stress tensor of membrane manifests a rich structure arising from the Chern-Simons term. The membrane stress tensor, if related to the bulk stress tensor in a special form, obeys the low-dimensional fluid continuity equation and the Navier-Stokes equation. This paradigm is applied to spherically symmetric static geometries, and in particular, the Schwarzschild black hole, which is a solution of a large class of dynamical Chern-Simons gravity.
Static solutions in Einstein-Chern-Simons gravity
Crisóstomo, J.; Gomez, F.; Mella, P.; Quinzacara, C.; Salgado, P.
2016-06-01
In this paper we study static solutions with more general symmetries than the spherical symmetry of the five-dimensional Einstein-Chern-Simons gravity. In this context, we study the coupling of the extra bosonic field ha with ordinary matter which is quantified by the introduction of an energy-momentum tensor field associated with ha. It is found that exist (i) a negative tangential pressure zone around low-mass distributions (μ < μ1) when the coupling constant α is greater than zero; (ii) a maximum in the tangential pressure, which can be observed in the outer region of a field distribution that satisfies μ < μ2 (iii) solutions that behave like those obtained from models with negative cosmological constant. In such a situation, the field ha plays the role of a cosmological constant.
Static solutions in Einstein-Chern-Simons gravity
Crisóstomo, Juan; Quinzacara, Cristian; Salgado, Patricio
2016-01-01
In this paper we study static solutions with more general symmetries than the spherical symmetry of the so called Einstein-Chern-Simons gravity. In this context, we study the coupling of the extra bosonic field $h^a$ with ordinary matter which is quantified by the introduction of an energy-momentum tensor field associated with $h^a$ . It is found that exist (i) a negative tangential pressure zone around low-mass distributions ($\\mu < \\mu_1$) when the coupling constant $\\alpha$ is greater than zero; (ii) a maximum in the tangential pressure, which can be observed in the outer region of a field distribution that satisfies $\\mu < \\mu_2$ ; (iii) solutions that behave like those obtained from models with negative cosmological constant. In such a situation, the field $h^a$ plays the role of a cosmological constant.
Chern-Simons states in spin-network quantum gravity
Gambini, R; Pullin, J; Gambini, Rodolfo; Griego, Jorge; Pullin, Jorge
1997-01-01
In the context of canonical quantum gravity in terms of Ashtekar's new variables, it is known that there exists a state that is annihilated by all the quantum constraints and that is given by the exponential of the Chern--Simons form constructed with the Asthekar connection. We make a first exploration of the transform of this state into the spin-network representation of quantum gravity. The discussion is limited to trivalent nets with planar intersections. We adapt an invariant of tangles to construct the transform and study the action of the Hamiltonian constraint on it. We show that the first two coefficients of the expansion of the invariant in terms of the inverse cosmological constant are annihilated by the Hamiltonian constraint. We also discuss issues of framing that arise in the construction.
Translational Chern-Simons Action and New Planar Particle Dynamics
Lukierski, J; Zakrzewski, W J
2000-01-01
We consider a nonstandard $D=2+1$ gravity described by a translational Chern--Simons action, and couple it to the nonrelativistic point particles. We fix the asymptotic coordinate transformations in such a way that the space part of the metric becomes asymptotically Euclidean. The residual symmetries are (local in time) translations and rigid rotations. The phase space Hamiltonian $H$ describing two-body interactions satisfies a nonlinear equation $H={\\cal H}(\\vec{x},\\vec{p};H)$ what implies, after quantization, a nonstandard form of the Schr\\"{o}dinger equation with energy-dependent fractional angular momentum eigenvalues. Quantum solutions of the two-body problem are discussed. The bound states with discrete energy levels correspond to a confined classical motion (for the planar distance between two particles $r\\leq r_0$) and the scattering states with continuous energy correspond to classical motion for $r>r_0$.
Ricci dark energy in Chern-Simons modified gravity
International Nuclear Information System (INIS)
Full text: Currently the accelerated expansion of the universe has been strongly confirmed by some independent experiments such as the Cosmic Microwave Background Radiation (CMBR) and Sloan Digital Sky Survey (SDSS). In an attempt to explain this phenomenon there are two possible paths; first option - propose corrections to general relativity, second option - assuming that there is a dominant component of the universe, a kind of antigravity called dark energy. Any way that we intend to follow, there are numerous models that attempt to explain this effect. One of the models of modified gravity that has stood out in recent years is the Chern-Simons modified gravity. This modification consists in the addition of the Pontryagin density, which displays violation of parity symmetry in Einstein-Hilbert action. From among the various models proposed for dark energy there are some that are based on the holographic principle, known as holographic dark energy. Such models are based on the idea that the energy density of a given system is proportional to the inverse square of some characteristic length of the system. From these studies, here we consider the model proposed by Gao et. al., a model of dark energy where the characteristic length is given by the average radius of the Ricci scalar. Thus, the dark energy density is proportional to the Ricci scalar, i.e., ρx ∝ R. It is a phenomenologically viable model and displays results similar to that presented by the cosmological model ACDM. In this work, we have considered the Ricci dark energy model in the dynamic Chern-Simons modified gravity. We show that in this context the evolution of the scale factor is similar to that displayed by the modified Chaplygin gas. (author)
Ricci dark energy in Chern-Simons modified gravity
Energy Technology Data Exchange (ETDEWEB)
Silva, J.G.; Santos, A.F. [Universidade Federal de Mato Grosso (UFMT), Campo Grande, MT (Brazil)
2013-07-01
Full text: Currently the accelerated expansion of the universe has been strongly confirmed by some independent experiments such as the Cosmic Microwave Background Radiation (CMBR) and Sloan Digital Sky Survey (SDSS). In an attempt to explain this phenomenon there are two possible paths; first option - propose corrections to general relativity, second option - assuming that there is a dominant component of the universe, a kind of antigravity called dark energy. Any way that we intend to follow, there are numerous models that attempt to explain this effect. One of the models of modified gravity that has stood out in recent years is the Chern-Simons modified gravity. This modification consists in the addition of the Pontryagin density, which displays violation of parity symmetry in Einstein-Hilbert action. From among the various models proposed for dark energy there are some that are based on the holographic principle, known as holographic dark energy. Such models are based on the idea that the energy density of a given system is proportional to the inverse square of some characteristic length of the system. From these studies, here we consider the model proposed by Gao et. al., a model of dark energy where the characteristic length is given by the average radius of the Ricci scalar. Thus, the dark energy density is proportional to the Ricci scalar, i.e., ρ{sub x} ∝ R. It is a phenomenologically viable model and displays results similar to that presented by the cosmological model ACDM. In this work, we have considered the Ricci dark energy model in the dynamic Chern-Simons modified gravity. We show that in this context the evolution of the scale factor is similar to that displayed by the modified Chaplygin gas. (author)
A New Look at Chern-Simons on Circle Bundles I: The Caloron Correspondence
Mickler, Ryan
2015-01-01
We consider Chern-Simons theory on 3-manifold $M$ that is the total space of a circle bundle over a 2d base $\\Sigma$. We show that this theory is equivalent to a new 2d TQFT on the base, which we call Caloron BF theory, that can be obtained by an appropriate type of push-forward. This is a gauge theory on a bundle with structure group given by the full affine level $k$ central extension of the loop group $LG$. The space of fields of this 2d theory is naturally symplectic, and this provides a new formulation of a result of Beasley-Witten about the equivariant localization of the Chern-Simons path integral. The main tool that we employ is the Caloron correspondence, originally due to Murray-Garland, that relates the space of gauge fields on $M$ with a certain enlarged space of connections on an equivariant version of the loop space of the $G$-bundle. We show that the symplectic structure that Beasley-Witten found is related to a looped version of the Atiyah-Bott construction in 2-dimensional Yang-Mills theory. ...
Low regularity solutions of the Chern-Simons-Higgs equations in the Lorentz gauge
Directory of Open Access Journals (Sweden)
Nikolaos Bournaveas
2009-09-01
Full Text Available We prove local well-posedness for the 2+1-dimensional Chern-Simons-Higgs equations in the Lorentz gauge with initial data of low regularity. Our result improves earlier results by Huh [10, 11].
Chern-Simons and Winding Number in a Tachyonic Electroweak Transition
van der Meulen, M; Smit, J; Tranberg, A; Meulen, Meindert van der; Sexty, Denes; Smit, Jan; Tranberg, Anders
2006-01-01
We investigate the development of winding number and Chern-Simons number in a tachyonic transition in the SU(2) Higgs model, motivated by the scenario of cold electroweak baryogenesis. We find that localized configurations with approximately half-integer winding number, dubbed half-knots, play an important role in this process. When the Chern-Simons number adjusts locally to the winding number, the half-knots can stabilize and acquire half-integer Chern-Simons number as well. We present two examples from numerical simulations: one half-knot that stabilizes early and one that gives rise to a late sphaleron transition. We also study the winding number distribution after the transition and present new results on the development of the Chern-Simons susceptibility.
Scattering Amplitude and Bosonization Duality in General Chern-Simons Vector Models
Yokoyama, Shuichi
2016-01-01
We present exact large N calculus of four point function in general Chern-Simons bosonic and fermionic vector models. Applying the LSZ formula to the four point function we determine two body scattering amplitudes in these theories taking a special care for a non-analytic term to achieve unitarity in the singlet channel. We show that the S-matrix enjoys the bosonization duality, unusual crossing relation and non-relativistic reduction to Aharonov-Bohm scattering. We also argue that the S-matr...
Light-Front Dynamics Of Massive Vector Chern-Simons Gravity
Aragone, C; Khoudeir, A
1993-01-01
We present a second order gravity action which consists of ordinary Einstein action augmented by a first-order, vector like, Chern-Simons quasi topological term. This theory is ghost-free and propagates a pure spin-2 mode. It is diffeomorphism invariant, although its local Lorentz invariance has been spontaneuosly broken. We perform the light-front (LF) analysis for both the linearized system and the exact curved model. In constrast to the 2+1 canonical analysis, in the quasi LF coordinates the differential constraints can be solved. Its solution is presented here.
Visible and hidden sectors in a model with Maxwell and Chern-Simons gauge dynamics
Ireson, Edwin; Tallarita, Gianni
2016-01-01
We study a $U(1) \\times U(1)$ gauge theory discussing its vortex solutions and supersymmetric extension. In our set-upon the dynamics of one of two Abelian gauge fields is governed by a Maxwell term, the other by a Chern-Simons term. The two sectors via a BF gauge field mixing and a Higgs portal term that connects the two complex scalars. We also consider the supersymmetric version of this system which allows to find for the bosonic sector BPS equations in which an additional real scalar field enters into play. We study numerically the field equations finding vortex solutions with both magnetic flux and electric charge.
Gravitational and gauge couplings in Chern-Simons fractional spin gravity
Boulanger, Nicolas; Valenzuela, Mauricio
2015-01-01
We propose an extension of Vasiliev's supertrace operation for the enveloping algebra of Wigner's deformed oscillator algebra to the fractional spin algebra given in arXiv:1312.5700. The resulting three-dimensional Chern-Simons theory unifies the Blencowe-Vasiliev higher spin gravity with fractional spin fields and internal gauge potentials. For integer or half-integer fractional spins, infinite dimensional ideals arise and decouple, leaving finite dimensional gauge algebras gl(2l+1) or gl(l|l+1) and various real forms thereof. We derive the relation between gravitational and internal gauge couplings.
Higher derivative extensions of 3 d Chern-Simons models: conservation laws and stability
Kaparulin, D. S.; Karataeva, I. Yu.; Lyakhovich, S. L.
2015-11-01
We consider the class of higher derivative 3 d vector field models with the field equation operator being a polynomial of the Chern-Simons operator. For the nth-order theory of this type, we provide a general recipe for constructing n-parameter family of conserved second rank tensors. The family includes the canonical energy-momentum tensor, which is unbounded, while there are bounded conserved tensors that provide classical stability of the system for certain combinations of the parameters in the Lagrangian. We also demonstrate the examples of consistent interactions which are compatible with the requirement of stability.
Quadratic gravity in (2+1)D with a topological Chern-Simons term
International Nuclear Information System (INIS)
Three-dimensional quadratic gravity, unlike general relativity in (2+1)D, is dynamically nontrivial and has a well behaved nonrelativistic potential. Here we analyse the changes that occur when a topological Chern-Simons term is added to this theory. It is found that the harmless massive scalar mode of the latter gives rise to a troublesome massive spin-0 ghost, while the massive spin-2 ghost is replaced by two massive physical particles both of spin 2. We also found that light deflection does not have the 'wrong sign' such as in the framework of three-dimensional quadratic gravity. (author)
Higher derivative extensions of 3d Chern-Simons models: conservation laws and stability
International Nuclear Information System (INIS)
We consider the class of higher derivative 3d vector field models with the field equation operator being a polynomial of the Chern-Simons operator. For the nth-order theory of this type, we provide a general recipe for constructing n-parameter family of conserved second rank tensors. The family includes the canonical energy-momentum tensor, which is unbounded, while there are bounded conserved tensors that provide classical stability of the system for certain combinations of the parameters in the Lagrangian. We also demonstrate the examples of consistent interactions which are compatible with the requirement of stability. (orig.)
Higher derivative extensions of 3d Chern-Simons models: conservation laws and stability
Energy Technology Data Exchange (ETDEWEB)
Kaparulin, D.S.; Karataeva, I.Yu.; Lyakhovich, S.L. [Tomsk State University, Physics Faculty, Tomsk (Russian Federation)
2015-11-15
We consider the class of higher derivative 3d vector field models with the field equation operator being a polynomial of the Chern-Simons operator. For the nth-order theory of this type, we provide a general recipe for constructing n-parameter family of conserved second rank tensors. The family includes the canonical energy-momentum tensor, which is unbounded, while there are bounded conserved tensors that provide classical stability of the system for certain combinations of the parameters in the Lagrangian. We also demonstrate the examples of consistent interactions which are compatible with the requirement of stability. (orig.)
Chern-Simons action for inhomogeneous Virasoro group as extension of three dimensional flat gravity
International Nuclear Information System (INIS)
We initiate the study of a Chern-Simons action associated to the semi-direct sum of the Virasoro algebra with its coadjoint representation. This model extends the standard Chern-Simons formulation of three dimensional flat gravity and is similar to the higher-spin extension of three dimensional anti-de Sitter or flat gravity. The extension can also be constructed for the exotic but not for the cosmological constant deformation of flat gravity
Barnich, Glenn; Giribet, Gaston; Leston, Mauricio
2015-01-01
We initiate the study of a Chern-Simons action associated to the semi-direct sum of the Virasoro algebra with its coadjoint representation. This model extends the standard Chern-Simons formulation of three dimensional flat gravity and is similar to the higher-spin extension of three dimensional anti-de Sitter or flat gravity. The extension can also be constructed for the exotic but not for the cosmological constant deformation of flat gravity.
Higher derivative Chern-Simons extension in the noncommutative QED$_{3}$
Bufalo, R
2014-01-01
The noncommutative (NC) massive quantum electrodynamics in $2+1$ dimensions is considered. We show explicitly that the one-loop effective action arising from the integrating out the fermionic fields leads to the ordinary NC Chern-Simons and NC Maxwell action at the long wavelength limit (large fermion mass). In the next to leading order, the higher-derivative contributions to NC Chern-Simons are also obtained. The gauge invariance of the outcome action is also carefully discussed.
Higher derivative Chern-Simons extension in the noncommutative QED$_{3}$
Ghasemkhani, M.; Bufalo, R.
2014-01-01
The noncommutative (NC) massive quantum electrodynamics in $2+1$ dimensions is considered. We show explicitly that the one-loop effective action arising from the integrating out the fermionic fields leads to the ordinary NC Chern-Simons and NC Maxwell action at the long wavelength limit (large fermion mass). In the next to leading order, the higher-derivative contributions to NC Chern-Simons are obtained. Moreover, the gauge invariance of the outcome action is carefully discussed. We then con...
International Nuclear Information System (INIS)
Having great accuracy in the range and range rate measurements, the GRACE mission and the planed GRACE follow on mission can in principle be employed to place strong constraints on certain relativistic gravitational theories. In this paper, we work out the range observable of the non-dynamical Chern-Simons modified gravity for the satellite-to-satellite tracking (SST) measurements. We find out that a characteristic time accumulating range signal appears in non-dynamical Chern-Simons gravity, which has no analogue found in the standard parity-preserving metric theories of gravity. The magnitude of this Chern-Simons range signal will reach a few times of χ cm for each free flight of these SST missions, here χ is the dimensionless post-Newtonian parameter of the non-dynamical Chern-Simons theory. Therefore, with the 12 years data of the GRACE mission, one expects that the mass scale MCS = (4ℎc)/(χa) of the non-dynamical Chern-Simons gravity could be constrained to be larger than 1.9 x 10.9 eV. For the GRACE FO mission that scheduled to be launched in 2017, the much stronger bound that MCS ≥ 5 x 10-7 eV is expected. (orig.)
A magnetic model with a possible Chern-Simons phase
Freedman, M H
2003-01-01
A rather elementary family of local Hamiltonians $H_{\\circ, \\ell}, \\ell = 1,2,3, ...$, is described for a 2-dimensional quantum mechanical system of spin ={1/2} particles. On the torus, the ground state space $G_{\\circ, \\ell}$ is essentially infinite dimensional but may collapse under $\\l$perturbation" to an anyonic system with a complete mathematical description: the quantum double of the SO(3)-Chern-Simons modular functor at $q= e^{2 \\pi i/\\ell +2}$ which we call $D E \\ell$. The Hamiltonian $H_\\circ, \\ell}$ defines a \\underline{quantum} \\underline{loop} \\underline{gas}. We argue that for $\\ell = 1$ and 2, $G_\\circ, \\ell}$ is unstable and the collapse to $G_{\\epsilon, \\ell} \\cong D E \\ell$ can occur truly by perturbation. For $\\ell \\geq 3 G_{\\circ, \\ell}$ is stable and in this case finding $G_{\\epsilon, \\ell} \\cong D E \\ell$ must require either $\\epsilon> \\epsilon_\\ell> 0$, help from finite system size, surface roughening (see section 3), or some other trick, hence the initial use of quotes $\\l\\quad$". A hyp...
Some cosmological solutions in Einstein-Chern-Simons gravity
Avilés, Luis; Quinzacara, Cristian; Salgado, Patricio
2016-01-01
In this paper we find new solutions for the so called Einstein-Chern-Simons Friedmann-Robertson-Walker field equations studied in refs. (Phys. Rev. D 84 (2011) 063506, Eur. Phys. J. C 74 (2014) 3087). We consider three cases:(i) in the first case we find some solutions of the five-dimensional ChS-FRW field equations when the $h^a$ field is a perfect fluid that obeys a barotropic equation of state; (ii) in the second case we study the solutions, for the cases $\\gamma =1/2,\\ 3/4$, when the $h^a$ field is a five dimensional politropic fluid that obeys the equation $P^{(h)}=\\omega ^{(h)}\\rho ^{(h)\\gamma }$; (iii) in the third case we find the scale factor and the state parameter $\\omega (t)$ when the $h^a$ field is a variable modified Chaplygin gas. We consider also a space-time metric which contains as a subspace to the usual four-dimensional FRW and then we study the same three cases considered in the five-dimensional, namely when (i) the $h^a$ field is a perfect fluid, (ii) the $h^a$ field is a five dimensiona...
Chern-Simons diffusion rate across different phase transitions
Rougemont, Romulo
2016-01-01
We investigate how the dimensionless ratio given by the Chern-Simons diffusion rate $\\Gamma_{\\textrm{CS}}$ divided by the product of the entropy density $s$ and temperature $T$ behaves across different kinds of phase transitions in the class of bottom-up non-conformal Einstein-dilaton holographic models originally proposed by Gubser and Nellore. By tuning the dilaton potential, one is able to holographically mimic a first order, a second order, or a crossover transition. In a first order phase transition, $\\Gamma_{\\textrm{CS}}/sT$ jumps at the critical temperature (as previously found in the holographic literature), while in a second order phase transition it develops an infinite slope. On the other hand, in a crossover, $\\Gamma_{\\textrm{CS}}/sT$ behaves smoothly, although displaying a fast variation around the pseudo-critical temperature. Furthermore, we also find that $\\Gamma_{\\textrm{CS}}/sT$ increases by orders of magnitude below the critical temperature in a second order phase transition and in a crossov...
Spherical Symmetric Gravitational Collapse in Chern-Simon Modified Gravity
Amir, M. Jamil; Ali, Sarfraz
2016-04-01
This paper is devoted to investigate the gravitational collapse in the framework of Chern-Simon (CS) modified gravity. For this purpose, we assume the spherically symmetric metric as an interior region and the Schwarzchild spacetime is considered as an exterior region of the star. Junction conditions are used to match the interior and exterior spacetimes. In dynamical formulation of CS modified gravity, we take the scalar field Θ as a function of radial parameter r and obtain the solution of the field equations. There arise two cases where in one case the apparent horizon forms first and then singularity while in second case the order of the formation is reversed. It means the first case results a black hole which supports the cosmic censorship hypothesis (CCH). Obviously, the second case yields a naked singularity. Further, we use Junction conditions have to calculate the gravitational mass. In non-dynamical formulation, the canonical choice of scalar field Θ is taken and it is shown that the obtained results of CS modified gravity simply reduce to those of the general relativity (GR). It is worth mentioning here that the results of dynamical case will reduce to those of GR, available in literature, if the scalar field is taken to be constant.
Entropy for gravitational Chern-Simons terms by squashed cone method
Guo, Wu-zhong
2015-01-01
In this paper we investigate the entropy of gravitational Chern-Simons terms for the horizon with non-vanishing extrinsic curvatures, or the holographic entanglement entropy for arbitrary entangling surface. In 3D we find no anomaly of entropy appears. But the squashed cone method can not be used directly to get the correct result. For higher dimensions the anomaly of entropy would appear, still, we can not use the squashed cone method directly. That is becasuse the Chern-Simons action is not gauge invariant. To get a reasonable result we suggest two methods. One is by adding a boundary term to recover the gauge invariance. This boundary term can be derived from the variation of the Chern-Simons action. The other one is by using the Chern-Simons relation $d\\bm{\\Omega_{4n-1}}=tr(\\bm{R}^{2n})$. We notice that the entropy of $tr(\\bm{R}^{2n})$ is a total derivative locally, i.e. $S=d s_{CS}$. We propose to identify $s_{CS}$ with the entropy of gravitational Chern-Simons terms $\\Omega_{4n-1}$. In the first method ...
Ferrari, Ruggero
2015-01-01
We resume a long-standing, yet not forgotten, debate on whether a Chern-Simons birefringence can be generated by a local term $b_\\mu\\bar\\psi\\gamma^\\mu \\gamma_5\\psi$ in the Lagrangian (where $b_\\mu$ are constants). In the present paper we implement a new way of managing $\\gamma_5$ in dimensional regularization. Gauge invariance in the underlying theory (QED) is enforced by this choice of defining divergent amplitudes. We investigate the singular behavior of the vector meson two-point-function around the $m^2=0$ and $p^2=0$ point. We find that the coefficient of the effective Chern-Simons can be finite or zero. It depends on how one takes the limits: they cannot be interchanged due to the associate change of symmetry. For $m^2=0$ we evaluate also the self-mass of the photon at the second orderin $b_\\mu$. We find zero.
Deformed N = 8 supergravity from IIA strings and its Chern-Simons duals
Energy Technology Data Exchange (ETDEWEB)
Guarino, Adolfo [Nikhef Theory Group, Amsterdam (Netherlands); Jafferis, Daniel L. [Center for the Fundamental Laws of Nature, Harvard University, Cambridge, MA (United States); Varela, Oscar [Center for the Fundamental Laws of Nature, Harvard University, Cambridge, MA (United States); Centre de Physique Theorique, Ecole Polytechnique, CNRS UMR 7644, Palaiseau (France)
2016-04-15
Do electric/magnetic deformations of N = 8 supergravity enjoy a string/M-theory origin, or are they just a fourdimensional artefact? We address this question for the gauging of a group closely related to SO(8): its contraction ISO(7). We argue that the deformed ISO(7) supergravity arises from consistent truncation of massive IIA supergravity on S{sup 6}, and its electric/magnetic deformation parameter descends directly from the Romans mass. The critical points of the supergravity uplift to AdS{sub 4} massive type IIA vacua and the corresponding CFT{sub 3} duals are identified as super-Chern-Simons-matter theories with gauge group SU(N) and level k given also by the Romans mass. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Poisson structure and symmetry in the Chern-Simons formulation of (2+1)-dimensional gravity
Meusburger, C
2003-01-01
In the formulation of (2+1)-dimensional gravity as a Chern-Simons gauge theory, the phase space is the moduli space of flat Poincar\\'e group connections. Using the combinatorial approach developed by Fock and Rosly, we give an explicit description of the phase space and its Poisson structure for the general case of a genus g oriented surface with punctures representing particles and a boundary playing the role of spatial infinity. We give a physical interpretation and explain how the degrees of freedom associated with each handle and each particle can be decoupled. The symmetry group of the theory combines an action of the mapping class group with asymptotic Poincar\\'e transformations in a non-trivial fashion. We derive the conserved quantities associated to the latter and show that the mapping class group of the surface acts on the phase space via Poisson isomorphisms.
Dyon of a non-Abelian Chern-Simons-Yang-Mills-Higgs system in 3+1 dimensions
Navarro-Lerida, Francisco
2013-01-01
Dyons of an SO(5) Chern-Simons-Yang-Mills-Higgs system in 3+1 dimensions are presented. These solitons carry both magnetic and electric global charges. The SO(3)xSO(2) solutions are constructed numerically. These are Chern-Simons dyons, differing radically from Julia-Zee dyons. The Chern-Simons densities employed are defined in 3+1 dimensions, and they are the first two of the 'new' Chern-Simons densities introduced recently. They are defined in terms of both Yang-Mills fields and a 5-component isomultiplet Higgs. When two or more of these Chern-Simons densities are present in the Lagrangian, solutions with vanishing electric charge but nonvanishing electrostatic potential may exist.
Chern-Simons effect on the dual hydrodynamics in the Maxwell-Gauss-Bonnet gravity
Energy Technology Data Exchange (ETDEWEB)
Hu Yapeng, E-mail: huyp@pku.edu.cn [Center for High-Energy Physics, Peking University, Beijing 100871 (China); Center for Quantum Spacetime, Sogang University, Seoul 121-742 (Korea, Republic of); Park, Chanyong, E-mail: cyong21@sogang.ac.kr [Center for Quantum Spacetime, Sogang University, Seoul 121-742 (Korea, Republic of)
2012-08-14
Following the previous work (arXiv:1103.3773 [hep-th]), we give a more general and systematic discussion on the Chern-Simons effect in the 5-dimensional Maxwell-Gauss-Bonnet gravity. After constructing the first order perturbative black brane solution, we extract the stress tensor and charge current of dual fluid. From these results, we find out the dependence of some transport coefficients on the Gauss-Bonnet coupling {alpha} and Chern-Simons coupling {kappa}{sub cs}. We also show that the new anomalous term can provide an additional contribution to the anomalous chiral magnetic conductivity.
Self-Dual Chern-Simons Solitons and Generalized Heisenberg Ferromagnet Models
Oh, P; Oh, Phillial
1996-01-01
We consider the (2+1)-dimensional gauged Heisenberg ferromagnet model coupled with the Chern-Simons gauge fields. Self-dual Chern-Simons solitons, the static zero energy solution saturating Bogomol'nyi bounds, are shown to exist when the generalized spin variable is valued in the Hermitian symmetric spaces G/H. By gauging the maximal torus subgroup of H, we obtain self-dual solitons which satisfy vortex-type nonlinear equations thereby extending the two dimensional instantons in a nontrivial way. An explicit example for the CP(N) case is given.
Abelian tensor hierarchy and Chern-Simons actions in 4D N=1 conformal supergravity
Yokokura, Ryo
2016-01-01
We consider Chern-Simons actions of Abelian tensor hierarchy of $p$-form gauge fields in four-dimensional ${\\cal N}=1$ supergravity. Using conformal superspace formalism, we solve the constraints on the field strengths of the $p$-form gauge superfields in the presence of the tensor hierarchy. The solutions are expressed by the prepotentials of the $p$-form gauge superfields. We show the internal and superconformal transformation laws of the prepotentials. The descent formalism for the Chern-Simons actions is exhibited.
Gravitational and gauge couplings in Chern-Simons fractional spin gravity
Boulanger, Nicolas; Sundell, Per; Valenzuela, Mauricio
2016-01-01
We propose an extension of Vasiliev's supertrace operation for the enveloping algebra of Wigner's deformed oscillator algebra to the fractional spin algebra given in arXiv:1312.5700. We provide a necessary and sufficient condition for the consistency of the supertrace, through the existence of a certain ground state projector. We build this projector and check its properties to the first two orders in the number operator and to all orders in the deformation parameter. We then find the relation between the gravitational and internal gauge couplings in the resulting unified three-dimensional Chern-Simons theory for Blencowe-Vasiliev higher spin gravity coupled to fractional spin fields and internal gauge potentials. We also examine the model for integer or half-integer fractional spins, where infinite dimensional ideals arise and decouple, leaving finite dimensional gauge algebras gl(2 ℓ + 1) or gl( ℓ| ℓ + 1) and various real forms thereof.
Kikuchi, Daiki; Yamada, Kei; Asada, Hideki
2014-01-01
Toward a test of parity violation in a gravity theory, possible effects of Chern-Simons (CS) gravity on an interferometer have been recently discussed. Continuing work initiated in an earlier publication [Okawara, Yamada and Asada, Phys. Rev. Lett. 109, 231101 (2012)], we study possible altitudinal and directional dependence of relativistic Sagnac effect in CS modified gravity. We compare the CS effects on Sagnac interferometers with the general relativistic Lense-Thirring (LT) effects. Numerical calculations show that the eastbound Sagnac interferometer might be preferred for testing CS separately, because LT effects on this interferometer cancel out. The size of the phase shift induced in the CS model might have an oscillatory dependence also on the altitude of the interferometer through the CS mass parameter $m_{CS}$. Therefore, the international space station site as well as a ground-based experiment is also discussed.
Remarks on the Taub-NUT solution in Chern-Simons modified gravity
Brihaye, Yves
2016-01-01
We discuss the generalization of the NUT spacetime in General Relativity (GR) within the framework of the (dynamical) Einstein--Chern-Simons (ECS) theory with a massless scalar field. These configurations approach asymptotically the NUT spacetime and are characterized by the `electric' and `magnetic' mass parameters and a scalar `charge'. %NUT parameter, the mass and a scalar 'charge'. The solutions are found both analytically and numerically. The analytical approach is perturbative around the Einstein gravity background. Our results indicate that the ECS configurations share all basic properties of the NUT spacetime in GR. However, when considering the solutions inside the event horizon, we find that in contrast to the GR case, the spacetime curvature grows (apparently) without bound.
The Hamiltonian Form of Three-Dimensional Chern-Simons-like Gravity Models
Bergshoeff, Eric A; Merbis, Wout; Routh, Alasdair J; Townsend, Paul K
2014-01-01
A wide class of three-dimensional gravity models can be put into ``Chern-Simons-like'' form. We perform a Hamiltonian analysis of the general model and then specialise to Einstein-Cartan Gravity, General Massive Gravity, the recently proposed Zwei-Dreibein Gravity and a further parity violating generalisation combining the latter two.
On the causality aspects of the dynamical Chern-Simons modified gravity
Porfirio, P J; Nascimento, J R; Petrov, A Yu
2016-01-01
We verify the consistency of the G\\"odel-type solutions within the dynamical Chern-Simons modified gravity in four dimensions, for different forms of matter including dust, fluid, scalar and electromagnetic fields and their combinations, and discuss the possibility of arising the closed timelike curves.
Induced Chern-Simons term in lattice QCD at finite temperature
International Nuclear Information System (INIS)
The general conditions when the Chern-Simons action could arise (in continuum limit) as non universal contribution of fermionic determinant of finite-temperature lattice QCD are formulated. The dependence of this action coefficient on non universal parameters (a chemical potential, vacuum features, etc.) is investigated in detail. Special attention is paid to the role of possible 0>-condensate existence. 42 refs. (author)
Canizares, Priscilla; Gair, Jonathan R.; Sopuerta, Carlos F.
2012-08-01
The detection of gravitational waves from extreme-mass-ratio inspirals (EMRI) binaries, comprising a stellar-mass compact object orbiting around a massive black hole, is one of the main targets for low-frequency gravitational-wave detectors in space, like the Laser Interferometer Space Antenna (LISA) or evolved LISA/New Gravitational Observatory (eLISA/NGO). The long-duration gravitational-waveforms emitted by such systems encode the structure of the strong field region of the massive black hole, in which the inspiral occurs. The detection and analysis of EMRIs will therefore allow us to study the geometry of massive black holes and determine whether their nature is as predicted by general relativity and even to test whether general relativity is the correct theory to describe the dynamics of these systems. To achieve this, EMRI modeling in alternative theories of gravity is required to describe the generation of gravitational waves. However, up to now, only a restricted class of theories has been investigated. In this paper, we explore to what extent EMRI observations with a space-based gravitational-wave observatory like LISA or eLISA/NGO might be able to distinguish between general relativity and a particular modification of it, known as dynamical Chern-Simons modified gravity. Our analysis is based on a parameter estimation study which uses approximate gravitational waveforms obtained via a radiative-adiabatic method. In this framework, the trajectory of the stellar object is modeled as a sequence of geodesics in the spacetime of the modified-gravity massive black hole. The evolution between geodesics is determined by flux formulae based on general relativistic post-Newtonian and black hole perturbation theory computations. Once the trajectory of the stellar compact object has been obtained, the waveforms are computed using the standard multipole formulae for gravitational radiation applied to this trajectory. Our analysis is restricted to a five
Lorentz and U(1) Chern-Simons terms in new minimal supergravity
International Nuclear Information System (INIS)
We couple a linear multiplet to new minimal supergravity, modified by the addition of both the U(1) and Lorentz superfield Chern-Simons terms. We write the lagrangian in component form and find that it contains pieces quadratic in the curvature tensor and has only a finite number of terms. We also find that the auxiliary fields am and G tildem become propagating and massive. Very interestingly, however, for a particular ratio of the U(1) and Lorentz Chern-Simons terms, G tildem can be eliminated. This leads to a lagrangian with only a finite number of terms containing a propagating, massive vector field am and terms quadratic in the curvature tensor. (orig.)
Qiang, Li-E
2016-01-01
With continuous advances in related technologies, relativistic gravitational experiments with orbiting gradiometers becomes feasible, which could naturally be incorporated into future satellite gravity missions. Tests of Chern-Simons modified gravity are meaningful since such a modification gives us insights into (possible) parity-violations in gravitation. In this work, we derive, at the post-Newtonian level, the new observables of secular gradients from the non-dynamical Chern-Simons modified gravity, which will greatly improve the constraint on the mass scale $M_{CS}$ that may be drawn from satellite gradiometry measurements. For superconducting gradiometers, a strong bound $M_{CS}\\geq 10^{-7}\\ eV$ could in principle be obtained. For future optical gradiometers based on similar technologies from the LISA PathFinder mission, a even stronger bound $M_{CS}\\geq 10^{-5}\\ eV$ might be expected.
Some quantum aspects of complex vector fields with Chern-Simons term
Del Cima, O M
1993-01-01
Complex vector fields with Maxwell, Chern-Simons and Proca terms are minimally coupled to an Abelian gauge field. The consistency of the spectrum is analysed and 1-loop quantum corrections to the self-energy are explicitly computed and discussed. The incorporation of 2-loop contributions and the behaviour of tree-level scattering amplitudes in the limit of high center-of-mass energies are also commented.
Higgs-and Skyrme-Chern-Simons densities in all dimensions
Tchrakian, D. H.
2015-09-01
Two types of new Chern-Simons (CS) densities, both defined in all odd and even dimensions, are proposed. These new CS densities feature a scalar field interacting with the gauge field. In one case this is a Higgs scalar while in the other it is a Skyrme scalar. The motivation is to study the effects of adding these new CS terms to a Lagrangian which supports static soliton solutions prior to their introduction.
N=2-Maxwell-Chern-Simons Model with Anomalous Magnetic Moment Coupling via Dimensional Reduction
Christiansen, H R; Helayël-Neto, José A; Mansur, L R; Nogueira, A L M A
1999-01-01
An N=1--supersymmetric version of the Cremmer-Scherk-Kalb-Ramond model with non-minimal coupling to matter is built up both in terms of superfields and in a component-field formalism. By adopting a dimensional reduction procedure, the N=2--D=3 counterpart of the model comes out, with two main features: a genuine (diagonal) Chern-Simons term and an anomalous magnetic moment coupling between matter and the gauge potential.
Possible daily and seasonal variations in quantum interference induced by Chern-Simons gravity
Okawara, Hiroki; Asada, Hideki
2012-01-01
Possible effects of Chern-Simons (CS) gravity on a quantum interferometer turn out to be dependent on the latitude and direction of the interferometer on the Earth in orbital motion around the Sun. Daily and seasonal variations in phase shifts are predicted with an estimate of the size of the effects, wherefore neutron interferometry with $\\sim 5$ meters arm length and $\\sim 10^{-4}$ phase measurement accuracy would place a bound on a CS parameter comparable to Gravity Probe B satellite.
Chern-Simons functions on toric Calabi-Yau threefolds and virtual motives
Hua, Zheng
2011-01-01
In this note, we give a construction of Chern-Simons functions for toric Calabi-Yau stacks of dimension three using strong exceptional collections. The moduli spaces of sheaves on such stacks can be identified with critical loci of these functions. As an application, we prove a dimension reduction formula for virtual motives. We also compute several recursion formulas for motivic Donaldson-Thomas invariants.
Chern-Simons Path Integrals in S2 × S1
Directory of Open Access Journals (Sweden)
Adrian P. C. Lim
2015-08-01
Full Text Available Using torus gauge fixing, Hahn in 2008 wrote down an expression for a Chern-Simons path integral to compute the Wilson Loop observable, using the Chern-Simons action \\(S_{CS}^\\kappa\\, \\(\\kappa\\ is some parameter. Instead of making sense of the path integral over the space of \\(\\mathfrak{g}\\-valued smooth 1-forms on \\(S^2 \\times S^1\\, we use the Segal Bargmann transform to define the path integral over \\(B_i\\, the space of \\(\\mathfrak{g}\\-valued holomorphic functions over \\(\\mathbb{C}^2 \\times \\mathbb{C}^{i-1}\\. This approach was first used by us in 2011. The main tool used is Abstract Wiener measure and applying analytic continuation to the Wiener integral. Using the above approach, we will show that the Chern-Simons path integral can be written as a linear functional defined on \\(C(B_1^{\\times^4} \\times B_2^{\\times^2}, \\mathbb{C}\\ and this linear functional is similar to the Chern-Simons linear functional defined by us in 2011, for the Chern-Simons path integral in the case of \\(\\mathbb{R}^3\\. We will define the Wilson Loop observable using this linear functional and explicitly compute it, and the expression is dependent on the parameter \\(\\kappa\\. The second half of the article concentrates on taking \\(\\kappa\\ goes to infinity for the Wilson Loop observable, to obtain link invariants. As an application, we will compute the Wilson Loop observable in the case of \\(SU(N\\ and \\(SO(N\\. In these cases, the Wilson Loop observable reduces to a state model. We will show that the state models satisfy a Jones type skein relation in the case of \\(SU(N\\ and a Conway type skein relation in the case of \\(SO(N\\. By imposing quantization condition on the charge of the link \\(L\\, we will show that the state models are invariant under the Reidemeister Moves and hence the Wilson Loop observables indeed define a framed link invariant. This approach follows that used in an article written by us in 2012, for the case of
On the Higher-Spin Spectrum in Large N Chern-Simons Vector Models
Giombi, S; Kirilin, V; Prakash, S; Skvortsov, E
2016-01-01
Chern-Simons gauge theories coupled to massless fundamental scalars or fermions define interesting non-supersymmetric 3d CFTs that possess approximate higher-spin symmetries at large N. In this paper, we compute the scaling dimensions of the higher-spin operators in these models, to leading order in the 1/N expansion and exactly in the 't Hooft coupling. We obtain these results in two independent ways: by using conformal symmetry and the classical equations of motion to fix the structure of the current non-conservation, and by a direct Feynman diagram calculation. The full dependence on the 't Hooft coupling can be restored by using results that follow from the weakly broken higher-spin symmetry. This analysis also allows us to obtain some explicit results for the non-conserved, parity-breaking structures that appear in planar three-point functions of the higher-spin operators. At large spin, we find that the anomalous dimensions grow logarithmically with the spin, in agreement with general expectations. This...
Effect of VSR invariant Chern-Simons Lagrangian on photon polarization
Energy Technology Data Exchange (ETDEWEB)
Nayak, Alekha C.; Verma, Ravindra K.; Jain, Pankaj [Department of Physics, Indian institute of Technology,Kanpur, 208016 (India)
2015-07-21
We propose a generalization of the Chern-Simons (CS) Lagrangian which is invariant under the SIM(2) transformations but not under the full Lorentz group. The generalized lagrangian is also invariant under a SIM(2) gauge transformation. We study the effect of such a term on radiation propagating over cosmological distances. We find that the dominant effect of this term is to produce circular polarization as radiation propagates through space. We use the circular polarization data from distant radio sources in order to impose a limit on this term.
Enhancing Gauge Symmetries of Non-Abelian Supersymmetric Chern-Simons Model
Gharavi, Kh. Bahalke; Monemzadeh, M.; Nejad, S. Abarghouei
2016-07-01
In this article, we study gauge symmetries of the Non-Abelian Supersymmetric Chern-Simons model (SCS) of SU(2) group at (2+1)-dimensions in the framework of the formalism of constrained systems. Since, broken gauge symmetries in this physical system lead to the presence of nonphysical degrees of freedom, the Non-Abelian SCS model is strictly constrained to second-class constraints. Hence, by introducing some auxiliary fields and using finite order BFT method, we obtain a gauge symmetric model by converting second-class constraint to first-class ones. Ultimately, the partition function of the model is obtained in the extended phase space.
Chern-Simons Actions and Their Gaugings in 4D, N=1 Superspace
Becker, Katrin; Linch, William D; Robbins, Daniel
2016-01-01
We gauge the abelian hierarchy of tensor fields in 4D by a Lie algebra. The resulting non-abelian tensor hierarchy can be interpreted via an equivariant chain complex. We lift this structure to N=1 superspace by constructing superfield analogs for the tensor fields, along with covariant superfield strengths. Next we construct Chern-Simons actions, for both the bosonic and N=1 cases, and note that the condition of gauge invariance can be presented cohomologically. Finally, we provide an explicit realization of these structures by dimensional reduction, for example by reducing the three-form of eleven-dimensional supergravity into a superspace with manifest 4D, N=1 supersymmetry.
Energy Technology Data Exchange (ETDEWEB)
Pasqua, Antonio [University of Trieste, Department of Physics, Trieste (Italy); Rocha, Roldao da [Universidade Federal do ABC, Centro de Matematica, Computacao e Cognicao, Santo Andre, SP (Brazil); International School for Advanced Studies (SISSA), Trieste (Italy); Chattopadhyay, Surajit [Bengal Pailan Park, Pailan College of Management and Technology, Kolkata (India)
2015-02-01
Dark energy models are here investigated and studied in the framework of the Chern-Simons modified gravity model. We bring into focus the holographic dark energy model with Granda-Oliveros cut-off, the modified holographic Ricci dark energy model and a model with higher derivatives of the Hubble parameter. The relevant expressions of the scale factor a(t) for a Friedmann-Robertson-Walker Universe are derived and studied, and, in this context, the evolution of the scale factor is shown to be similar to the one displayed by the modified Chaplygin gas in two of the above models. (orig.)
A Study of Holographic Dark Energy Models in Chern-Simon Modified Gravity
Ali, Sarfraz; Amir, M. Jamil
2016-09-01
This paper is devoted to study some holographic dark energy models in the context of Chern-Simon modified gravity by considering FRW universe. We analyze the equation of state parameter using Granda and Oliveros infrared cut-off proposal which describes the accelerated expansion of the universe under the restrictions on the parameter α. It is shown that for the accelerated expansion phase -1fashion. To discuss the accelerated expansion of the universe, we explore the potential and the dynamics of quintessence, K-essence, tachyon and dilaton field models.
N=2-Maxwell-Chern-Simons model with anomalous magnetic moment coupling via dimensional reduction
Energy Technology Data Exchange (ETDEWEB)
Christiansen, H.R.; Cunha, M.S.; Helayel Neto, Jose A.; Manssur, L.R.U; Nogueira, A.L.M.A. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). Dept. de Campos e Particulas
1998-02-01
An N=1-supersymmetric version of the Cremmer-Scherk-Kalb-Ramond model with non-minimal coupling to matter is built up both in terms of superfields and in a component field formalism. By adopting a dimensional reduction procedure, the N=2-D=3 counterpart of the model comes out, with two main features: a genuine (diagonal) Chern-Simons term and an anomalous magnetic moment coupling between matter and the gauge potential. (author) 14 refs.; e-mail: hugo, macony, helayel, leon, nogue at cat.cbpf.br
Dimensional Reduction of a Lorentz- and CPT-violating Chern-Simons Model
Belich, H; Orlando, M T D
2003-01-01
Taking as starting point a Lorentz and CPT non-invariant Chern-Simons-like model defined in 1+3 dimensions, we proceed realizing its dimensional reduction to D=1+2. One then obtains a new planar model, composed by the Maxwell-Chern-Simons (MCS)sector, a Klein-Gordon massless scalar field, and a coupling term that mixes the gauge field to the external vector, $v^{\\mu}$. In spite of breaking Lorentz invariance in the particle frame, this model may preserve the CPT symmetry for a single particular choice of $v^{\\mu}$. The solution of the wave equations shows a behavior similar but which deviates from the usual MCS electrodynamics by some correction-terms (dependent on the background field). These solutions also indicate the existence of spatial-anisotropy in the case $v^{\\mu}$ is purely space-like, which is consistent with the determination of a privileged direction is space, v. The reduced model exhibits stability, but the causality can be jeopardized by some modes. PACS numbers: 11.10.Kk; 11.30.Cp; 11.30.Er; 1...
The Chern-Simons Source as a Conformal Family and Its Vertex Operators
Balachandran, A P; Sen-Gupta, K; Stern, A
1992-01-01
In a previous work, a straightforward canonical approach to the source-free quantum Chern-Simons dynamics was developed. It makes use of neither gauge conditions nor functional integrals and needs only ideas known from QCD and quantum gravity. It gives Witten's conformal edge states in a simple way when the spatial slice is a disc. Here we extend the formalism by including sources as well. The quantum states of a source with a fixed spatial location are shown to be those of a conformal family, a result also discovered first by Witten. The internal states of a source are not thus associated with just a single ray of a Hilbert space. Vertex operators for both abelian and nonabelian sources are constructed. The regularized abelian Wilson line is proved to be a vertex operator. We also argue in favor of a similar nonabelian result. The spin-statistics theorem is established for Chern-Simons dynamics even though the sources are not described by relativistic quantum fields. The proof employs geometrical methods whi...
Does the Higgs mechanism favour electron-electron bound states in Maxwell-Chern-Simons QED_3?
Belich, H.; Del Cima, O. M.; Ferreira Jr, M. M.; Helayel-Neto, J. A.
2000-01-01
The low-energy electron-electron scattering potential is derived and discussed for the Maxwell-Chern-Simons model coupled to QED_3 with spontaneous symmetry breaking. One shows that the Higgs mechanism might favour electron-electron bound states.
Chern-Simons functional and the no-boundary proposal in Bianchi IX quantum cosmology
Louko, J
1995-01-01
The Chern-Simons functional S_{\\rm CS} is an exact solution to the Ashtekar-Hamilton-Jacobi equation of general relativity with a nonzero cosmological constant. In this paper we consider S_{\\rm CS} in Bianchi type IX cosmology with S^3 spatial surfaces. We show that among the classical solutions generated by~S_{\\rm CS}, there is a two-parameter family of Euclidean spacetimes that have a regular NUT-type closing. When two of the three scale factors are equal, these spacetimes reduce to a one-parameter family within the Euclidean Taub-NUT-de~Sitter metrics. For a nonzero cosmological constant, \\exp(iS_{\\rm CS}) therefore provides a semiclassical estimate to the Bianchi~IX no-boundary wave function in Ashtekar's variables.
Phase space structure of non-abelian Chern-Simons particles
Kim, M H; Myung-Ho Kim; Phillial Oh
1994-01-01
We investigate the classical phase space structure of N SU(n+1) non-Abelian Chern-Simons (NACS) particles by first constructing the product space of associated SU(n+1) bundle with {\\bf CP}^n as the fiber. We calculate the Poisson bracket using the symplectic structure on the associated bundle and find that the minimal substitution in the presence of external gauge fields is equivalent to the modification of symplectic structure by the addition of field strength two form. Then, we take a direct product of the associated bundle by the space of all connections and choose a specific connection by the condition of vanishing momentum map corresponding to the gauge transformation, thus recovering the quantum mechanical model of NACS particles in Ref.\\cite{lo1}.
Thermodynamics in dynamical Chern-Simons modified gravity with canonical scalar field
Rani, Shamaila; Nawaz, Tanzeela; Jawad, Abdul
2016-09-01
We take the scalar field dark energy model possessing a non-canonical kinetic term in the framework of modified Chern-Simon gravity. We assume the flat FRW universe model and interacting scenario between dark matter and non-canonical dark energy part. Under this scenario, we check the stability of the model using squared speed of sound which represents the stable behavior for a specific choice of model parameters. We also discuss the validity of generalized second law of thermodynamics by assuming the usual entropy and its corrected forms (logarithmic and power law) at the apparent horizon. This law satisfied for all cases versus redshift parameter at the present as well as later epoch.
Diphoton excess via Chern-Simons interaction in a warped geometry scenario
Chakrabarty, Nabarun; SenGupta, Soumitra
2016-01-01
We offer an explanation of the recently observed 750 GeV diphoton peak at the Large Hadron Collider (LHC) in terms of an axion related to the 5-dimensional Kalb-Ramond (KR) field in a Randall-Sundrum warped geometry scenario. The KR field, identifiable with bulk torsion, has Chern-Simons interactions with gauge boson pairs. These in turn yield unsuppressed coupling of the torsion to gluon as well as photon pairs in (3+1) dimensions, while the warped geometry enforces ultra-suppressed interaction with fermion pairs . We show that the observed results can be numerically justified when the warp factor is precisely in the range required for stabilisation of the electroweak scale.
International Nuclear Information System (INIS)
The possibility of dual equivalence between the self-dual and the Maxwell-Chern-Simons (MCS) models when the latter is coupled to dynamical, U(1) fermionic charged matter is examined. The proper coupling in the self-dual model is then disclosed using the iterative gauge embedding approach. We found that the self-dual potential needs to couple directly to the Chern kernel of the source in order to establish this equivalence besides the need for a self-interaction term to render the matter sector unchanged
Institute of Scientific and Technical Information of China (English)
YAN Jun; SU Wen-Jie
2012-01-01
The （2＋1）-dimensional Maxwell-Chern Simons gravity with phantom dilaton field coupling is studied in this paper. It is shown that black hole solution to exist when electromagnetic coupled to dilaton field in the non-trivial way. Moreover, asymptotic index and distribution parameter of current density are calculated by using black hole solution, some new features of this solution are briefly discussed.
Santangelo, E M
2008-01-01
This talk presents a study of massless relativistic Dirac fields in three Euclidean dimensions, at finite temperature and density, in the presence of a uniform electromagnetic background. Apart from explaining the behavior of Hall's conductivity for graphene, our results show a direct relationship between the selection of a phase for the Dirac determinant and the generation (or lack thereof) of Berry's phases and Chern-Simons terms.
Makhfudz, Imam; Pujol, Pierre
We propose a mechanism for the protection against spin gapped states in doped antiferromagnets. It requires the presence of a Chern-Simons term that can be generated by a coupling between spin and an insulator.We first demonstrate that in the presence of this term the vortex loop excitations of the spin sector behave as anyons with fractional statistics. To generate such a term, the fermions should have a massive Dirac spectrum coupled to the emergent spin field of the spin sector. The Dirac spectrum can be realized by a planar spin configuration arising as the lowest-energy configuration of a square lattice antiferromagnet Hamiltonian involving a Dzyaloshinskii- Moriya interaction. The mass is provided by a combination of dimerization and staggered chemical potential.We finally showthat for realistic parameters, anyonic vortex loop condensationwill likely never occur and thus the spin gapped state is prevented.We also propose real magnetic materials for an experimental verification of our theory. Reference: Imam Makhfudz and Pierre Pujol,Phys.Rev. B 92, 144507 (2015).
Chern-Simons improved Hamiltonians for strings in three space dimensions
Gordeli, Ivan; Melnikov, Dmitry; Niemi, Antti J.; Sedrakyan, Ara
2016-07-01
In the case of a structureless string the extrinsic curvature and torsion determine uniquely its shape in three-dimensional ambient space, by way of solution of the Frenet equation. In many physical scenarios there are in addition symmetries that constrain the functional form of the ensuing energy function. For example, the energy of a structureless string should be independent of the way the string is framed in the Frenet equation. Thus the energy should only involve the curvature and torsion as dynamical variables, in a manner that resembles the Hamiltonian of the Abelian Higgs model. Here we investigate the effect of symmetry principles in the construction of Hamiltonians for structureless strings. We deduce from the concept of frame independence that in addition to extrinsic curvature and torsion, the string can also engage a three-dimensional Abelian bulk gauge field as a dynamical variable. We find that the presence of a bulk gauge field gives rise to a long-range interaction between different strings. Moreover, when this gauge field is subject to Chern-Simons self-interaction, it becomes plausible that interacting strings are subject to fractional statistics in three space dimensions.
The Structure of Space-Time Emerging from the Two-Superbody Problem in Chern Simons Supergravity
Kim, Sunme; Mansouri, Freydoon
1996-01-01
We show that the exact solution of the two_superbody problem in N=2 Chern Simons Supergravity in 2+1 dimensions leads to a supermultiplet of space-times. This supersymmetric space-time is characterized by the two gauge invariant observables of the super Poincare' group, which may be viewed as the Casimir invariants of an equivalent one-superbody state. The metric of this space-time supermultiplet can be cast into the form of the metric for a spinning cone in which the coordinates do not commu...
Chern-Weil Construction for Twisted K-Theory
Gomi, Kiyonori; Terashima, Yuji
2010-10-01
We give a finite-dimensional and geometric construction of a Chern character for twisted K-theory, introducing a notion of connection on a twisted vectorial bundle which can be considered as a finite-dimensional approximation of a twisted family of Fredholm operators. Our construction is applicable to the case of any classes giving the twisting, and agrees with the Chern character of bundle gerbe modules in the case of torsion classes.
Witten's top Chern class via K-theory
Chiodo, Alessandro
2002-01-01
The Witten top Chern class is the crucial cohomology class needed to state a conjecture by Witten relating the Gelfand-Dikii hierarchies to higher spin curves. In math.AG/0011032, Polishchuk and Vaintrob provide an algebraic construction of such a class. We present a more straightforward construction via K-theory. In this way we short-circuit the passage through bivariant intersection theory and the use of MacPherson's graph construction. Furthermore, we show that the Witten top Chern class a...
Quinto, A G
2016-01-01
In this paper we study the Nielsen identity for the supersymmetric Chern-Simons-matter model in the superfield formalism, in three spacetime dimensions. The Nielsen identity is essential to understand the gauge invariance of the symmetry breaking mechanism, and it is calculated by using the BRST invariance of the model. We discuss the technical difficulties in applying this identity to the complete effective superpotential, but we show how we can study in detail the gauge independence of one part of the effective superpotential, $K_{eff}$. We calculate the renormalization group functions of the model for arbitrary gauge-fixing parameter, finding them to be independent of the gauge choice. This result can be used to argue that $K_{eff}$ also does not depend on the gauge parameter. We discuss the possibility of the extension of these results to the complete effective superpotential.
Knot invariants, Chern–Simons theory and the topological recursion
Stevan, Sébastien
2014-01-01
Cette thèse concerne la théorie de Chern-Simons, les invariants de noeuds, les intégrales matricielles formelles et à la théorie des cordes topologiques, ainsi que les relations entre ces différents domaines. Dans un premier temps, nous étudions les polynômes de HOMFLY et de Kauffman colorés des noeuds du tore àl’aide de la théorie de Chern–Simons. Nous obtenons une généralisation de la formule de Rosso-Jones, valable pour les noeuds du tore dans les espaces lenticulaires. Dans une deuxième p...
Energy Technology Data Exchange (ETDEWEB)
Cantanhede, Carlisson M. [Instituto de Fisica Teorica (IFT/UNESP), Sao Paulo, SP (Brazil); Casana, Rodolfo; Ferreira Junior, Manoel M. [Universidade Federal do Maranhao (UFMA), MA (Brazil). Dept. de Fisica; Hora, Eduardo da [Universidade Federal da Paraiba (UFPB), PB (Brazil). Dept. de Fisica
2012-07-01
Full text: Since the seminal works by Abrikosov [1] and Nielsen-Olesen [2] showing the existence of uncharged vortex, such nonperturbative solutions have been a theoretical issue of enduring interest. Already, the electrically charged vortices are obtained only in abelian models endowed with the Chern-Simons term [3,4]. This remains valid even in the context of highly nonlinear models, such as the Born-Infield electrodynamics. In this work, we demonstrated the existence of electrically charged BPS vortices in a Maxwell-Higgs model without the Chern- Simons term but endowed with a CPT-even and parity-odd Lorentz-violating (LV) structure. The LV term belonging to the CPT-even electrodynamics of the Standard Model Extension [5] plays a similar role that of the Chern-Simons term, mixing the electric and magnetic sectors. Besides the LV coefficients provide a very rich set of vortex configurations exhibiting electric's field inversion also are responsible by controlling the characteristic length of the vortex and by the flipping of the magnetic flux. [1] A. Abrikosov, Sov. Phys. JETP 32, 1442 (1957). [2] H. Nielsen, P. Olesen, Nucl. Phys. B 61, 45 (1973). [3] R. Jackiw and E. J. Weinberg, Phys. Rev. Lett. 64, 2234 (1990). [4] C.K. Lee, K.M. Lee, H. Min, Phys. Lett. B 252, 79 (1990) [5] D. Colladay and V. A. Kostelecky, Phys. Rev. D 55, 6760 (1997); Phys. Rev. D 58, 116002 (1998). (author)
Caruso, F; Martins, J; Oguri, V
2012-01-01
The hydrogen atom in two dimensions, described by a Schr\\"odinger equation with a Chern-Simons potential, is numerically solved. Both its wave functions and eigenvalues were determined for small values of the principal quantum number $n$ The only possible states correspond to $l=0$ . How the result depends on the topological mass of the photon is also discussed. In the case $n=1$, the energy of the fundamental state corresponding to different choice for the photon mass scale are found to be comprehended in the interval $-3,5 \\times 10^{-3} eV \\leq E \\leq -9,0 \\times 10^{-2} eV$, corresponding to a mean radius of the electron in the range $ (5.637 \\pm 0.005) \\times 10^{-8} \\leq \\leq (48.87 \\pm 0.03) \\times 10^{-8} cm$. In any case, the planar atom is found to be very weekly bounded showing some features similar to the Rydberg atoms in three dimensions with a Coulombian interaction.
Comments on Dirac-like monopole, Maxwell and Maxwell-Chern-Simons electrodynamics in D=(2+1)
Energy Technology Data Exchange (ETDEWEB)
Moura-Melo, Winder A. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil). E-mail: winder@cbpf.br; Helayel Neto, J.A. [Universidade Catolica de Petropolis, RJ (Brazil). Grupo de Fisica Teorica. E-mail: helayel@cbpf.br
2000-05-01
Classical Maxwell and Maxwell-Chern-Simons Electrodynamics in (2+1) D are studied in some details. General expressions for the potential and fields are obtained for both models, and some particular cases are explicitly solved. Conceptual and technical difficulties arise, however, for accelerated charges. The propagation of electromagnetic signals is also studied and their reverberation is worked out and discussed. Furthermore, we show that a Dirac-like monopole yields a (static) tangential electric field. We also discuss some classical and quantum consequences of the field created by such a monopole when acting upon an usual electric charge. In particular, we show that at large distances, the dynamics of one single charged particle under the action of such a potential and a constant (external) magnetic field as well, reduces to that of one central harmonic oscillator, presenting, however, an interesting angular sector which admits energy-eigenvalues. For example, the quantisation of these eigenvalues yields a Dirac-like condition on the product of the charges. Moreover, such eigenvalues are shown to feel (and respond) to discrete shift of the angle variable. We also raise the question on the possibility of the formation pf bound states in this system. (author)
Chern–Simons theory in SIM(1) superspace
Energy Technology Data Exchange (ETDEWEB)
Vohánka, Jiří [Department of Theoretical Physics and Astrophysics, Masaryk University, Kotlářská 267/2, 611 37, Brno (Czech Republic); Faizal, Mir, E-mail: mirfaizalmir@gmail.com [Department of Physics and Astronomy, University of Waterloo, N2L 3G1, Waterloo, ON (Canada)
2015-12-14
In this paper, we will analyze a three-dimensional supersymmetric Chern–Simons theory in SIM(1) superspace formalism. The breaking of the Lorentz symmetry down to the SIM(1) symmetry breaks half the supersymmetry of the Lorentz invariant theory. So, the supersymmetry of the Lorentz invariant Chern–Simons theory with N=1 supersymmetry will break down to N=1/2 supersymmetry, when the Lorentz symmetry is broken down to the SIM(1) symmetry. First, we will write the Chern–Simons action using SIM(1) projections of N=1 superfields. However, as the SIM(1) transformations of these projections are very complicated, we will define SIM(1) superfields which transform simply under SIM(1) transformations. We will then express the Chern–Simons action using these SIM(1) superfields. Furthermore, we will analyze the gauge symmetry of this Chern–Simons theory. This is the first time that a Chern–Simons theory with N=1/2 supersymmetry will be constructed on a manifold without a boundary.
Inner Structure of Gauss-Bonnet-Chern Theorem and the Morse Theory
Duan, Yi-Shi; Zhang, Peng-Ming
We define a new one-form HA based on the second fundamental tensor HabA¯, the Gauss-Bonnet-Chern form can be novelly expressed with this one-form. Using the φ-mapping theory we find that the Gauss-Bonnet-Chern density can be expressed in terms of the δ-function δ(φ) and the relationship between the Gauss-Bonnet-Chern theorem and Hopf-Poincaré theorem is given straightforwardly. The topological current of the Gauss-Bonnet-Chern theorem and its topological structure are discussed in details. At last, the Morse theory formula of the Euler characteristic is generalized.
Lukierski, Jerzy; Stichel, Peter C.; Zakrzewski, Wojtek J.
1996-01-01
We consider a new D=2 nonrelativistic classical mechanics model providing via the Noether theorem the (2+1)-Galilean symmetry algebra with two central charges: mass m and the coupling constant k of a Chern-Simons-like term. In this way we provide the dynamical interpretation of the second central charge of the (2+1)-dimensional Galilean algebra. We discuss also the interpretation of k as describing the noncommutativity of D=2 space coordinates. The model is quantized in two ways: using the Os...
Casimir effect of the Maxwell-Chern-Simons field for tow non-parallel lines boundary
International Nuclear Information System (INIS)
Based on the Faddeev formalism of path-integral quantization for a constrained Hamiltonian system, the Casimir effect between two non-parallel lines in the (2 +1)-dimensional space is calculated by using conformal mapping and Plana summation formula in the theory of complex variable function. Without introducing any cutoff of parameter, the finite analytical expression is obtained
Navarro-Lérida, Francisco; Tchrakian, D. H.
2015-05-01
We study spherically symmetric finite energy solutions of two Higgs-Chern-Simons-Yang-Mills-Higgs (HCS-YMH) models in 3+1 dimensions, one with gauge group SO(5) and the other with SU(3). The Chern-Simons (CS) densities are defined in terms of both the Yang-Mills (YM) and Higgs fields and the choice of the two gauge groups is made so that they do not vanish. The solutions of the SO(5) model carry only electric charge and zero magnetic charge, while the solutions of the SU(3) model are dyons carrying both electric and magnetic charges like the Julia-Zee (JZ) dyon. Unlike the latter, however, the electric charge in both models receives an important contribution from the CS dynamics. We pay special attention to the relation between the energies and charges of these solutions. In contrast with the electrically charged JZ dyon of the Yang-Mills-Higgs (YMH) system, whose mass is larger than that of the electrically neutral (magnetic monopole) solutions, the masses of the electrically charged solutions of our HCS-YMH models can be smaller than their electrically neutral counterparts in some parts of the parameter space. To establish this is the main task of this work, which is performed by constructing the HCS-YMH solutions numerically. In the case of the SU(3) HCS-YMH, we have considered the question of angular momentum and it turns out that it vanishes.
Navarro-Lerida, Francisco
2014-01-01
We study spherically symmetric finite energy solutions of two Higgs-Chern-Simons--Yang-Mills-Higgs (HCS-YMH) models in $3+1$ dimensions, one with gauge group $SO(5)$ and the other with $SU(3)$. The Chern-Simons (CS) densities are defined in terms of both the Yang-Mills (YM) and Higgs fields and the choice of the two gauge groups is made so they do not vanish. The solutions of the $SO(5)$ model carry only electric charge and zero magnetic charge, while the solutions of the $SU(3)$ model are dyons carrying both electric and magnetic charges like the Julia-Zee (JZ) dyon. Unlike the latter however, the electric charge in both models receives an important contribution from the CS dynamics. We pay special attention to the relation between the energies and charges of these solutions. In contrast with the electrically charged JZ dyon of the Yang-Mills-Higgs (YMH) system, whose mass is larger than that of the electrically neutral (magnetic monopole) solutions, the masses of the electrically charged solutions of our HC...
Zadeh, S Rostam
2015-01-01
We study simultaneous evolution of fermion asymmetries and large scale hypermagnetic fields in the symmetric phase of the electroweak plasma in the temperature range $100$GeV$\\leq T\\leq 10$TeV, taking into account the chirality flip processes via Higgs inverse decays and fermion number violation due to Abelian anomalies for electrons, neutrinos and quarks in the presence of hypermagnetic fields. We present a derivation of the coefficient of the Chern-Simons term for the hypercharge gauge field, showing that the left-handed and right-handed components of each fermion species contribute with opposite sign. This is in contrast to the results presented in some of the previous works. The Chern-Simons term affects the resulting anomalous magnetohydrodynamic (AMHD) equations. We solve the resulting coupled evolution equations for the lepton and baryon asymmetries, as well as the hypermagnetic field to obtain their time evolution along with their values at the electroweak phase transition ($T_{EW} \\sim 100$GeV) for a...
Huang, Yong-Chang
2008-01-01
Using Faddeev-Senjanovic path integral quantization for constrained Hamilton system, we quantize SU(n) N=2 supersymmetric gauge field system with non-abelian Chern-Simons topological term in 2+1 dimensions, and use consistency of a gauge condition naturally to deduce another gauge condition. Further, we get the generating functional of Green function in phase space, deduce the angular momentum based on the global canonical Noether theorem at quantum level, obtain the fractional spin of this supersymmetric system, and show that the total angular momentum has the orbital angular momentum and spin angular momentum of the non-abelian gauge field. Finally, we find out the anomalous fractional spin and discover that the fractional spin has the contributions of both the group superscript components and the charge.
A Relation Between Topological Quantum Field Theory and the Kodama State
Oda, Ichiro
2003-01-01
We study a relation between topological quantum field theory and the Kodama (Chern-Simons) state. It is shown that the Kodama (Chern-Simons) state describes a topological state with unbroken diffeomorphism invariance in Yang-Mills theory and Einstein's general relativity in four dimensions. We give a clear explanation of "why" such a topological state exists.
Institute of Scientific and Technical Information of China (English)
杨树政†; 林恺
2013-01-01
用Hamilton-Jacobi方法研究了动态球对称Einstein-Yang-Mills-Chern-Simons黑洞事件视界处的隧穿辐射特征及其黑洞事件视界处的温度。其结果表明，黑洞温度及隧穿率与黑洞的固有性质及其动态特征有关。这对于进一步研究动态黑洞的热力学性质及其相关问题是有意义的。其方法的重要意义在于研究这类动态黑洞的霍金辐射时，不仅适用于标量场隧穿辐射的情形，同时也适用于研究旋量场、矢量场以及引力波的隧穿辐射。%Using Hamilton-Jacobi method, the Hawking tunneling radiation and temperature are investigated near the event horizon of the Einstein-Yang-Mills-Chern-Simons black hole. The results show that the temperature and tunneling rate depend on the charge and horizon of black holes, and the conclusion is significant for investigating other dynamical black holes. What is more, we also prove that this method can be used to study Hawking radiation in the scalar, vector, Dirac field and gravitational wave cases.
Hopf cyclic cohomology and Chern character of equivariant K-theories
Nikonov, I. M.; Sharygin, G. I.
2015-07-01
We extend the Chern character construction of Neshveyev and Tuset to a map whose values lie in Hopf cyclic homology with coefficients, generalizing their definition of K-theory as well. We also introduce the sheaf of equivariant K-theory (with and without coefficients) similar to the equivariant cohomology of Block and Getzler. This construction is much more geometric (it is defined only for the case in which the Hopf algebra and the Hopfmodule algebra are both algebras of functions on some spaces). Thus, we give a geometric definition of the corresponding Chern character, which takes values in a version of Block—Getzler's sheaf of equivariant cohomology.
Zadeh, S Rostam
2016-01-01
We study simultaneous evolution of baryon and the first generation lepton asymmetries and long range hypermagnetic fields in the temperature range $T_{EW} \\sim 100$GeV$\\leq T \\leq 10$TeV, taking into account fermion number violation due to Abelian anomalies and the chirality flip reactions via inverse Higgs decays. More importantly, in addition to the usual contribution of the first generation leptonic chemical potentials, in this paper we also take into account the contribution of baryonic chemical potentials to the U$_\\textrm{Y}$(1) Chern-Simons term which affects the evolution equations through AMHD equations. We solve the coupled equations for the fermion asymmetries and the hypermagnetic field to obtain their evolution as well as their final values at $T=T_{EW}$ for various critical ranges of initial values, and compare our results with those of our previous study. We find that, strong hypermagnetic fields make the asymmetries grow from their zero initial values. However, the final asymmetries are about ...
Path-integral invariants in abelian Chern–Simons theory
International Nuclear Information System (INIS)
We consider the U(1) Chern–Simons gauge theory defined in a general closed oriented 3-manifold M; the functional integration is used to compute the normalized partition function and the expectation values of the link holonomies. The non-perturbative path-integral is defined in the space of the gauge orbits of the connections which belong to the various inequivalent U(1) principal bundles over M; the different sectors of configuration space are labelled by the elements of the first homology group of M and are characterized by appropriate background connections. The gauge orbits of flat connections, whose classification is also based on the homology group, control the non-perturbative contributions to the mean values. The functional integration is carried out in any 3-manifold M, and the corresponding path-integral invariants turn out to be strictly related with the abelian Reshetikhin–Turaev surgery invariants
Kählerian effective potentials for Chern–Simons-matter theories
Directory of Open Access Journals (Sweden)
J.M. Queiruga
2016-01-01
Full Text Available In this paper, we will calculate the effective potential for a theory of multiple M2-branes. As the theory of multiple M2-branes can be described by a Chern–Simons-matter theory, this will be done by calculating the Kählerian effective potential for a Chern–Simons-matter theory. This calculation will be performed in N=1 superspace formalism. We will initially study an Abelian Chern–Simons-matter theory, and then generalize those results to the full non-Abelian Chern–Simons-matter theory. We will obtain explicit expressions for the superpropagators for this theory. These superpropagators will be used to calculate the one-loop effective potential.
Passage from scalar to vector optics and the Mukunda-Simon-Sudarshan theory for paraxial systems
Khan, Sameen Ahmed
2016-09-01
The way to generalize scalar to wave optics, thus including polarization in the treatment consistent with the Maxwell equations was shown by Mukunda, Simon and Sudarshan for paraxial systems, based on a group theoretical analysis. Here, the Mukunda-Simon-Sudarshan (MSS) theory for the passage from scalar to vector optics is derived by casting the basic formalism in a framework very similar to the Dirac electron theory. The resulting formalism is suitable for extending the MSS-theory beyond the paraxial approximation.
Quantitative K-Theory Related to Spin Chern Numbers
Loring, Terry A.
2014-07-01
We examine the various indices defined on pairs of almost commuting unitary matrices that can detect pairs that are far from commuting pairs. We do this in two symmetry classes, that of general unitary matrices and that of self-dual matrices, with an emphasis on quantitative results. We determine which values of the norm of the commutator guarantee that the indices are defined, where they are equal, and what quantitative results on the distance to a pair with a different index are possible. We validate a method of computing spin Chern numbers that was developed with Hastings and only conjectured to be correct. Specifically, the Pfaffian-Bott index can be computed by the ''log method'' for commutator norms up to a specific constant.
Three dimensional lattice gravity as supersymmetric Yang-Mills theory
Catterall, Simon
2010-01-01
We argue that a certain twisted supersymmetric Yang-Mills theory in three dimensions with gauge group SU(2) possesses a set of topological observables whose expectation values can be computed in a related Chern Simons theory. This Chern Simons theory has been proposed as a definition of three dimensional Euclidean quantum gravity. Since the YM theory admits a discretization which preserves the values of topological observables we conjecture that it can be used as a non-perturbative definition...
Higher Spin Lifshitz Theory and Integrable Systems
Gutperle, Michael; Li, Yi
2014-01-01
In this note we construct asymptotically Lifshitz spacetimes in the Chern-Simons formulation of three dimensional higher spin gravity and relate the resulting theories to integrable systems which are elements of the KdV hierarchy.
New Products, Chern Classes, and Power Operations in Orbifold K-theory
Edidin, Dan; Kimura, Takashi
2012-01-01
We develop a theory of inertial pairs on smooth, separated Deligne-Mumford quotient stacks. An inertial pair determines inertial products and an inertial Chern character. Every vector bundle V on such a stack defines two new inertial pairs and we recover, as special cases, both the orbifold product and the virtual product of [GLSUX07]. We show that for strongly Gorenstein inertial pairs there is also a theory of Chern classes and compatible power operations. An important application is to show that there is a theory of Chern classes and compatible power operations for the virtual product. We also show that when the stack is a quotient [X/G], with G diagonalizable, inertial K-theory has a lambda-ring structure. This implies that for toric Deligne-Mumford stacks there is a corresponding lambda-ring structure associated to virtual K-theory. As an example we compute the semi-group of lambda-positive elements in the virtual lambda-ring of the weighted projective stack P(1,2). Using the virtual orbifold line elemen...
A loop group extension of the odd Chern character
Wilson, Scott O.
2016-04-01
We show that the universal odd Chern form, defined on the stable unitary group U, extends to the loop group LU as an equivariantly closed differential form. This provides an odd analogue to the Bismut-Chern form that appears in supersymmetric field theories. We also describe the associated transgression form, the so-called Bismut-Chern-Simons form, and explicate some properties it inherits as a differential form on the space of maps of a cylinder into the stable unitary group. As one corollary, we show that in a precise sense the spectral flow of a loop of self adjoint Fredholm operators equals the lowest degree component of the Bismut-Chern-Simons form, and the latter, when restricted to cylinders which are tori, is an equivariantly closed extension of spectral flow. As another corollary, we construct the Chern character homomorphism from odd K-theory to the periodic cohomology of the free loop space, represented geometrically on the level of differential forms.
Canizares, Priscilla; Sopuerta, Carlos F
2012-01-01
[abridged] The detection of gravitational waves from extreme-mass-ratio (EMRI) binaries, comprising a stellar-mass compact object orbiting around a massive black hole, is one of the main targets for low-frequency gravitational-wave detectors in space, like the Laser Interferometer Space Antenna (LISA or eLISA/NGO). The long-duration gravitational-waveforms emitted by such systems encode the structure of the strong field region of the massive black hole, in which the inspiral occurs. The detection and analysis of EMRIs will therefore allow us to study the geometry of massive black holes and determine whether their nature is as predicted by General Relativity and even to test whether General Relativity is the correct theory to describe the dynamics of these systems. To achieve this, EMRI modeling in alternative theories of gravity is required to describe the generation of gravitational waves. In this paper, we explore to what extent EMRI observations with LISA or eLISA/NGO might be able to distinguish between G...
The Hitchin-Witten Connection and Complex Quantum Chern-Simons Theory
DEFF Research Database (Denmark)
Andersen, Jørgen Ellegaard; Gammelgaard, Niels Leth
We give a direct calculation of the curvature of the Hitchin connection, in geometric quantization on a symplectic manifold, using only differential geometric techniques. In particular, we establish that the curvature acts as a first-order operator on the quantum spaces. Projective flatness follows...
Supersymmetric Chern–Simons theory in presence of a boundary in the light-like direction
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Jiří Vohánka
2016-03-01
Full Text Available In this paper, we will analyze a three dimensional supersymmetric Chern–Simons theory on a manifold with a boundary. The boundary we will consider in this paper will be defined by n⋅x=0, where n is a light-like vector. It will be demonstrated that this boundary is preserved under the action of the SIM(1 subgroup of the Lorentz group. Furthermore, the presence of this boundary will break half of the supersymmetry of the original theory. As the original Chern–Simons theory had N=1 supersymmetry in absence of a boundary, it will only have N=1/2 supersymmetry in presence of this boundary. We will also observe that the Chern–Simons theory can be made gauge invariant by introducing new degrees of freedom on the boundary. The gauge transformation of these new degrees of freedom will exactly cancel the boundary term obtained from the gauge transformation of the Chern–Simons theory.
SIM(1)–VSR Maxwell–Chern–Simons electrodynamics
Bufalo, R.
2016-01-01
In this paper we propose a very special relativity (VSR)-inspired generalization of the Maxwell-Chern-Simons (MCS) electrodynamics. This proposal is based upon the construction of a proper study of the SIM$(1)$--VSR gauge-symmetry. It is shown that the VSR nonlocal effects present a significant and health departure from the usual MCS theory. The classical dynamics is analysed in full detail, by studying the solution for the electric field and static energy for this configuration. Afterwards, ...
Lectures on RCFT [Rational Conformal Field Theory
International Nuclear Information System (INIS)
We review some recent results in two dimensional Rational Conformal Field Theory. We discuss these theories as a generalization of group theory. The relation to a three dimensional topological theory is explained and the particle example of Chern-Simons-Witten theory is analyzed in detail. This study leads to a natural conjecture regarding the classification of all RCFT's. 62 refs
Novel BPS Wilson loops in three-dimensional quiver Chern–Simons-matter theories
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Hao Ouyang
2016-02-01
Full Text Available We show that generic three-dimensional N=2 quiver super Chern–Simons-matter theories admit Bogomol'nyi–Prasad–Sommerfield (BPS Drukker–Trancanelli (DT type Wilson loops. We investigate both Wilson loops along timelike infinite straight lines in Minkowski spacetime and circular Wilson loops in Euclidean space. In Aharnoy–Bergman–Jafferis–Maldacena theory, we find that generic BPS DT type Wilson loops preserve the same number of supersymmetries as Gaiotto–Yin type Wilson loops. There are several free parameters for generic BPS DT type Wilson loops in the construction, and supersymmetry enhancement for Wilson loops happens for special values of the parameters.
International Nuclear Information System (INIS)
We elaborate on the suggestion made in arXiv:0806.3498 that the 3d N=8 superconformal SU(N) Chern-Simons-matter theory of 'Lorentzian' Bagger-Lambert-Gustavson type (L-BLG) can be obtained by a scaling limit (involving sending the level k to infinity and redefining the fields) from the N=6 superconformal U(N)xU(N) Chern-Simons-matter theory of Aharony, Bergman, Jafferis, and Maldacena (ABJM). We show that to implement such limit in a consistent way one is to extend the ABJM theory by an Abelian 'ghost' multiplet. The corresponding limit at the 3-algebra level also requires extending the nonantisymmetric Bagger-Lambert 3-algebra underlying the ABJM theory by a negative-norm generator. We draw analogy with similar scaling limits discussed previously for bosonic Chern-Simons theory and comment on some implications of this relation between the ABJM and L-BLG theories.
Undergraduate Lecture Notes in Topological Quantum Field Theory
Ivancevic, Vladimir G.; Ivancevic, Tijana T.
2008-01-01
These third-year lecture notes are designed for a 1-semester course in topological quantum field theory (TQFT). Assumed background in mathematics and physics are only standard second-year subjects: multivariable calculus, introduction to quantum mechanics and basic electromagnetism. Keywords: quantum mechanics/field theory, path integral, Hodge decomposition, Chern-Simons and Yang-Mills gauge theories, conformal field theory
Duality in Noncommutative Topologically Massive Gauge Field Theory Revisited
Cantcheff, M B; Minces, Pablo
2003-01-01
We introduce a master action in noncommutative space, out of which we obtain the action of the noncommutative Maxwell-Chern-Simons theory. Then, performing calculations to the first non-trivial order in the noncommutative parameter, we compute the corresponding dual theory, which happens to be, precisely, the action obtained from the usual commutative Self-Dual model by generalizing the Chern-Simons term to its noncommutative version, including a cubic term. Since this resulting theory is also equivalent to the noncommutative massive Thirring model in the large fermion mass limit, we obtain, as a byproduct, the generalization to noncommutative space of the bosonization in three dimensions. Our result also strongly contributes to solve ambiguities arising when defining the generalizations to noncommutative space of the Maxwell-Chern-Simons theory and the Self-Dual model.
Higher derivative extensions of 3 d Chern–Simons models: conservation laws and stability
Kaparulin, D. S.; Karataeva, I. Yu.; Lyakhovich, S. L.
2015-01-01
We consider the class of higher derivative $3d$ vector field models with the field equation operator being a polynomial of the Chern-Simons operator. For $n$-th order theory of this type, we provide a general receipt for constructing $n$-parameter family of conserved second rank tensors. The family includes the canonical energy-momentum tensor, which is unbounded, while there are bounded conserved tensors that provide classical stability of the system for certain combinations of the parameter...
On The Quantum Theory of Hall Effect
Ghaboussi, F.
1996-01-01
We discuss a model of both classical and integer quantum Hall-effect which is based on a semi-classical Schroedinger-Chern-Simons-action, where the Ohm-equations result as equations of motion. The quantization of the classical Chern-Simons-part of action under typical quantum Hall conditions results in the quantized Hall conductivity. We show further that the classical Hall-effect is described by a theory which arises as the classical limit of a theory of quantum Hall-effect. The model explai...
Composite particle and field theory in atomic quantum Hall effect
Institute of Scientific and Technical Information of China (English)
Zhao Bo; Chen Zeng-Bing
2005-01-01
In this paper, we explore the composite particle description of the atomic quantum Hall (QH) effect. We further give the Chern-Simon-Gross-Pitaevskii (CSGP) effective theory for the atomic Hall liquid, which is the counterpart of Chern-Simon theory in electron Hall effect. What we obtained is equivalent to the Laughlin wavefunction approach.Our results show that in terms of composite particles, the atomic Hall effect is really the same as the electronic QH effect. The CSGP effective theory would shed new light on the atomic QH effect.
Huang, Yu-tin; Johansson, Henrik
2013-04-26
We show that three-dimensional supergravity amplitudes can be obtained as double copies of either three-algebra super-Chern-Simons matter theory or two-algebra super-Yang-Mills theory when either theory is organized to display the color-kinematics duality. We prove that only helicity-conserving four-dimensional gravity amplitudes have nonvanishing descendants when reduced to three dimensions, implying the vanishing of odd-multiplicity S-matrix elements, in agreement with Chern-Simons matter theory. We explicitly verify the double-copy correspondence at four and six points for N = 12,10,8 supergravity theories and discuss its validity for all multiplicity.
Research program in elementary particle theory
International Nuclear Information System (INIS)
The Syracuse High Energy Theory group has continued to make significant contributions to many areas. Many novel aspects of Chern-Simons terms and effective Lagrangians were investigated. Various interesting aspects of quantum gravity and string theory were explored. Gauge models of elementary particles were studied in depth. The investigations of QCD at finite temperatures and multiply connected configuration spaces continued. 24 refs
Construction and classification of novel BPS Wilson loops in quiver Chern–Simons-matter theories
Directory of Open Access Journals (Sweden)
Hao Ouyang
2016-09-01
Full Text Available In this paper we construct and classify novel Drukker–Trancanelli (DT type BPS Wilson loops along infinite straight lines and circles in N=2,3 quiver superconformal Chern–Simons-matter theories, Aharony–Bergman–Jafferis–Maldacena (ABJM theory, and N=4 orbifold ABJM theory. Generally we have four classes of Wilson loops, and all of them preserve the same supersymmetries as the BPS Gaiotto–Yin (GY type Wilson loops. There are several free complex parameters in the DT type BPS Wilson loops, and for two classes of Wilson loops in ABJM theory and N=4 orbifold ABJM theory there are supersymmetry enhancements at special values of the parameters. We check that the differences of the DT type and GY type Wilson loops are Q-exact with Q being some supercharges preserved by both the DT type and GY type Wilson loops. The results would be useful to calculate vacuum expectation values of the DT type Wilson loops in matrix models if they are still BPS quantum mechanically.
Suwa, Tatsuo; 諏訪, 立雄
2003-01-01
If we have a finite number of sections of a complex vector bundle E over a manifold M, certain Chern classes of E are localized at the singular set S, i.e., the set of points where the sections fail to be linearly independent. When S is compact, the localizations define the residues at each connected component of S by the Alexander duality. If M itself is compact, the sum of the residues is equal to the Poincaré dual of the corresponding Chern class. This type of theory is also developed for ...
Suwa, Tatsuo
2003-01-01
If we have a finite number of sections of a complex vector bundle $E$ over a manifold $M$ , certain Chern classes of $E$ are localized at the singular set $S$ , i.e., the set of points where the sections fail to be linearly independent. When $S$ is compact, the localizations define the residues at each connected component of $S$ by the Alexander duality. If $M$ itself is compact, the sum of the residues is equal to the Poincaré dual of the corresponding Chern class. This type of theory is als...
The Chern Character of Certain Infinite Rank Bundles arising in Gauge Theory
Mickelsson, Jouko
2012-01-01
A cocycle $\\Omega: P \\times G \\to H$ taking values in a Lie group $H$ for a free right action of $G$ on $P$ defines a principal bundle $Q$ with the structure group $H$ over $P/G.$ The Chern character of a vector bundle associated to $Q$ defines then characteristic classes on $X.$ This observation becomes useful in the case of infinite dimensional groups. It typically happens that a representation of $G$ is not given by linear operators which differ from the indentity by a trace-class operator. For this reason the Chern character of a vector bundle associated to the principal fibration $P \\to P/G$ is ill-defined. But it may happen that the Lie algebra representations of the group $H$ are given in terms of trace-class operators and therefore the Chern character is well-defined; this observation is useful especially if the map $g\\mapsto \\Omega(p;g)$ is a homotopy equivalence on the image for any $p\\in P.$ We apply this method to the case $P= \\Cal A,$ the space of gauge connections in a finite-dimensional vector ...
Nekrasov, Nikita
2004-01-01
We present the evidence for the existence of the topological string analogue of M-theory, which we call Z-theory. The corners of Z-theory moduli space correspond to the Donaldson-Thomas theory, Kodaira-Spencer theory, Gromov-Witten theory, and Donaldson-Witten theory. We discuss the relations of Z-theory with Hitchin's gravities in six and seven dimensions, and make our own proposal, involving spinor generalization of Chern-Simons theory of three-forms. Based on the talk at Strings'04 in Paris.
On higher holonomy invariants in higher gauge theory I
Zucchini, Roberto
2016-05-01
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.
Research program in elementary particle theory
International Nuclear Information System (INIS)
In this paper we give a brief account of the work of the group during the past year. The topics covered here include (1) Effective Lagrangians and Solitons; (2) Chern-Simons and Conformal Field Theories; (3) Spin and Statistics; (4) The Standard Model and Beyond; (5) Non-Abelian Monopoles; (6) The Inflationary Universe; (7) The Hubbard Model, and (8) Miscellaneous
Probing Wilson loops in N=4 Chern–Simons-matter theories at weak coupling
Directory of Open Access Journals (Sweden)
Luca Griguolo
2016-02-01
Full Text Available For three-dimensional N=4 super-Chern–Simons-matter theories associated to necklace quivers U(N0×U(N1×⋯U(N2r−1, we study at quantum level the two kinds of 1/2 BPS Wilson loop operators recently introduced in arXiv:1506.07614. We perform a two-loop evaluation and find the same result for the two kinds of operators, so moving to higher loops a possible quantum uplift of the classical degeneracy. We also compute the 1/4 BPS bosonic Wilson loop and discuss the quantum version of the cohomological equivalence between fermionic and bosonic Wilson loops. We compare the perturbative result with the Matrix Model prediction and find perfect matching, after identification and remotion of a suitable framing factor. Finally, we discuss the potential appearance of three-loop contributions that might break the classical degeneracy and briefly analyze possible implications on the BPS nature of these operators.
Topics in low-dimensional field theory
International Nuclear Information System (INIS)
Conformal field theory is a natural tool for understanding two- dimensional critical systems. This work presents results in the lagrangian approach to conformal field theory. The first sections are chiefly about a particular class of field theories called coset constructions and the last part is an exposition of the connection between two-dimensional conformal theory and a three-dimensional gauge theory whose lagrangian is the Chern-Simons density
Topics in low-dimensional field theory
Energy Technology Data Exchange (ETDEWEB)
Crescimanno, M.J.
1991-04-30
Conformal field theory is a natural tool for understanding two- dimensional critical systems. This work presents results in the lagrangian approach to conformal field theory. The first sections are chiefly about a particular class of field theories called coset constructions and the last part is an exposition of the connection between two-dimensional conformal theory and a three-dimensional gauge theory whose lagrangian is the Chern-Simons density.
Computing Black Hole entropy in Loop Quantum Gravity from a Conformal Field Theory perspective
Agullo, Ivan; Diaz-Polo, Jacobo
2009-01-01
Motivated by the analogy proposed by Witten between Chern-Simons and Conformal Field Theories, we explore an alternative way of computing the entropy of a black hole starting from the isolated horizon framework in Loop Quantum Gravity. The consistency of the result opens a window for the interplay between Conformal Field Theory and the description of black holes in Loop Quantum Gravity.
Computing black hole entropy in loop quantum gravity from a conformal field theory perspective
Energy Technology Data Exchange (ETDEWEB)
Agulló, Iván [Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, IL 60637 (United States); Borja, Enrique F. [Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Facultad de Física, Universidad de Valencia, Burjassot-46100, Valencia (Spain); Díaz-Polo, Jacobo, E-mail: Ivan.Agullo@uv.es, E-mail: Enrique.Fernandez@uv.es, E-mail: Jacobo.Diaz@uv.es [Institute for Gravitation and the Cosmos, Physics Department, Penn State, University Park, PA 16802 (United States)
2009-07-01
Motivated by the analogy proposed by Witten between Chern-Simons and conformal field theories, we explore an alternative way of computing the entropy of a black hole starting from the isolated horizon framework in loop quantum gravity. The consistency of the result opens a window for the interplay between conformal field theory and the description of black holes in loop quantum gravity.
Directory of Open Access Journals (Sweden)
M.R. Setare
2016-01-01
Full Text Available In the first order formalism of gravity theories, there are some theories which are not Lorentz-diffeomorphism covariant. In the framework of such theories we cannot apply the method of conserved charge calculation used in Lorentz-diffeomorphism covariant theories. In this paper we firstly introduce the total variation of a quantity due to an infinitesimal Lorentz-diffeomorphism transformation. Secondly, in order to obtain the conserved charges of Lorentz-diffeomorphism non-covariant theories, we extend the Tachikawa method [1]. This extension includes not only Lorentz gauge transformation but also the diffeomorphism. We apply this method to the Chern–Simons-like theories of gravity (CSLTG and obtain a general formula for the entropy of black holes in those theories. Finally, some examples on CSLTG are provided and the entropy of the BTZ black hole is calculated in the context of the examples.
Phase diagram of 4D field theories with chiral anomaly from holography
Ammon, Martin; Macedo, Rodrigo P
2016-01-01
Within gauge/gravity duality, we study the class of four dimensional CFTs with chiral anomaly described by Einstein-Maxwell-Chern-Simons theory in five dimensions. In particular we determine the phase diagram at finite temperature, chemical potential and magnetic field. At high temperatures the solution is given by an electrically and magnetically charged AdS Reissner-Nordstroem black brane. For sufficiently large Chern-Simons coupling and at sufficiently low temperatures and small magnetic fields, we find a new phase with helical order, breaking translational invariance spontaneously. For the Chern-Simons couplings studied, the phase transition is second order with mean field exponents. Since the entropy density vanishes in the limit of zero temperature we are confident that this is the true ground state which is the holographic version of a chiral magnetic spiral.
Framing anomaly in the effective theory of the fractional quantum Hall effect.
Gromov, Andrey; Cho, Gil Young; You, Yizhi; Abanov, Alexander G; Fradkin, Eduardo
2015-01-01
We consider the geometric part of the effective action for the fractional quantum Hall effect (FQHE). It is shown that accounting for the framing anomaly of the quantum Chern-Simons theory is essential to obtain the correct gravitational linear response functions. In the lowest order in gradients, the linear response generating functional includes Chern-Simons, Wen-Zee, and gravitational Chern-Simons terms. The latter term has a contribution from the framing anomaly which fixes the value of thermal Hall conductivity and contributes to the Hall viscosity of the FQH states on a sphere. We also discuss the effects of the framing anomaly on linear responses for non-Abelian FQH states.
Remarks on Lorentz and CPT violation in field theory
Mariz, T; Passos, E
2006-01-01
In this brief review we explicitly calculate the radiative corrections to the Chern-Simons-like term in the cases of zero and finite temperature, and in the gravity theory. Our results are obtained under the general guidance of dimensional regularization.
The entropy of isolated horizons in non-minimally coupling scalar field theory from BF theory
Wang, Jingbo
2015-01-01
In this paper, the entropy of isolated horizons in non-minimally coupling scalar field theory and in the scalar-tensor theory of gravitation is calculated by counting the degree of freedom of quantum states in loop quantum gravity. Instead of boundary Chern-Simons theory, the boundary BF theory is used. The advantages of the new approaches are that no spherical symmetry is needed, and that the final result matches exactly with the Wald entropy formula.
5-brane webs, symmetry enhancement, and duality in 5d supersymmetric gauge theory
International Nuclear Information System (INIS)
We present a number of investigations of 5d N=1 supersymmetric gauge theories that make use of 5-brane web constructions and the 5d superconformal index. These include an observation of enhanced global symmetry in the 5d fixed point theory corresponding to SU(N) gauge theory with Chern-Simons level ±N, enhanced global symmetries in quiver theories, and dualities between quiver theories and non-quiver theories. Instanton contributions play a crucial role throughout
Entanglement Entropy in Warped Conformal Field Theories
Castro, Alejandra; Iqbal, Nabil
2015-01-01
We present a detailed discussion of entanglement entropy in (1+1)-dimensional Warped Conformal Field Theories (WCFTs). We implement the Rindler method to evaluate entanglement and Renyi entropies for a single interval and along the way we interpret our results in terms of twist field correlation functions. Holographically a WCFT can be described in terms of Lower Spin Gravity, a SL(2,R)xU(1) Chern-Simons theory in three dimensions. We show how to obtain the universal field theory results for entanglement in a WCFT via holography. For the geometrical description of the theory we introduce the concept of geodesic and massive point particles in the warped geometry associated to Lower Spin Gravity. In the Chern-Simons description we evaluate the appropriate Wilson line that captures the dynamics of a massive particle.
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.)
Conformal Invariance in Classical Field Theory
Grigore, D. R.
1993-01-01
A geometric generalization of first-order Lagrangian formalism is used to analyse a conformal field theory for an arbitrary primary field. We require that global conformal transformations are Noetherian symmetries and we prove that the action functional can be taken strictly invariant with respect to these transformations. In other words, there does not exists a "Chern-Simons" type Lagrangian for a conformally invariant Lagrangian theory.
Symmetries of topological field theories in the BV-framework
Gieres, F.; Grimstrup, J. M.; Nieder, H.; Pisar, T.; Schweda, M.
2001-01-01
Topological field theories of Schwarz-type generally admit symmetries whose algebra does not close off-shell, e.g. the basic symmetries of BF models or vector supersymmetry of the gauge-fixed action for Chern-Simons theory (this symmetry being at the origin of the perturbative finiteness of the theory). We present a detailed discussion of all these symmetries within the algebraic approach to the Batalin-Vilkovisky formalism. Moreover, we discuss the general algebraic construction of topologic...
A novel supersymmetry in 2-dimensional Yang-Mills theory on Riemann surfaces
International Nuclear Information System (INIS)
We find a novel supersymmetry in 2-dimensional Maxwell and Yang-Mills theories. Using this supersymmetry, it is shown that the 2-dimensional Euclidean pure gauge theory on a closed Riemann surface Σ can be reduced to a topological field theory which is the 3-dimensional Chern-Simons gauge theory in the special space-time topology Σ x R. Related problems are also discussed. (author)
Wörterbuchregister. Grundlagen einer Theorie der Register in modernen Printwörterbüchern
Directory of Open Access Journals (Sweden)
Herbert Ernst Wiegand
2011-10-01
ANGABENSTRUKTUR,ZENTRALE ALPHABETISCHE REGISTERZUGRIFFSSTRUKTUR, REGISTEREINGANG,REGISTERVERWEISANGABE, REGISTERVERWEISEINTRAG, REGISTERZUGRIFFSSTRUKTUR,WÖRTERBUCHREGISTER, ZUGRIFFSREGISTER
Abstract: Dictionary Indexes. Foundations of a Theory of Indexes in Modern-day Printed Dictionaries. This article presents the concepts needed for the analysis and development of all existing and future dictionary indexes according to a uniform theoretical perspective regarding their structures, functions and typology. For this purpose, the accessible index entries are examined. Numerous types of index entries are distinguished, e.g. according to the number and types of index items, the reduced, the complete, the single, the expanded and the enriched index entries, as well as according to the mediostructural orientation, among others the single and the multiple externally oriented index entries. For the index entry structures, hierarchical index internal constituent structures, hierarchical index internal microstructures, index internal addressing structures as well as hierarchical index internal item structures are introduced. Furthermore a typology of index access structures is presented in which, among others, mediostructural are distinguished from the non-mediostructural index access structures and both types are extensively subtypologised. On the basis of the different features and parts of indexes a typology of indexes is proposed. In conclusion, the functions of indexes are examined and, by using examples, the aspects of indexes worthy of criticism are shown.
Keywords: ACCESS INDEX, ACCESSIBLE INDEX ENTRY, CENTRAL ALPHABETICALINDEX ACCESS STRUCTURE, DICTIONARY INDEX, EXPANDED INDEX ENTRY, EXTERNALDATA ACCESSIBILITY, HIERARCHICAL INDEX INTERNAL MICROSTRUCTURE, INDEXACCESS STRUCTURE, INDEX ENTRY, INDEX FUNCTION, INDEX INTERNAL ADDRESSINGSTRUCTURE, INDEX INTERNAL ITEM STRUCTURE, INDEX REFERENCE ENTRY, ITEMGIVING THE INDEX CROSS-REFERENCE, MEDIOSTRUCTURAL INDEX
Directory of Open Access Journals (Sweden)
Hal M. Haggard
2015-11-01
Full Text Available We study the expectation value of a nonplanar Wilson graph operator in SL(2,C Chern–Simons theory on S3. In particular we analyze its asymptotic behavior in the double-scaling limit in which both the representation labels and the Chern–Simons coupling are taken to be large, but with fixed ratio. When the Wilson graph operator has a specific form, motivated by loop quantum gravity, the critical point equations obtained in this double-scaling limit describe a very specific class of flat connection on the graph complement manifold. We find that flat connections in this class are in correspondence with the geometries of constant curvature 4-simplices. The result is fully non-perturbative from the perspective of the reconstructed geometry. We also show that the asymptotic behavior of the amplitude contains, at the leading order, an oscillatory part proportional to the Regge action for the single 4-simplex in the presence of a cosmological constant. In particular, the cosmological term contains the full-fledged curved volume of the 4-simplex. Interestingly, the volume term stems from the asymptotics of the Chern–Simons action. This can be understood as arising from the relation between Chern–Simons theory on the boundary of a region, and a theory defined by an F2 action in the bulk. Another peculiarity of our approach is that the sign of the curvature of the reconstructed geometry, and hence of the cosmological constant in the Regge action, is not fixed a priori, but rather emerges semiclassically and dynamically from the solution of the equations of motion. In other words, this work suggests a relation between 4-dimensional loop quantum gravity with a cosmological constant and SL(2,C Chern–Simons theory in 3 dimensions with knotted graph defects.
Supersymmetric QFT, Super Loop Spaces and Bismut-Chern Character
Han, Fei
2007-01-01
In this paper, we give a quantum interpretation of the Bismut-Chern character form (the loop space lifting of the Chern character form) as well as the Chern character form associated to a complex vector bundle with connection over a smooth manifold in the framework of supersymmetric quantum field theories developed by Stolz and Teichner \\cite{ST07}. We show that the Bismut-Chern character form comes up via a loop-deloop process when one goes from $1|1$D theory over a manifold down to a $0|1$D...
Electric/magnetic duality for chiral gauge theories with anomaly cancellation
De Rydt, Jan; Schmidt, Torsten T.; Trigiante, Mario; Proeyen, Antoine; Zagermann, Marco
2008-01-01
We show that 4D gauge theories with Green-Schwarz anomaly cancellation and possible generalized Chern-Simons terms admit a formulation that is manifestly covariant with respect to electric/magnetic duality transformations. This generalizes previous work on the symplectically covariant formulation of anomaly-free gauge theories as they typically occur in extended supergravity, and now also includes general theories with (pseudo-)anomalous gauge interactions as they may occur in global or local...
Lattice Perturbation Theory in Noncommutative Geometry and Parity Anomaly in 3D Noncommutative QED
Nishimura, J
2003-01-01
We formulate lattice perturbation theory for gauge theories in noncommutative geometry. We apply it to three-dimensional noncommutative QED and calculate the effective action induced by Dirac fermions. In particular "parity invariance" of a massless theory receives an anomaly expressed by the noncommutative Chern-Simons action. The coefficient of the anomaly is labelled by an integer depending on the lattice action, which is a noncommutative counterpart of the phenomenon known in the commutative theory. The parity anomaly can also be obtained using Ginsparg-Wilson fermions, where the masslessness is guaranteed at finite lattice spacing. This suggests a natural definition of the lattice-regularized Chern-Simons theory on a noncommutative torus, which could enable nonperturbative studies of quantum Hall systems.
Topological field theories on manifolds with Wu structures
Monnier, Samuel
2016-01-01
We construct invertible field theories generalizing abelian prequantum spin Chern-Simons theory to manifolds of dimension 4k+3 endowed with a Wu structure of degree 2k+2. After analysing the anomalies of a certain discrete symmetry, we gauge it, producing topological field theories whose path integral reduces to a finite sum, akin to Dijkgraaf-Witten theories. We take a general point of view where the Chern-Simons gauge group and its couplings are encoded in a local system of integral lattices. The Lagrangian of these theories has to be interpreted as a class in a generalized cohomology theory in order to obtain a gauge invariant action. We develop a computationally friendly cochain model for this generalized cohomology and use it in a detailed study of the properties of the Wu Chern-Simons action. In the three-dimensional spin case, the latter provides a definition of the "fermionic correction" introduced recently in the literature on fermionic symmetry protected topological phases. In order to construct the...
Towards U(N|M) knot invariant from ABJM theory
Eynard, Bertrand
2014-01-01
We study U(N|M) character expectation value with the supermatrix Chern-Simons theory, known as the ABJM matrix model, with emphasis on its connection to the knot invariant. This average just gives the half BPS circular Wilson loop expectation value in ABJM theory, which shall correspond to the unknot invariant. We derive the determinantal formula, which gives U(N|M) character expectation values in terms of U(1|1) averages for a particular type of character representations. This means that the U(1|1) character expectation value is a building block for all the U(N|M) averages, and in particular, by an appropriate limit, for the U(N) invariants. In addition to the original model, we introduce another supermatrix model obtained through the symplectic transform, which is motivated by the torus knot Chern-Simons matrix model. We obtain the Rosso-Jones-type formula and the spectral curve for this case.
Ward identities and gauge flow for M-theory in N =3 superspace
Upadhyay, Sudhaker
2015-09-01
We derive the Becchi-Rouet-Stora-Tyutin (BRST) symmetry, Slavnov-Taylor identities, and Nielsen identities for the Aharony-Bergman-Jafferis-Maldacena theories in N =3 harmonic superspace. Further, the gauge dependence of one-particle irreducible amplitudes in this superconformal Chern-Simons theory is shown to be generated by a canonical flow with respect to the extended Slavnov-Taylor identity, induced by the extended BRST transformations (including the BRST transformations of the gauge parameters).
Ward identities and gauge flow for M-theory in ${\\cal N}{=}3$ superspace
Upadhyay, Sudhaker
2015-01-01
We derive the BRST symmetry, Slavnov-Taylor identities and Nielsen identities for the ABJM theories in ${\\cal N}{=}3$ harmonic superspace. Further, the gauge dependence of one-particle irreducible amplitudes in such superconformal Chern-Simons theory is shown to be generated by a canonical flow with respect to the extended Slavnov-Taylor identity, induced by the extended BRST transformations (including the BRST transformations of the gauge parameters).
Kim, S; Yee, H U; Kim, Seok; Lee, Ki-Myeong; Yee, Ho-Ung
2006-01-01
To a domain wall or string object, Noether charge and topological spatial objects can be attracted, forming a composite BPS (Bogomolny-Prasad-Sommerfield) object. We consider two field theories and derive a new BPS bound on composite linear solitons involving multiple charges. Among the BPS objects `supertubes' appear when the wall or string tension is canceled by the bound energy, and could take an arbitrary closed curve. In our theories, supertubes manifest as Chern-Simons solitons, dyonic instantons, charged semi-local vortices, and dyonic instantons on vortex flux sheet.
Directory of Open Access Journals (Sweden)
M.R. Setare
2016-08-01
Full Text Available The Chern–Simons-like theories of gravity (CSLTG are formulated at first order formalism. In this formalism, the derivation of the entropy of a black hole on bifurcation surface, as a quasi-local conserved charge is problematic. In this paper we overcome these problems by considering the concept of total variation and the Lorentz–Lie derivative. We firstly find an expression for the ADT conserved current in the context of the CSLTG which is based on the concept of the Killing vector fields. Then, we generalize it to be conserved for all diffeomorphism generators. Thus, we can extract an off-shell conserved charge for any vector field which generates a diffeomorphism. The formalism presented here is based on the concept of quasi-local conserved charges which are off-shell. The charges can be calculated on any codimension two space-like surface surrounding a black hole and the results are independent of the chosen surface. By using the off-shell quasi-local conserved charge, we investigate the Virasoro algebra and find a formula to calculate the central extension term. We apply the formalism to the BTZ black hole solution in the context of the Einstein gravity and the Generalized massive gravity, then we find the eigenvalues of their Virasoro generators as well as the corresponding central charges. Eventually, we calculate the entropy of the BTZ black hole by the Cardy formula and we show that the result exactly matches the one obtained by the concept of the off-shell conserved charges.
Towards a common theory for learning from reward, affect, and motivation: The SIMON framework
Directory of Open Access Journals (Sweden)
Christopher R Madan
2013-10-01
Full Text Available While the effects of reward, affect, and motivation on learning have each developed into their own fields of research, they largely have been investigated in isolation. As all three of these constructs are highly related, and use similar experimental procedures, an important advance in research would be to consider the interplay between these constructs. Here we first define each of the three constructs, and then discuss how they may influence each other within a common framework. Finally, we delineate several sources of evidence supporting the framework. By considering the constructs of reward, affect, and motivation within a single framework, we can develop a better understanding of the processes involved in learning and how they interplay, and work towards a comprehensive theory that encompasses reward, affect, and motivation.
Liu, Chien-Hao
2016-01-01
In earlier works, D(1) (arXiv:0709.1515 [math.AG]), D(11.1) (arXiv:1406.0929 [math.DG]), D(11.2) (arXiv:1412.0771 [hep-th]), and D(11.3.1) (arXiv:1508.02347 [math.DG]), we have explained why a D-brane in string theory, when treated as a fundamental dynamical object, can be described by a map $\\varphi$ from an Azumaya/matrix manifold $X^{Az}$ (cf. D-brane world-volume) with a fundamental module with a connection $(E,\
Intersection numbers with Witten's top Chern class
S. Shadrin; D. Zvonkine
2008-01-01
Witten’s top Chern class is a particular cohomology class on the moduli space of Riemann surfaces endowed with r-spin structures. It plays a key role in Witten’s conjecture relating to the intersection theory on these moduli spaces. Our first goal is to compute the integral of Witten’s class over th
Effective field theory of topological insulator and the Foldy-Wouthuysen transformation
Dayi, O F; Yunt, E
2011-01-01
Employing the Foldy-Wouthuysen transformation it is demonstrated straightforwardly that the first and second Chern numbers are equal to the coefficients of the 2+1 and 4+1 dimensional Chern-Simons actions which are generated by the massive Dirac fermions coupled to the Abelian gauge fields. A topological insulator model in 2+1 dimensions is discussed and by means of a dimensional reduction approach the 1+1 dimensional descendant of the 2+1 dimensional Chern-Simons theory is presented. Field strength of the Berry gauge field corresponding to the 4+1 dimensional Dirac theory is explicitly derived through the Foldy-Wouthuysen transformation. Acquainted with it the second Chern numbers are calculated for specific choices of the integration domain. A method is proposed to obtain 3+1 and 2+1 dimensional descendants of the effective field theory of the 4+1 dimensional time reversal invariant topological insulator theory. Inspired by the spin Hall effect in graphene, a hypothetical model of the time reversal invarian...
Mohammed, Asadig; Murugan, Jeff; Nastase, Horatiu
2012-11-01
We present an embedding of the three-dimensional relativistic Landau-Ginzburg model for condensed matter systems in an N = 6, U(N) × U(N) Chern-Simons-matter theory [the Aharony-Bergman-Jafferis-Maldacena model] by consistently truncating the latter to an Abelian effective field theory encoding the collective dynamics of O(N) of the O(N(2)) modes. In fact, depending on the vacuum expectation value on one of the Aharony-Bergman-Jafferis-Maldacena scalars, a mass deformation parameter μ and the Chern-Simons level number k, our Abelianization prescription allows us to interpolate between the Abelian Higgs model with its usual multivortex solutions and a Ø(4) theory. We sketch a simple condensed matter model that reproduces all the salient features of the Abelianization. In this context, the Abelianization can be interpreted as giving a dimensional reduction from four dimensions. PMID:23215268
Mohammed, Asadig; Murugan, Jeff; Nastase, Horatiu
2012-11-01
We present an embedding of the three-dimensional relativistic Landau-Ginzburg model for condensed matter systems in an N = 6, U(N) × U(N) Chern-Simons-matter theory [the Aharony-Bergman-Jafferis-Maldacena model] by consistently truncating the latter to an Abelian effective field theory encoding the collective dynamics of O(N) of the O(N(2)) modes. In fact, depending on the vacuum expectation value on one of the Aharony-Bergman-Jafferis-Maldacena scalars, a mass deformation parameter μ and the Chern-Simons level number k, our Abelianization prescription allows us to interpolate between the Abelian Higgs model with its usual multivortex solutions and a Ø(4) theory. We sketch a simple condensed matter model that reproduces all the salient features of the Abelianization. In this context, the Abelianization can be interpreted as giving a dimensional reduction from four dimensions.
Topological Field Theory of Time-Reversal Invariant Insulators
Energy Technology Data Exchange (ETDEWEB)
Qi, Xiao-Liang; Hughes, Taylor; Zhang, Shou-Cheng; /Stanford U., Phys. Dept.
2010-03-19
We show that the fundamental time reversal invariant (TRI) insulator exists in 4 + 1 dimensions, where the effective field theory is described by the 4 + 1 dimensional Chern-Simons theory and the topological properties of the electronic structure is classified by the second Chern number. These topological properties are the natural generalizations of the time reversal breaking (TRB) quantum Hall insulator in 2 + 1 dimensions. The TRI quantum spin Hall insulator in 2 + 1 dimensions and the topological insulator in 3 + 1 dimension can be obtained as descendants from the fundamental TRI insulator in 4 + 1 dimensions through a dimensional reduction procedure. The effective topological field theory, and the Z{sub 2} topological classification for the TRI insulators in 2+1 and 3+1 dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of novel and measurable phenomena, the most striking of which is the topological magneto-electric effect, where an electric field generates a magnetic field in the same direction, with an universal constant of proportionality quantized in odd multiples of the fine structure constant {alpha} = e{sup 2}/hc. Finally, we present a general classification of all topological insulators in various dimensions, and describe them in terms of a unified topological Chern-Simons field theory in phase space.
Ketov, Sergei V.
1996-01-01
The (2,2) world-sheet supersymmetric string theory is discussed from the viewpoint of string/membrane unification. The effective field theory in the closed string target space is known to be the 2+2 dimensional (integrable) theory of self-dual gravity (SDG). A world-volume supersymmetrization of the Pleba'nski action for SDG naturally implies the maximal N=8 world-volume supersymmetry, while the maximal supersymmetrization of the dual covariant K"ahler-Lorentz-Chern-Simons action for SDG impl...
Vector supersymmetry in topological field theory
International Nuclear Information System (INIS)
We consider a type of supersymmetry which is present in the Chern-Simons and BF-type topological field theories in terms of a superconnection formalism. The combined global supersymmetry and BRST symmetry are realized in this superspace when non-covariant constraints on the supercurvature are chosen. This construction extends naturally within the bundle of frames approach to superspace, and we present a formalism which may lead to the construction of vector supergravity theories and their coupling to the topological field theories considered here. (orig.)
Experimental Observation of Large Chern Numbers in Photonic Crystals.
Skirlo, Scott A; Lu, Ling; Igarashi, Yuichi; Yan, Qinghui; Joannopoulos, John; Soljačić, Marin
2015-12-18
Despite great interest in the quantum anomalous Hall phase and its analogs, all experimental studies in electronic and bosonic systems have been limited to a Chern number of one. Here, we perform microwave transmission measurements in the bulk and at the edge of ferrimagnetic photonic crystals. Band gaps with large Chern numbers of 2, 3, and 4 are present in the experimental results, which show excellent agreement with theory. We measure the mode profiles and Fourier transform them to produce dispersion relations of the edge modes, whose number and direction match our Chern number calculations. PMID:26722920
Transgression forms as unifying principle in field theory
Mora, P
2005-01-01
In this work I consider extensions of Chern-Simons gravities and supergravities associated to the use of Transgression forms as actions, instead of Chern-Simons forms. It is noted that Transgression Forms yields a essencially unique prescription of boundary terms which allows: (i) to make Chern-Simons theories truly gauge invariant, instead of just quasi-invariant, (ii) to have a well defined action principle, so that the action is an extremum when the field equations hold, (iii) to compute covariant finite conserved charges in agreement with those obtained using hamiltonian methods, (iv) to regularize the action so that the euclidean action is finite and the black hole thermodynamics derived from this action agrees with the one obtained by hamiltonian methods. In addition a class of models for extended objects or branes with or without supersymmetry is introduced and studied. The actions for those models and the space-time in which they propagate is given by the sum of integrals of transgression forms for or...
Model Fractional Chern Insulators
Behrmann, Jörg; Liu, Zhao; Bergholtz, Emil J.
2016-05-01
We devise local lattice models whose ground states are model fractional Chern insulators—Abelian and non-Abelian topologically ordered states characterized by exact ground state degeneracies at any finite size and infinite entanglement gaps. Most saliently, we construct exact parent Hamiltonians for two distinct families of bosonic lattice generalizations of the Zk parafermion quantum Hall states: (i) color-entangled fractional Chern insulators at band filling fractions ν =k /(C +1 ) and (ii) nematic states at ν =k /2 , where C is the Chern number of the lowest band. In spite of a fluctuating Berry curvature, our construction is partially frustration free: the ground states reside entirely within the lowest band and exactly minimize a local (k +1 ) body repulsion term by term. In addition to providing the first known models hosting intriguing states such as higher Chern number generalizations of the Fibonacci anyon quantum Hall states, the remarkable stability and finite-size properties make our models particularly well suited for the study of novel phenomena involving, e.g., twist defects and proximity induced superconductivity, as well as being a guide for designing experiments.
Herbert Simon's Information Theory and Its Practical Enlightenment%西蒙的决策情报信息论及实践启示
Institute of Scientific and Technical Information of China (English)
颜茵
2014-01-01
有关赫伯特·西蒙理论与学术造诣的研究，学界多聚焦于其管理决策思想，而对其并不十分系统和“显赫”的情报信息论，理论界显然未给予集中关注与研究。以西蒙的文献著述为依据，沿着其“管理就是决策”的总命题，对其情报信息论进行尝试性发掘与总结。西蒙的情报信息论论直接导源于他的“管理就是决策”思想。而“有限理性模型”奠定了其决策情报支持系统的主体框架。作为西蒙决策情报理论中最具应用价值的一部分，情报信息能力建设的方法论，对我们今天建设决策情报支持系统、进而推进国家治理体系和治理能力现代化具有较强的实践意义。%The academicspay more attention on Herbert Simon's administrative decision rather than his information theory. The article tries summarizing his information theory on the base of his thoughts that administration is decision-making in his works. Simon's information theory is directly from his thoughts that administration is decision-making. His bounded rationality model lays a solid foundation for the decision and information support system. Methodology of the information ability architecture, which is the most valuable part in Simon's decision information theory, has the practical significance for us to establish decision information support system, and promote the modern-ization of the national administration system.
Exact vacuum solution of a (1+2)-dimensional Poincare gauge theory BTZ solution with torsion
Garcia, A A; Heinicke, C; Macías, A; Garcia, Alberto A.; Hehl, Friedrich W.; Heinicke, Christian; Macias, Alfredo
2003-01-01
In (1+2)-dimensional Poincar\\'e gauge gravity, we start from a Lagrangian depending on torsion and curvature which includes additionally {\\em translational} and {\\em Lorentzian} Chern-Simons terms. Limiting ourselves to to a specific subcase, the Mielke-Baekler (MB) model, we derive the corresponding field equations (of Einstein-Cartan-Chern-Simons type) and find the general vacuum solution. We determine the properties of this solution, in particular its mass and its angular momentum. For vanishing torsion, we recover the BTZ-solution. We also derive the general conformally flat vacuum solution with torsion. In this framework, we discuss {\\em Cartan's} (3-dimensional) {\\em spiral staircase} and find that it is not only a special case of our new vacuum solution, but can alternatively be understood as a solution of the 3-dimensional Einstein-Cartan theory with matter of constant pressure and constant torque. {\\em file 3dexact15.tex}
Global Anomalies and Effective Field Theory
Golkar, Siavash
2015-01-01
We show that matching anomalies under large gauge transformations and large diffeomorphisms can explain the appearance and non-renormalization of couplings in effective field theory. We focus on %thermal partition functions and thermal effective field theory where we argue that the appearance of certain unusual Chern-Simons couplings is a consequence of global anomalies. As an example, we show that a mixed global anomaly in four dimensions fixes the chiral vortical effect coefficient. This is an experimentally measurable prediction from a global anomaly. For certain situations, we propose a simpler method for calculating global anomalies which uses correlation functions rather than eta invariants.
Political and Legal Doctrine of Simon Bolivar
Mixail V. Fedorov
2014-01-01
Present article is devoted to the legal, political and constitutional ideas of the outstanding leader of war of independence in Latin America Simon Bolivar that was called by his countrymen and contemporaries to be a LIBERATOR. In the present article author discusses complex genesis and evolution of the political and legal doctrine of Simon Bolivar. Review is conducted by author in the context of developing theory and practice of Latin American constitutionalism in the XIX century. Author con...
Exact results for Wilson loops in orbifold ABJM theory
Ouyang, Hao; Zhang, Jia-ju
2015-01-01
We investigate the exact results for circular 1/4 and 1/2 BPS Wilson loops in the d=3 N=4 super Chern-Simons-matter theory that could be obtained by orbifolding Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. In literature there is the partition function of the N=4 orbifold ABJM theory, and we re-derive it in a slightly different method. We calculate the vacuum expectation values of the circular 1/4 and 1/2 BPS Wilson loops in both the saddle point approach and Fermi gas approach, and the results are in accord to the gravity ones.
Effective Field Theory of Fractional Quantized Hall Nematics
Energy Technology Data Exchange (ETDEWEB)
Mulligan, Michael; /MIT, LNS; Nayak, Chetan; /Station Q, UCSB; Kachru, Shamit; /Stanford U., Phys. Dept. /SLAC
2012-06-06
We present a Landau-Ginzburg theory for a fractional quantized Hall nematic state and the transition to it from an isotropic fractional quantum Hall state. This justifies Lifshitz-Chern-Simons theory - which is shown to be its dual - on a more microscopic basis and enables us to compute a ground state wave function in the symmetry-broken phase. In such a state of matter, the Hall resistance remains quantized while the longitudinal DC resistivity due to thermally-excited quasiparticles is anisotropic. We interpret recent experiments at Landau level filling factor {nu} = 7/3 in terms of our theory.
Confined Vortices in Topologically Massive U(1)$\\times$U(1) Theory
Anber, Mohamed M; Sabancilar, Eray; Shaposhnikov, Mikhail
2015-01-01
We report on a new topological vortex solution in U(1)$\\times$U(1) Maxwell-Chern-Simons theory. The existence of the vortex is envisaged by analytical means, and a numerical solution is obtained by integrating the equations of motion. These vortices have a long-range force because one of the U(1)s remains unbroken in the infrared, which is guarded by the Coleman-Hill theorem. The sum of the winding numbers of an ensemble of vortices has to vanish; otherwise the system would have a logarithmically divergent energy. In turn, these vortices exhibit classical confinement. We investigate the rich parameter space of the solutions, and show that one recovers the Abrikosov-Nielsen-Olesen, U(1) Maxwell-Chern-Simons, U(1) pure Chern-Simons and global vortices as various limiting cases. Unlike these limiting cases, the higher winding solutions of our vortices carry non-integer charges under the broken U(1). This is the first vortex solution exhibiting such behavior.
The a-function for N=2 supersymmetric gauge theories in three dimensions
Gracey, J A; Poole, C; Schroder, Y
2016-01-01
Recently, the existence of a candidate a-function for renormalisable theories in three dimensions was demonstrated for a general theory at leading order and for a scalar-fermion theory at next-to-leading order. Here we extend this work by constructing the a-function at next-to-leading order for an N=2 supersymmetric Chern-Simons theory. This increase in precision for the a-function necessitated the evaluation of the underlying renormalization-group functions at four loops.
Kukk, Jaak, 1904-2001
1992-01-01
Aleksander Simon õppis veterinaariat, kuid ei lõpetanud, korporatsiooni astus kohe selle asutamisel ja Jaak Kukk oli tema akadeemiline kasuisa, kellele anti teada, et 1944. a Saksamaale rännanud A. Simon üritas 1946 salaja Rootsi põgeneda
Edge excitations in fractional Chern insulators
Luo, Wei-Wei; Chen, Wen-Chao; Wang, Yi-Fei; Gong, Chang-De
2013-10-01
Recent theoretical papers have demonstrated the realization of fractional quantum anomalous Hall states (also called fractional Chern insulators) in topological flat band lattice models without an external magnetic field. Such newly proposed lattice systems play a vital role in obtaining a large class of fractional topological phases. Here we report the exact numerical studies of edge excitations for such systems in a disk geometry loaded with hard-core bosons, which will serve as a more viable experimental probe for such topologically ordered states. We find convincing numerical evidence of a series of edge excitations characterized by the chiral Luttinger liquid theory for the bosonic fractional Chern insulators in both the honeycomb disk Haldane model and the kagome-lattice disk model. We further verify these current-carrying chiral edge states by inserting a central flux to test their compressibility.
Large N behavior of mass deformed ABJM theory
Nosaka, Tomoki; Shimizu, Kazuma; Terashima, Seiji
2016-03-01
In this paper, using the localization technique we analyze the large N limit of the mass deformed Aharony-Bergman-Jafferis-Maldacena (ABJM) theory on the three sphere with a finite mass parameter and finite Chern-Simons levels. We find two different solutions of the saddle point equations in the large N limit. With these solutions we compute the free energy limit and find that there is a first order phase transition. Our results may predict a phase transition in the dual gravity theory.
Large N behavior of mass deformed ABJM theory
Nosaka, Tomoki; Terashima, Seiji
2015-01-01
In this paper, using the localization technique we analyze the large N limit of the mass deformed Aharony-Bergman-Jafferis-Maldacena (ABJM) theory on the three sphere with a finite mass parameter and finite Chern-Simons levels. We find two different solutions of the saddle point equations in the large N limit. With these solutions we compute the free energy and find that there is a first order phase transition. Our results may predict a phase transition in the dual gravity theory.
Toda Theory From Six Dimensions
Cordova, Clay
2016-01-01
We describe a compactification of the six-dimensional (2,0) theory on a four-sphere which gives rise to a two-dimensional Toda theory at long distances. This construction realizes chiral Toda fields as edge modes trapped near the poles of the sphere. We relate our setup to compactifications of the (2,0) theory on the five and six-sphere. In this way, we explain a connection between half-BPS operators of the (2,0) theory and two-dimensional W-algebras, and derive an equality between their conformal anomalies. As we explain, all such relationships between the six-dimensional (2,0) theory and Toda field theory can be interpreted as statements about the edge modes of complex Chern-Simons on various three-manifolds with boundary.
Political and Legal Doctrine of Simon Bolivar
Directory of Open Access Journals (Sweden)
Mixail V. Fedorov
2014-03-01
Full Text Available Present article is devoted to the legal, political and constitutional ideas of the outstanding leader of war of independence in Latin America Simon Bolivar that was called by his countrymen and contemporaries to be a LIBERATOR. In the present article author discusses complex genesis and evolution of the political and legal doctrine of Simon Bolivar. Review is conducted by author in the context of developing theory and practice of Latin American constitutionalism in the XIX century. Author conceptualized and revealed basic historical patterns of formation and development of Latin American countries during the War of Independence (1810-1826 period. Author conducted comprehensive analysis of the draft constitution which was developed by Simon Bolivar for the newly independent states of Latin America and reveals theoretical and practical problem of choosing Simon Bolivar republican form of government, such as a peculiar institution in the form of principle of the separation of powers, containing the fourth power. Author focuses on the questions of Simon Bolivar’s relationship to the constitutional institute of human rights, idea of relationship between state and church. Article also researches many other political, legal and constitutional ideas of Simon Bolivar, present views of historians, lawyers, political scientists, statesmen and public activists.
Equivalence of Wilson Loops in ABJM and N = 4 SYM Theory
Wiegandt, Konstantin
2011-01-01
In previous investigations, it was found that four-sided polygonal light-like Wilson loops in ABJM theory calculated to two-loop order have the same form as the corresponding Wilson loop in N = 4 SYM at one-loop order. Here we study light-like polygonal Wilson loops with n cusps in planar three-dimensional Chern-Simons and ABJM theory to two loops. Remarkably, the result in ABJM theory precisely agrees with the corresponding Wilson loop in N = 4 SYM at one-loop order for arbitrary n. In parti...
On the duality in CPT-even Lorentz-breaking theories
Energy Technology Data Exchange (ETDEWEB)
Scarpelli, A.P.B. [Departamento de Policia Federal, Sao Paulo (Brazil); Ribeiro, R.F.; Nascimento, J.R.; Petrov, A.Yu. [Universidade Federal da Paraiba, Departamento de Fisica (Brazil)
2015-07-15
We generalize the duality between self-dual and Maxwell-Chern-Simons theories for the case of a CPT-even Lorentz-breaking extension of these theories. The duality is shown using the gauge embedding procedure, both in free and coupled cases, and with the master action approach. The physical spectra of both Lorentz-breaking theories are studied. The massive poles are shown to coincide and to respect the requirements for unitarity and causality at tree level. The extra massless poles which are present in the dualized model are shown to be nondynamical. (orig.)
Instanton Effects in Orbifold ABJM Theory
Honda, Masazumi
2014-01-01
We study the partition function of the orbifold ABJM theory, which is the N=4 necklace quiver Chern-Simons-matter theory with alternating levels, in the Fermi gas formalism. We find that the grand potential of the orbifold ABJM theory is expressed explicitly in terms of that of the ABJM theory. As shown previously, the ABJM grand potential consists of the naive but primary non-oscillatory term and the subsidiary infinitely-replicated oscillatory terms. We find that the subsidiary oscillatory terms of the ABJM theory actually give a non-oscillatory primary term of the orbifold ABJM theory. Also, interestingly, the perturbative part in the ABJM theory results in a novel instanton contribution in the orbifold theory. We also present a physical interpretation for the non-perturbative instanton effects.
Levin, Simon, 1928-2008
1987-01-01
Simon Levini seletus Eesti NSV Ülemkohtu Kriminaalasjade kohtukolleegiumi istungil 24. juunil 1982. aastal. Vastav seletus pälvis Eesti NSV advokaatide kohtukõnede konkursil esimese preemia kriminaalasjades peetud kõnede hulgas. Lisatud selgitused kohtuasjale
High spin-Chern insulators with magnetic order.
Ezawa, Motohiko
2013-01-01
As a topological insulator, the quantum Hall (QH) effect is indexed by the Chern and spin-Chern numbers C and Cspin. We have only Cspin = 0 or ± 1/2 in conventional QH systems. We investigate QH effects in generic monolayer honeycomb systems. We search for spin-resolved characteristic patterns by exploring Hofstadter's butterfly diagrams in the lattice theory and fan diagrams in the low-energy Dirac theory. It is shown that the spin-Chern number can takes an arbitrary high value for certain QH systems. This is a new type of topological insulators, which we may call high spin-Chern insulators. Samples may be provided by graphene on the SiC substrate with ferromagnetic order, transition-metal dichalcogenides with ferromagnetic order, transition-metal oxide with antiferromagnetic order and silicene with ferromagnetic order. Actually high spin-Chern insulators are ubiquitous in any systems with magnetic order. Nevertheless, the honeycomb system would provide us with unique materials for practical materialization.
Directory of Open Access Journals (Sweden)
Herbert Ernst Wiegand
2011-10-01
Full Text Available
ZUSAMMENFASSUNG: In diesem Beitrag werden die Begriffe eingeführt, die man benötigt, um das Datenakzessivitätsprofil von Printwörterbüchern genau beschreiben zu können. Es wird zwischen externer und interner Datenakzessivität unterschieden; erstere ist obligatorisch, letztere ist fakultativ. Die externe Datenakzessivität wird durch äußere, die interne Datenakzessivität durch innere Zugriffsstrukturen innerhalb von akzessiven Wörterbucheinträgen hergestellt. Es werden unterschiedliche Typen von äußeren Zugriffsstrukturen als lineare Ordnungsstrukturen, wie z.B. alphabetische äußere Zugriffsstrukturen, numerische mediostrukturelle Zugriffsstrukturen, Regis-terzugriffsstrukturen u.a., beschrieben und ihr Funktionieren erklärt. Weiterhin werden äußere Zugriffsstrukturen von Zugriffspfaden abgegrenzt, die durch die Ausführung externer Zugriffs-handlungen der Benutzer etabliert werden. Der Beitrag gibt insgesamt fünf Einblicke, aber keine zusammenhängende Übersicht über die vielfachen Ausprägungen der Eigenschaften der Wörter-buchform, die die Datenakzessivität sicherstellen.
Stichwörter: AKZESSIVER WÖRTERBUCHEINTRAG, ALPHABET, ALPHABETISCHE ÄU-ßERE ZUGRIFFSSTRUKTUR, ÄUßERER ZUGRIFFSPFAD, EXTERNE DATENAKZESSIVITÄT, EXTERNE ZUGRIFFSHANDLUNG, INNERE ZUGRIFFSSTRUKTUR, INTERNE DATENAKZES-SIVITÄT, MEDIOSTRUKTURELLES LEITELEMENT, MEDIOSTRUKTURELLE ZUGRIFFSSTRUK-TUR, MONOAKZESSIVES WÖRTERBUCH, REGISTER, REGISTERZUGRIFFSSTRUKTUR, POLY-AKZESSIVES WÖRTERBUCH, SCHNELLZUGRIFFSSTRUKTUR, ZUGRIFFSTEXTELEMENT
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ABSTRACT: On the Data Accessibility in Printed Dictionaries. Insights into Recent Developments of a Theory of the Form of Dictionaries. In this contribu-tion, concepts are introduced that are needed for a precise description of the data accessibility pro-file of printed dictionaries. A distinction is made between external and internal data accessibility, with the first being obligatory and the
Remembering Roger I. Simon: A Pedagogy of Public Possibility
Farley, Lisa; Tarc, Aparna Mishra
2014-01-01
This special issue of "Canadian Social Studies" is dedicated to Roger I. Simon. Simon's scholarship bequeaths to theorists, teachers, and curators across Canada and beyond a theory of education that opens up responsibilities to past and present others. The papers gathered for this special issue address many of the difficulties that he…
Chiral four-dimensional F-theory compactifications with SU(5) and multiple U(1)-factors
Cvetič, Mirjam; Grassi, Antonella; Klevers, Denis; Piragua, Hernan
2014-04-01
We develop geometric techniques to determine the spectrum and the chiral indices of matter multiplets for four-dimensional F-theory compactifications on elliptic Calabi-Yau fourfolds with rank two Mordell-Weil group. The general elliptic fiber is the Calabi-Yau onefold in dP 2. We classify its resolved elliptic fibrations over a general base B. The study of singularities of these fibrations leads to explicit matter representations, that we determine both for U(1) × U(1) and SU(5) × U(1) × U(1) constructions. We determine for the first time certain matter curves and surfaces using techniques involving prime ideals. The vertical cohomology ring of these fourfolds is calculated for both cases and general formulas for the Euler numbers are derived. Explicit calculations are presented for a specific base B = ℙ3. We determine the general G 4-flux that belongs to of the resolved Calabi-Yau fourfolds. As a by-product, we derive for the first time all conditions on G 4-flux in general F-theory compactifications with a non-holomorphic zero section. These conditions have to be formulated after a circle reduction in terms of Chern-Simons terms on the 3D Coulomb branch and invoke M-theory/F-theory duality. New Chern-Simons terms are generated by Kaluza-Klein states of the circle compactification. We explicitly perform the relevant field theory computations, that yield non-vanishing results precisely for fourfolds with a non-holomorphic zero section. Taking into account the new Chern-Simons terms, all 4D matter chiralities are determined via 3D M-theory/F-theory duality. We independently check these chiralities using the subset of matter surfaces we determined. The presented techniques are general and do not rely on toric data.
Light-Front quantization of field theory
Srivastava, P P
1996-01-01
Some basic topics in Light-Front (LF) quantized field theory are reviewed. Poincarè algebra and the LF Spin operator are discussed. The local scalar field theory of the conventional framework is shown to correspond to a non-local Hamiltonian theory on the LF in view of the constraint equations on the phase space, which relate the bosonic condensates to the non-zero modes. This new ingredient is useful to describe the spontaneous symmetry breaking on the LF. The instability of the symmetric phase in two dimensional scalar theory when the coupling constant grows is shown in the LF theory renormalized to one loop order. Chern-Simons gauge theory regarded to describe excitations with fractional statistics, is quantized in the light-cone gauge and a simple LF Hamiltonian obtained which may allow us to construct renormalized theory of anyons.
Light-front quantization of field theory
Energy Technology Data Exchange (ETDEWEB)
Srivastava, Prem P. [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Inst. de Fisica]|[Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)
1996-07-01
Some basic topics in Light-Front (LF) quantized field theory are reviewed. Poincare algebra and the LF spin operator are discussed. The local scalar field theory of the conventional framework is shown to correspond to a non-local Hamiltonian theory on the LF in view of the constraint equations on the phase space, which relate the bosonic condensates to the non-zero modes. This new ingredient is useful to describe the spontaneous symmetry breaking on the LF. The instability of the symmetric phase in two dimensional scalar theory when the coupling constant grows is shown in the LF theory renormalized to one loop order. Chern-Simons gauge theory, regarded to describe excitations with fractional statistics, is quantized in the light-cone gauge and a simple LF Hamiltonian obtained which may allow us to construct renormalized theory of anyons. (author). 20 refs.
Energy Technology Data Exchange (ETDEWEB)
Tze, Chia-Hsiung (Virginia Polytechnic Inst., Blacksburg, VA (USA). Dept. of Physics)
1989-01-01
By way of the Gauss-Bonnet-Chern theorem, we present a higher dimensional extension of Polyakov's regularization of Wilson loops of point solitons. Spacetime paths of extended objects become hyper-ribbons with self-linking, twisting and writhing numbers. specifically we discuss the exotic spin and statistical phase entanglements of geometric n-membrane solitons of D-dimensional KP{sub 1} {sigma}-models with an added Hopf-Chern-Simons term where (n, D, K) = (0, 3, C), (2, 7, H), (6, 15, {Omega}). They are uniquely linked to the complex and quaternion and octonion division algebras. 22 refs.
Baryon asymmetry generation in the electroweak theory. A lattice study
International Nuclear Information System (INIS)
We study the baryon asymmetry generation within the framework of the standard electroweak theory. The assumed first order finite temperature phase transition to the spontaneously broken phase is simulated on the lattice. The Monte Carlo data suggest that the high temperature plasma is populated with gauge-Higgs fluctuations, which produce a change Q in the Chern-Simons number during the transition, thereby creating fermions due to the electroweak anomaly. We provide evidence and arguments in favour of a uniform distribution of Q. This being the case, the baryon asymmetry produced during the phase transition is large enough to explain the asymmetry observed today. (orig.)
Quantization of open-closed BCOV theory, I
Costello, Kevin
2015-01-01
This is the first in a series of papers which analyze the problem of quantizing the theory coupling Kodaira-Spencer gravity (or BCOV theory) on Calabi-Yau manifolds using the formalism for perturbative QFT developed by the first author. In this paper, we focus on flat space $\\mathbb{C}^d$ for $d$ odd. We prove that there exists a unique quantization of the theory coupling BCOV theory and holomorphic Chern-Simons theory with gauge group the supergroup $GL(N \\mid N)$. We deduce a canonically defined quantization of BCOV theory on its own. We also discuss some conjectural links between BCOV theory in various dimensions and twists of physical theories: in complex dimension $3$ we conjecture a relationship to twists of $(1,0)$ supersymmetric theories and in complex dimension $5$ to a twist of type IIB supergravity.
Superstring theories as low-energy limit of supergroup gauge theories
Popov, Alexander D
2016-01-01
We consider Yang-Mills theory with $N=2$ super translation group in $d=10$ auxiliary dimensions as the structure group. The gauge theory is defined on a direct product manifold $\\Sigma_2\\times H^2$, where $\\Sigma_2$ is a two-dimensional Lorentzian manifold and $H^2$ is the open disc in $\\mathbb{R}^2$ with the boundary $S^1=\\partial H^2$. We show that in the adiabatic limit, when the metric on $H^2$ is scaled down, the Yang-Mills action supplemented by the $d=5$ Chern-Simons term becomes the Green-Schwarz superstring action. More concretely, the Yang-Mills action in the infrared limit flows to the kinetic part of the superstring action and the $d=5$ Chern-Simons action, defined on a 5-manifold with the boundary $\\Sigma_2\\times H^2$, flows to the Wess-Zumino part of the superstring action. The same kind of duality between gauge fields and strings is established for type IIB superstring on AdS$_5\\times S^5$ background and a supergroup gauge theory with PSU(2,2$|$4) as the structure group.
Modifications of Einstein's theory of gravity at large distances
2015-01-01
In the last few years modified gravity theories have been proposed as extensions of Einstein's theory of gravity. Their main motivation is to explain the latest cosmological and astrophysical data on dark energy and dark matter. The study of general relativity at small scales has already produced important results (cf e.g. LNP 863 Quantum Gravity and Quantum Cosmology) while its study at large scales is challenging because recent and upcoming observational results will provide important information on the validity of these modified theories. In this volume, various aspects of modified gravity at large scales will be discussed: high-curvature gravity theories; general scalar-tensor theories; Galileon theories and their cosmological applications; F(R) gravity theories; massive, new massive and topologically massive gravity; Chern-Simons modifications of general relativity (including holographic variants) and higher-spin gravity theories, to name but a few of the most important recent developments. Edite...
DEFF Research Database (Denmark)
Heidemann, Lene Nyhøj; Thomsen, Jørn Bo; Sørensen, Jens Ahm
2016-01-01
This case report describes a female patient diagnosed with Barraquer-Simons syndrome, a rare form of acquired partial lipodystrophy characterised by symmetrical loss of adipose tissue from face, neck, upper extremities and the trunk with onset in early childhood. Initial symptoms were seen...
Mathematical aspects of quantum field theories
Strobl, Thomas
2015-01-01
Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homolo...
Ketov, S V
1996-01-01
The (2,2) world-sheet supersymmetric string theory is discussed from the viewpoint of string/membrane unification. The effective field theory in the closed string target space is known to be the 2+2 dimensional (integrable) theory of self-dual gravity (SDG). A world-volume supersymmetrization of the Pleba'nski action for SDG naturally implies the maximal N=8 world-volume supersymmetry, while the maximal supersymmetrization of the dual covariant K"ahler-Lorentz-Chern-Simons action for SDG implies gauging a self-dual part of the super-Lorentz symmetry in 2+10 dimensions. The proposed OSp(32|1) supersymmetric action for the M-brane may be useful for a fundamental formulation of uncompactified F theory, with the self-duality being playing the central role both in the world-volume and in the target space of the M-brane.
DEFF Research Database (Denmark)
for bedste orkesterværk ved det nyligt overståede musikdage i Donaueschingen samt med Nordisk Råds Musikpris i 2014. Med dette fokus ønsker Seismograf/DMT at fejre komponisten Simon Steen-Andersen. I både en dansk og i en international kontekst ønsker vi at præsentere og reflektere over et lille hjørne af...
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.
Relative Topological Integrals and Relative Cheeger-Simons Differential Characters
Zucchini, R
2000-01-01
Topological integrals appear frequently in Lagrangian field theories. On manifolds without boundary, they can be treated in the framework of ordinary (co)homology using the formalism of Cheeger-Simons differential characters. String and D-brane theory involve field theoretic models on worldvolumes with border. On manifolds with boundary, the proper treatment of topological integrals requires a generalization of the usual differential topological set up and leads naturally to relative (co)homology and relative Cheeger-Simons differential characters. In this paper, we present a construction of relative Cheeger-Simons differential characters which is computable in principle and which contains the ordinary Cheeger-Simons differential characters as a particular case.
DEFF Research Database (Denmark)
Foss, Kirsten; Foss, Nicolai Juul
2006-01-01
as a general approach to problem solving. We apply these Simonian ideas to organisational issues, specifically new organisational forms. Specifically, Simonian ideas allow us to develop a morphology of new organisational forms and to point to some design problems that characterise these forms.......Two of Herbert Simon's best-known papers are 'The Architecture of Complexity' and 'The Structure of Ill-Structured Problems.' We discuss the neglected links between these two papers, highlighting the role of decomposition in the context of problems on which constraints have been imposed...
Arun, K G
2013-01-01
Gravitational Wave (GW) observations of coalescing compact binaries will be unique probes of strong-field, dynamical aspects of relativistic gravity. We present a short review of various schemes proposed in the literature to test General Relativity (GR) and alternative theories of gravity using inspiral waveforms. Broadly these schemes may be classified into two types: model dependent and model independent. In the model dependent category, GW observations are compared against a specific waveform model representative of a particular theory or a class of theories like Scalar-Tensor theories, Dynamical Chern-Simons theory and Massive graviton theories. Model independent tests are attempts to write down a parametrised gravitational waveform where the free parameters take different values for different theories and (at least some of) which can be constrained by GW observations. We revisit some of the proposed bounds in the case of downscaled LISA configuration (eLISA) and compare them with the original LISA config...
N=4 supersymmetric Yang-Mills theories in AdS{sub 3}
Energy Technology Data Exchange (ETDEWEB)
Kuzenko, Sergei M.; Tartaglino-Mazzucchelli, Gabriele [School of Physics M013, The University of Western Australia,35 Stirling Highway, Crawley W.A. 6009 (Australia)
2014-05-06
For all types of N=4 anti-de Sitter (AdS) supersymmetry in three dimensions, we construct manifestly supersymmetric actions for Abelian vector multiplets and explain how to extend the construction to the non-Abelian case. Manifestly N=4 supersymmetric Yang-Mills (SYM) actions are explicitly given in the cases of (2,2) and critical (4,0) AdS supersymmetries. The N=4 vector multiplets and the corresponding actions are then reduced to (2,0) AdS superspace, in which only N=2 supersymmetry is manifest. Using the off-shell structure of the N=4 vector multiplets, we provide complete N=4 SYM actions in (2,0) AdS superspace for all types of N=4 AdS supersymmetry. In the case of (4,0) AdS supersymmetry, which admits a Euclidean counterpart, the resulting N=2 action contains a Chern-Simons term proportional to q/r, where r is the radius of AdS{sub 3} and q is the R-charge of a chiral scalar superfield. The R-charge is a linear inhomogeneous function of X, an expectation value of the N=4 Cotton superfield. Thus our results explain the mysterious structure of N=4 supersymmetric Yang-Mills theories on S{sup 3} discovered in arXiv:1401.7952. In the case of (3,1) AdS supersymmetry, which has no Euclidean counterpart, the SYM action contains both a Chern-Simons term and a chiral mass-like term. In the case of (2,2) AdS supersymmetry, which admits a Euclidean counterpart, the SYM action has no Chern-Simons and chiral mass-like terms.
Exact holography and black hole entropy in N=8 and N=4 string theory
Gomes, Joao
2015-01-01
We compute the exact entropy of one-eighth and one-quarter BPS black holes in N=8 and N=4 string theory respectively. This includes all the N=4 CHL models in both K3 and T^4 compactifications. The main result is a measure for the finite dimensional integral that one obtains after localization of supergravity on AdS_2xS^2. This measure is determined entirely by an anomaly in supersymmetric Chern-Simons theory on local AdS_3 and takes into account the contribution from all the supergravity multiplets. In Chern-Simons theory on compact manifolds this is the anomaly that computes a certain one-loop dependence on the volume of the manifold. For one-eighth BPS black holes our results are a first principles derivation of a measure proposed in arXiv:1111.1161, while in the case of one-quarter BPS black holes our result computes exactly all the perturbative or area corrections. Moreover, we argue that instantonic contributions can be incorporated and give evidence by computing the measure which matches precisely the m...
Resurgent Analysis of Localizable Observables in Supersymmetric Gauge Theories
Aniceto, Inês; Schiappa, Ricardo
2015-01-01
Localization methods have recently led to a plethora of new exact results in supersymmetric gauge theories, as certain observables may be computed in terms of matrix integrals. These can then be evaluated by making use of standard large N techniques, or else via perturbative expansions in the gauge coupling. Either approximation often leads to observables given in terms of asymptotic series, which need to be properly defined in order to obtain nonperturbative results. At the same time, resurgent analysis has recently been successfully applied to several problems, e.g., in quantum, field and string theories, precisely to overcome this issue and construct nonperturbative answers out of asymptotic perturbative expansions. The present work uses exact results from supersymmetric localization to address the resurgent structure of the free energy and partition function of Chern-Simons and ABJM gauge theories in three dimensions, and of N=2 supersymmetric Yang-Mills theories in four dimensions. For each case, the com...
The tensor hierarchy of 8-dimensional field theories
Andino, Oscar Lasso
2016-01-01
We construct the tensor hierarchy of generic, bosonic, 8-dimensional field theories. We first study the form of the most general 8-dimensional bosonic theory with Abelian gauge symmetries only and no massive deformations. This study determines the tensors that occur in the Chern-Simons terms of the (electric and magnetic) field strengths and the action for the electric fields, which we determine. Having constructed the most general Abelian theory we study the most general gaugings of its global symmetries and the possible massive deformations using the embedding tensor formalism, constructing the complete tensor hierarchy using the Bianchi identities. We find the explicit form of all the field strengths of the gauged theory up to the 6-forms. Finally, we find the equations of motion comparing the Noether identities with the identities satisfied by the Bianchi identities themselves. We find that some equations of motion are not simply the Bianchi identities of the dual fields, but combinations of them.
Gauged diffeomorphisms and hidden symmetries in Kaluza-Klein theories
Energy Technology Data Exchange (ETDEWEB)
Hohm, Olaf [Spinoza Institute and Institute for Theoretical Physics, Leuvenlaan 4, 3584 CE Utrecht (Netherlands)
2007-06-07
We analyse the symmetries that are realized on the massive Kaluza-Klein modes in generic D-dimensional backgrounds with three non-compact directions. For this, we construct the unbroken phase given by the decompactification limit, in which the higher Kaluza-Klein modes are massless. The latter admits an infinite-dimensional extension of the three-dimensional diffeomorphism group as local symmetry and, moreover, a current algebra associated with SL(D-2,R) together with the diffeomorphism algebra of the internal manifold as global symmetries. It is shown that the 'broken phase' can be reconstructed by gauging a certain subgroup of the global symmetries. This deforms the three-dimensional diffeomorphisms to a gauged version, and it is shown that they can be governed by a Chern-Simons theory, which unifies the spin-2 modes with the Kaluza-Klein vectors. This provides a reformulation of D-dimensional Einstein gravity, in which the physical degrees of freedom are described by the scalars of a gauged nonlinear {sigma}-model based on SL(D-2,R)/SO(D-2), while the metric appears in a purely topological Chern-Simons form.
Directory of Open Access Journals (Sweden)
Matthieu Noucher
2014-07-01
Full Text Available Simon Chignard est l’auteur de « L’open data, comprendre l’ouverture des données publiques » (FYP éditions, mars 2012. Dans ce livre il propose des repères pour replacer l’open data dans le contexte français et comprendre les enjeux et les limites de l’ouverture des données publiques. Il a participé dès 2010 à l’animation de l’ouverture des données publiques de Rennes Métropole, territoire pionnier en France. Consultant et formateur indépendant, il est à titre bénévole président de l’association Bug (innovation sociale et numérique et vice-président de la Cantine numérique rennaise. Il anime le blog : http://donneesouvertes.info/
On p -form theories with gauge invariant second order field equations
Deffayet, Cédric; Mukohyama, Shinji; Sivanesan, Vishagan
2016-04-01
We explore field theories of a single p -form with equations of motions of order strictly equal to 2 and gauge invariance. We give a general method for the classification of such theories which are extensions to the p -forms of the Galileon models for scalars. Our classification scheme allows us to compute an upper bound on the number of different such theories depending on p and on the space-time dimension. We are also able to build a nontrivial Galileon-like theory for a 3-form with gauge invariance and an action which is polynomial into the derivatives of the form. This theory has gauge invariant field equations but an action which is not, like a Chern-Simons theory. Hence the recently discovered no-go theorem stating that there are no nontrivial gauge invariant vector Galileons (which we are also able here to confirm with our method) does not extend to other odd-p cases.
On p-form theories with gauge invariant second order field equations
Deffayet, Cédric; Sivanesan, Vishagan
2016-01-01
We explore field theories of a single p-form with equations of motions of order strictly equal to two and gauge invariance. We give a general method for the classification of such theories which are extensions to the p-forms of the Galileon models for scalars. Our classification scheme allows to compute an upper bound on the number of different such theories depending on p and on the space-time dimension. We are also able to build a non trivial Galileon like theory for a 3-form with gauge invariance and an action which is polynomial into the derivatives of the form. This theory has gauge invariant field equations but an action which is not, like a Chern-Simons theory. Hence the recently discovered no-go theorem stating that there are no non trivial gauge invariant vector Galileons (which we are also able here to confirm with our method) does not extend to other odd p cases.
Energy Technology Data Exchange (ETDEWEB)
Ezawa, Motohiko, E-mail: ezawa@ap.t.u-tokyo.ac.jp
2014-03-01
The Chern number is a genuine topological number. On the other hand, a symmetry protected topological (SPT) charge is a topological number only when a symmetry exists. We propose a formula for the SPT charge as a derivative of the Chern number in terms of the Green function in such a way that it is valid and related to the associated Hall current even when the symmetry is broken. We estimate the amount of deviation from the quantized value as a function of the strength of the broken symmetry. We present two examples. First, we consider Dirac electrons with the spin–orbit coupling on honeycomb lattice, where the SPT charges are given by the spin-Chern, valley-Chern and spin-valley-Chern numbers. Though the spin-Chern charge is not quantized in the presence of the Rashba coupling, the deviation is estimated to be 10{sup −7} in the case of silicene, a silicon cousin of graphene. Second, we analyze the effect of the mirror-symmetry breaking of the mirror-Chern number in a thin-film of topological crystalline insulator.
Higher Derivative Corrections To Extended Supersymmetric Theories
Braun, G A
2004-01-01
We investigate higher-derivative terms in N = 2 supersymmetric effective actions. We systematically construct such terms in harmonic superspace despite the infinite redundancy in their description due to the infinite number of auxiliary fields. We write all 3- and 4-derivative terms on Higgs, Coulomb, and mixed branches, modulo the existence of superspace Chern-Simons-like terms. Among these terms are several with only holomorphic dependence on fields, and at least one satisfies a non-renormalization theorem. We then search for superspace Chern-Simons-like terms, which are those gauge-invariant terms which cannot be written solely in terms of field strength superfields and covariant derivatives, but in which gauge potential superfield appears explicitly. We find a class of four- derivative terms with N = 2 supersymmetry which, though locally on the Coulomb branch can be written solely in terms of field strengths, globally on the Coulomb branch are superspace Chern- Simons-like.
The Transitional Space of History: Reflections on the Play of Roger Simon's Remembrance Pedagogy
Farley, Lisa
2014-01-01
This paper reads Roger Simon's concept of "transactional memory" in relationship to D. W. Winnicott's theory of "transitional space" to examine the emotional dimensions of making historical significance. Drawing on a personal memory of archival study with Simon, I suggest that his attention to the ethical qualities of…
On skew tau-functions in higher spin theory
Melnikov, D; Morozov, A
2016-01-01
Recent studies of higher spin theory in three dimensions concentrate on Wilson loops in Chern-Simons theory, which in the classical limit reduce to peculiar corner matrix elements between the highest and lowest weight states in a given representation of SL(N). Despite these "skew" tau-functions can seem very different from conventional ones, which are the matrix elements between the two highest weight states, they also satisfy the Toda recursion between different fundamental representations. Moreover, in the most popular examples they possess simple representations in terms of matrix models and Schur functions. We provide a brief introduction to this new interesting field, which, after quantization, can serve as an additional bridge between knot and integrability theories.
Exact results for Wilson loops in orbifold ABJM theory
Ouyang, Hao; Wu, Jun-Bao; Zhang, Jia-Ju
2016-08-01
We investigate the exact results for circular 1/4 and 1/2 BPS Wilson loops in the d = 3 mathcal = 4 super Chern-Simons-matter theory that could be obtained by orbifolding Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. The partition function of the mathcal = 4 orbifold ABJM theory has been computed previously in the literature. In this paper, we re-derive it using a slightly different method. We calculate the vacuum expectation values of the circular 1/4 BPS Wilson loops in fundamental representation and of circular 1/2 BPS Wilson loops in arbitrary representations. We use both the saddle point approach and Fermi gas approach. The results for Wilson loops are in accord with the available gravity results. Supported by NSFC (11222549, 11575202), K. C. Wong Education Foundation and Youth Innovation Promotion Association of CAS (2011016)
On skew tau-functions in higher spin theory
Melnikov, D.; Mironov, A.; Morozov, A.
2016-05-01
Recent studies of higher spin theory in three dimensions concentrate on Wilson loops in Chern-Simons theory, which in the classical limit reduce to peculiar corner matrix elements between the highest and lowest weight states in a given representation of SL( N ). Despite these "skew" tau-functions can seem very different from conventional ones, which are the matrix elements between the two highest weight states, they also satisfy the Toda recursion between different fundamental representations. Moreover, in the most popular examples they possess simple representations in terms of matrix models and Schur functions. We provide a brief introduction to this new interesting field, which, after quantization, can serve as an additional bridge between knot and integrability theories.
Consistent chiral kinetic theory in Weyl materials: chiral magnetic plasmons
Gorbar, E V; Shovkovy, I A; Sukhachov, P O
2016-01-01
We argue that the correct definition of the electric current in the chiral kinetic theory for Weyl materials should include the Chern--Simons contribution that makes the theory consistent with the local conservation of the electric charge in electromagnetic and strain-induced pseudoelectromagnetic fields. By making use of such a kinetic theory, we study the plasma frequencies of collective modes in Weyl materials in constant magnetic and pseudomagnetic fields taking into account the effects of dynamical electromagnetism. We show that the collective modes are chiral plasmons. While the plasma frequency of the longitudinal collective mode coincides with the Langmuir one, this mode is unusual because it is characterized not only by oscillations of the electric current density, but also oscillations of the chiral current density. The latter are triggered by a dynamical version of the chiral electric separation effect. We also find that the plasma frequencies of the transverse modes split up in a magnetic field. T...
Spectrum of conformal gauge theories on a torus
Thomson, Alex
2016-01-01
Many model quantum spin systems have been proposed to realize critical points or phases described by 2+1 dimensional conformal gauge theories. On a torus of size $L$ and modular parameter $\\tau$, the energy levels of such gauge theories equal $(1/L)$ times universal functions of $\\tau$. We compute the universal spectrum of QED$_3$, a U(1) gauge theory with $N_f$ two-component massless Dirac fermions, in the large $N_f$ limit. We also allow for a Chern-Simons term at level $k$, and show how the topological $k$-fold ground state degeneracy in the absence of fermions transforms into the universal spectrum in the presence of fermions; these computations are performed at fixed $N_f/k$ in the large $N_f$ limit.
2011-01-01
Daniel Simon, PS Division Leader from 1994 to 1999, died on 2 June, 2011, at the age of 74, in Nancy. CERN owes him for a great number of contributions to the experimental areas around the PS and the existence of the Antiproton Decelerator (AD). Daniel came to CERN in 1962 from the University of Nancy. He first worked in the Nuclear Physics Apparatus (NPA) Division on the electrostatic separators for the secondary beams at the PS, a subject he also chose for his thesis. Then, as a member of the PS-Division, he designed a variety of beam lines, including those providing protons and antiprotons to ICE, the decisive experiment for CERN to launch the antiproton project, based on stochastic cooling. His contributions to the initial layout and further evolution of the experimental areas of LEAR were essential for the success of the LEAR programme. He subsequently drove the decision and worked on the conversion of LEAR into LEIR for the provision of lead-ions to the LHC. He was one of the leaders of t...
Observation of a non-Abelian Yang Monopole: From New Chern Numbers to a Topological Transition
Sugawa, Seiji; Perry, Abigail R; Yue, Yuchen; Spielman, Ian B
2016-01-01
Because global topological properties are robust against local perturbations, understanding and manipulating the topological properties of physical systems is essential in advancing quantum science and technology. For quantum computation, topologically protected qubit operations can increase computational robustness, and for metrology the quantized Hall effect directly defines the von Klitzing constant. Fundamentally, topological order is generated by singularities called topological defects in extended spaces, and is quantified in terms of Chern numbers, each of which measures different sorts of fields traversing surfaces enclosing these topological singularities. Here, inspired by high energy theories, we describe our synthesis and characterization of a singularity present in non-Abelian gauge theories - a Yang monopole - using atomic Bose-Einstein condensates in a five-dimensional space, and quantify the monopole in terms of Chern numbers measured on enclosing manifolds. While the well-known 1st Chern numb...
F-theory and 2d (0, 2) theories
Schäfer-Nameki, Sakura; Weigand, Timo
2016-05-01
F-theory compactified on singular, elliptically fibered Calabi-Yau five-folds gives rise to two-dimensional gauge theories preserving N = (0 , 2) supersymmetry. In this paper we initiate the study of such compactifications and determine the dictionary between the geometric data of the elliptic fibration and the 2d gauge theory such as the matter content in terms of (0 , 2) superfields and their supersymmetric couplings. We study this setup both from a gauge-theoretic point of view, in terms of the partially twisted 7-brane theory, and provide a global geometric description based on the structure of the elliptic fibration and its singularities. Global consistency conditions are determined and checked against the dual M-theory compactification to one dimension. This includes a discussion of gauge anomalies, the structure of the Green-Schwarz terms and the Chern-Simons couplings in the dual M-theory supersymmetric quantum mechanics. Furthermore, by interpreting the resulting 2d (0 , 2) theories as heterotic worldsheet theories, we propose a correspondence between the geometric data of elliptically fibered Calabi-Yau five-folds and the target space of a heterotic gauged linear sigma-model (GLSM). In particular the correspondence between the Landau-Ginsburg and sigma-model phase of a 2d (0 , 2) GLSM is realized via different T-branes or gluing data in F-theory.
Institute of Scientific and Technical Information of China (English)
盛利
2014-01-01
一般认为，量子自旋霍尔效应只有受到时间反演对称性的保护才是稳定的。但是，因为在实际材料中破坏时间反演对称性的微扰往往无法避免，这种受时间反演对称性保护的量子自旋霍尔效应在真实环境中并不稳定。本综述将介绍近期在寻找无需时间反演对称性保护的量子自旋霍尔效应方向上的系列研究进展。我们将证明量子自旋霍尔体系的非平庸拓扑性质在时间反演对称性被破坏后仍然可以完好存在，并通过一个规范讨论，将边缘态一般性质和体能带的非平庸拓扑性质联系起来。进一步，将探讨通过人工消除边缘态时间反演对称性而实现稳定的量子自旋霍尔效应的方案。此外，我们还将介绍自旋陈数理论，自旋陈数是在没有时间反演对称性存在时，表征量子自旋霍尔体系所处不同拓扑相的有效工具。%In this review, we introduce a series of recent developments in the search of the quan-tum spin Hall effect in the absence of time-reversal symmetry. We first show that the nontrivial topological properties of the quantum spin Hall system remain to be intact when the time-reversal symmetry is broken weakly. Then by a Laughlin-like gauge argument, the connection between the general properties of the edge states and the bulk band topology is established. Furthermore, the possibility to realize robust quantum spin Hall effect by artificial removal of the time-reversal symmetry of the edge states is explored. We will also introduce the spin Chern number theory, as a powerful tool to characterize topological phases without the TR symmetry.
Cryptanalysis of SIMON Variants with Connections
DEFF Research Database (Denmark)
Alizadeh, Javad; Alkhzaimi, Hoda A.; Aref, Mohammad Reza;
2014-01-01
for a key-recovery attack and extend them further to attack other variants of SIMON. Moreover, we provide results of key recovery analysis using several impossible differential characteristics starting from 14 out of 32 rounds for SIMON32/64 to 22 out of 72 rounds for SIMON128/256. In some cases...... attacks extend to all variants of SIMON covering more rounds compared to any known results using linear cryptanalysis. We present a key recovery attack against SIMON128/256 which covers 35 out of 72 rounds with data complexity 2123. We have implemented our attacks for small scale variants of SIMON and our...
Instanton bound states in ABJM theory
Energy Technology Data Exchange (ETDEWEB)
Hatsuda, Yasuyuki [DESY Hamburg (Germany). Theory Group; Tokyo Institute of Technology (Japan). Dept. of Physics; Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst. and Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics
2013-06-15
The partition function of the ABJM theory receives non-perturbative corrections due to instanton effects. We study these non-perturbative corrections, including bound states of worldsheet instantons and membrane instantons, in the Fermi-gas approach. We require that the total non-perturbative correction should be always finite for arbitrary Chern-Simons level. This finiteness is realized quite non-trivially because each bound state contribution naively diverges at some levels. The poles of each contribution should be canceled out in total. We use this pole cancellation mechanism to find unknown bound state corrections from known ones. We conjecture a general expression of the bound state contribution. Summing up all the bound state contributions, we find that the effect of bound states is simply incorporated into the worldsheet instanton correction by a redefinition of the chemical potential in the Fermi-gas system. Analytic expressions of the 3- and 4-membrane instanton corrections are also proposed.
M-Theory Brane as Giant Graviton and the Fractional Quantum Hall Effect
Huo, R
2006-01-01
A small number of M-theory branes as giant gravitons in the M-theory sector of LLM geometry is studied as a probe. The abelian way shows that the low energy effective action for M-theory brane is exactly the 2d electron subject to a vertical magnetic field. We also briefly discuss the microscopic description of M2-brane giant graviton in this geometry, in the language of a combination of D0-branes as fuzzy 2-spheres. Then we go to the well-established Noncommutative Chern-Simons theory description. After quantization, well behaved Fractional Quantum Hall Effect is demonstrated. This goes beyond the original LLM description and should be some indication of novel geometry.
On the Brauer groups of symmetries of abelian Dijkgraaf-Witten theories
Fuchs, Jürgen; Schweigert, Christoph; Valentino, Alessandro
2014-01-01
Symmetries of three-dimensional topological field theories are naturally defined in terms of invertible topological surface defects. Symmetry groups are thus Brauer-Picard groups. We present a gauge theoretic realization of all symmetries of abelian Dijkgraaf-Witten theories. The symmetry group for a Dijkgraaf-Witten theory with gauge group a finite abelian group $A$, and with vanishing 3-cocycle, is generated by group automorphisms of $A$, by automorphisms of the trivial Chern-Simons 2-gerbe on the stack of $A$-bundles, and by partial e-m dualities. We show that transmission functors naturally extracted from extended topological field theories with surface defects give a physical realization of the bijection between invertible bimodule categories of a fusion category and braided auto-equivalences of its Drinfeld center. The latter provides the labels for bulk Wilson lines; it follows that a symmetry is completely characterized by its action on bulk Wilson lines.
Superconformal quantum field theories in string. Gauge theory dualities
Energy Technology Data Exchange (ETDEWEB)
Wiegandt, Konstantin
2012-08-14
In this thesis aspects of superconformal field theories that are of interest in the so-called AdS/CFT correspondence are investigated. The AdS/CFT correspondence states a duality between string theories living on Anti-de Sitter space and superconformal quantum field theories in Minkowski space. In the context of the AdS/CFT correspondence the so-called Wilson loop/amplitude duality was discovered, stating the equality of the finite parts of n-gluon MHV amplitudes and n-sided lightlike polygonal Wilson loops in N=4 supersymmetric Yang-Mills (SYM) theory. It is the subject of the first part of this thesis to investigate the Wilson loop side of a possible similar duality in N=6 superconformal Chern-Simons matter (ABJM) theory. The main result is, that the expectation value of n-sided lightlike polygonal Wilson loops vanishes at one-loop order and at two-loop order is identical in its functional form to the Wilson loop in N=4 SYM theory at one-loop order. Furthermore, an anomalous conformal Ward identity for Wilson loops in Chern-Simons theory is derived. Related developments and symmetries of amplitudes and correlators in ABJM theory are discussed as well. In the second part of this thesis we calculate three-point functions of two protected operators and one twist-two operator with arbitrary even spin j in N=4 SYM theory. In order to carry out the calculations, the indices of the spin j operator are projected to the light-cone and the correlator is evaluated in a soft-limit where the momentum coming in at the spin j operator becomes zero. This limit largely simplifies the perturbative calculation, since all three-point diagrams effectively reduce to two-point diagrams and the dependence on the one-loop mixing matrix drops out completely. The result is in agreement with the analysis of the operator product expansion of four-point functions of half-BPS operators by Dolan and Osborn in 2004.
On equivariant Chern-Weil forms and determinant lines
Freed, Daniel S
2016-01-01
A strong from of invariance under a group G is manifested in a family over the classifying space BG. We advocate a differential-geometric avatar of BG when G is a Lie group. Applied to G-equivariant connections on smooth principal or vector bundles, the equivariance-->families principle converts the G-equivariant extensions of curvature and Chern-Weil forms to the standard nonequivariant versions. An application of this technique yields the moment map of the determinant line of a G-equivariant Dirac operator, which in turn sheds light on some anomaly formulas in quantum field theory.
Perturbative expansion in gauge theories on compact manifolds
Adams, D H
1996-01-01
A geometric formal method for perturbatively expanding functional integrals arising in quantum gauge theories is described when the spacetime is a compact riemannian manifold without boundary. This involves a refined version of the Faddeev-Popov procedure using a generalised Lorentz gauge-fixing condition with background gauge field chosen to be a general critical point for the action functional. The refinement takes into account the gauge-fixing ambiguities coming from gauge transformations which leave the critical point unchanged, resulting in the absence of infrared divergences when the critical point is isolated modulo gauge transformations. The procedure can be carried out using only the subgroup of gauge transformations which are topologically trivial, possibly avoiding the usual problems which arise due to gauge-fixing ambiguities. For Chern-Simons gauge theory the method enables the partition function to be perturbatively expanded for a number of simple spacetime manifolds such as S^3 and lens spaces,...
DEFF Research Database (Denmark)
Foss, Kirsten; Foss, Nicolai
as a general approach to problem solving. We apply these Simonian ideas to organizational issues, specifically new organizational forms. Specifically, Simonian ideas allow us to develop a morphology of new organizational forms and to point to some design problems that characterize these forms.Keywords: Herbert...... Simon, problem-solving, new organizational forms. JEL Code: D23, D83......Two of Herbert Simon's best-known papers are "The Architecture of Complexity" and "The Structure of Ill-Structured Problems." We discuss the neglected links between these two papers, highlighting the role of decomposition in the context of problems on which constraints have been imposed...
F-theory and 2d (0,2) Theories
Schafer-Nameki, Sakura
2016-01-01
F-theory compactified on singular, elliptically fibered Calabi-Yau five-folds gives rise to two-dimensional gauge theories preserving N=(0,2) supersymmetry. In this paper we initiate the study of such compactifications and determine the dictionary between the geometric data of the elliptic fibration and the 2d gauge theory such as the matter content in terms of (0,2) superfields and their supersymmetric couplings. We study this setup both from a gauge-theoretic point of view, in terms of the partially twisted 7-brane theory, and provide a global geometric description based on the structure of the elliptic fibration and its singularities. Global consistency conditions are determined and checked against the dual M-theory compactification to one dimension. This includes a discussion of gauge anomalies, the structure of the Green-Schwarz terms and the Chern-Simons couplings in the dual M-theory supersymmetric quantum mechanics. Furthermore, by interpreting the resulting 2d (0,2) theories as heterotic worldsheet t...
Topological Structure and Topological Tensor Current of Gauss-Bonnet-Chern Theorem
Institute of Scientific and Technical Information of China (English)
DUAN Yi-Shi; WU Shao-Feng; ZHANG Peng-Ming
2006-01-01
We offer an intrinsic theoretical framework to reveal the inner relationships among three theories for Euler we consider the Gauss-Bonnet-Chern (GBC) form imbedded in arbitrary higher-dimensional manifold, which suggests a Hodge dual tensor current. We show the brane structure inherent in the GBC tensor current and obtain the generalized Nambu action for the multi branes with quantized topological charge.
Chern Kondo Insulator in an Optical Lattice.
Chen, Hua; Liu, Xiong-Jun; Xie, X C
2016-01-29
We propose to realize and observe Chern Kondo insulators in an optical superlattice with laser-assisted s and p orbital hybridization and a synthetic gauge field, which can be engineered based on the recent cold atom experiments. Considering a double-well square optical lattice, the localized s orbitals are decoupled from itinerant p bands and are driven into a Mott insulator due to the strong Hubbard interaction. Raman laser beams are then applied to induce tunnelings between s and p orbitals, and generate a staggered flux simultaneously. Because of the strong Hubbard interaction of s orbital states, we predict the existence of a critical Raman laser-assisted coupling, beyond which the Kondo screening is achieved, and then a fully gapped Chern Kondo phase emerges, with the topology characterized by integer Chern numbers. Being a strongly correlated topological state, the Chern Kondo phase is different from the single-particle quantum anomalous Hall state, and can be identified by measuring the band topology and double occupancy of s orbitals. The experimental realization and detection of the predicted Chern Kondo insulator are also proposed. PMID:26871345
Holography, unfolding and higher spin theory
Vasiliev, M. A.
2013-05-01
Holographic duality is argued to relate classes of models that have equivalent unfolded formulation, hence exhibiting different space-time visualizations for the same theory. This general phenomenon is illustrated by the AdS4 higher spin gauge theory shown to be dual to the theory of 3d conformal currents of all spins interacting with 3d conformal higher spin fields of Chern-Simons type. Generally, the resulting 3d boundary conformal theory is nonlinear, providing an interacting version of the 3d boundary sigma model conjectured by Klebanov and Polyakov to be dual to the AdS4 higher spin theory in the large N limit. Being a gauge theory, it escapes the conditions of the theorem of Maldacena and Zhiboedov, which force a 3d boundary conformal theory to be free. Two reductions of particular higher spin gauge theories where boundary higher spin gauge fields decouple from the currents and which have free-boundary duals are identified. Higher spin holographic duality is also discussed for the cases of AdS3/CFT2 and duality between higher spin theories and nonrelativistic quantum mechanics. In the latter case, it is shown in particular that (dS) AdS geometry in the higher spin setup is dual to the (inverted) harmonic potential in the quantum-mechanical setup. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Higher spin theories and holography’.
Large-N expansion, conformal field theory and renormalization-group flows in three dimensions
Anselmi, D
2000-01-01
I study a class of interacting conformal field theories and conformal windows in three dimensions, formulated using the Parisi large-N approach and a modified dimensional-regularization technique. Bosons are associated with composite operators and their propagators are dynamically generated by fermion bubbles. Renormalization-group flows between pairs of interacting fixed points satisfy a set of non-perturbative g 1/g dualities. There is an exact relation between the beta function and the anomalous dimension of the composite boson. Non-Abelian gauge fields have a non-renormalized and quantized gauge coupling, although no Chern-Simons term is present. A problem of the naive dimensional-regularization technique for these theories is uncovered and removed with a non-local, evanescent, non-renormalized kinetic term. The models are expected to be a fruitful arena for the study of odd-dimensional conformal field theory.
The Hilbert series of 3d N=2 Yang-Mills theories with vectorlike matter
Cremonesi, Stefano
2015-01-01
This paper presents a formula for the Hilbert series that counts gauge invariant chiral operators in 3d N=2 Yang-Mills theories with vectorlike matter and no Chern-Simons interactions. The formula counts 't Hooft monopole operators dressed by gauge invariants of a residual gauge theory of massless fields in the monopole background, which is determined by the Higgs mechanism. The sum over magnetic charges is restricted due to instanton effects that partially lift the classical Coulomb branch. The formalism is applied to unitary and symplectic gauge theories with fundamental matter, reproducing old results for the moduli space of vacua and the chiral ring, without resorting to any further effective superpotential on the moduli space.
Horava-Lifshitz Gravity and Effective Theory of the Fractional Quantum Hall Effect
Wu, Chaolun
2014-01-01
We show that Horava-Lifshitz gravity theory can be employed as a covariant framework to build an effective field theory for the fractional quantum Hall effect that respects all the spacetime symmetries such as non-relativistic diffeomorphism invariance and anisotropic Weyl invariance as well as the gauge symmetry. The key to this formalism is a set of correspondence relations that maps all the field degrees of freedom in the Horava-Lifshitz gravity theory to external background (source) fields among others in the effective action of the quantum Hall effect, according to their symmetry transformation properties. We originally derive the map as a holographic dictionary, but its form is independent of the existence of holographic duality. This paves the way for the application of Horava-Lifshitz holography on fractional quantum Hall effect. Using the simplest holographic Chern-Simons model, we compute the low energy effective action at leading orders and show that it captures universal electromagnetic and geomet...
Study of Planar Models in Quantum Mechanics, Field theory and Gravity
Kumar, Sarmistha
2014-01-01
Instantons, monopoles and vortices have become paradigms of topological structures in field theory and quantum mechanics, with important applications in particle physics, astrophysics, condensed matter physics and mathematics. We have discussed here the self-dual Chern-Simons theory specially in (2+1) dimensions. we start with a relevant topological quantum mechanical model (such as Landau problem consisting of two basic chiral oscillators) and extrapolate the analysis to (2+1)dimensional vector field theory. Aspects of selfdual symmetry in topologically massive gravity model were also considered using three different approaches. We have demonstrated how duality symmetric (or chiral) actions are already present in the quantum mechanical examples such as in usual harmonic oscillator. Using the chiral oscillator form, we will briefly develop the key concepts of the soldering mechanism. We have also discussed the non commutative property of such quantum models. Models involving higher order derivative of Abelian...
Chern-Simons Violation of Lorentz and PCT Symmetries in Electrodynamics
Jackiw, Roman W
1999-01-01
Recently proposed Lorentz-PCT noninvariant modifications of electromagnetism are reviewed. Their experimental consequences are described, and it is argued that available data decisively rules out their occurrence in Nature.
Classical Solutions in a Lorentz-violating Maxwell-Chern-Simons Electrodynamics
Belich, H; Orlando, M T D
2003-01-01
We take as starting point the planar model arising from the dimensional reduction of the Maxwell Electrodynamics with the (Lorentz-violating) Carroll-Field-Jackiw term. We then write and study the extended Maxwell equations and the corresponding wave equations for the potentials. The solution to these equations show some interesting deviations from the usual MCS Electrodynamics, with background-dependent correction terms. In the case of a time-like background, the correction terms dominate over the MCS sector in the region far from the origin, and establish the behaviour of a massless Electrodynamics (in the electric sector). In the space-like case, the solutions indicate the clear manifestation of spatial anisotropy, which is consistent with the existence of a privileged direction is space.
The Chern-Simons state for the non-diagonal Bianchi IX model
Paternoga, Robert; Graham, Robert
1998-01-01
The Bianchi IX mixmaster model is quantized in its non-diagonal form, imposing spatial diffeomorphism, time reparametrization and Lorentz invariance as constraints on physical state vectors before gauge-fixing. The result turns out to be different from quantizing the diagonal model obtained by gauge-fixing already on the classical level. For the non-diagonal model a generalized 9-dimensional Fourier transformation over a suitably chosen manifold connects the representations in metric variable...
Topological insulators and superconductors from string theory
Ryu, Shinsei; Takayanagi, Tadashi
2010-10-01
Topological insulators and superconductors in different spatial dimensions and with different discrete symmetries have been fully classified recently, revealing a periodic structure for the pattern of possible types of topological insulators and superconductors, both in terms of spatial dimensions and in terms of symmetry classes. It was proposed that K theory is behind the periodicity. On the other hand, D-branes, a solitonic object in string theory, are also known to be classified by K theory. In this paper, by inspecting low-energy effective field theories realized by two parallel D-branes, we establish a one-to-one correspondence between the K-theory classification of topological insulators/superconductors and D-brane charges. In addition, the string theory realization of topological insulators and superconductors comes naturally with gauge interactions, and the Wess-Zumino term of the D-branes gives rise to a gauge field theory of topological nature, such as ones with the Chern-Simons term or the θ term in various dimensions. This sheds light on topological insulators and superconductors beyond noninteracting systems, and the underlying topological field theory description thereof. In particular, our string theory realization includes the honeycomb lattice Kitaev model in two spatial dimensions, and its higher-dimensional extensions. Increasing the number of D-branes naturally leads to a realization of topological insulators and superconductors in terms of holography (AdS/CFT).
A Piagetian Critique of Kohlberg's 'Moral Development' and of Simon's 'Values Clarification.'
Lewis, Frank W.
The paper presents key features of Jean Piaget's theory of moral development, compares Piaget's theory with Lawrence Kohlberg's theory of moral development and Sidney Simon's theory of values clarification, and evaluates the values clarification movement in light of Piaget's theoretical and practical conclusions. The focus is twofold: first, on…
DEFF Research Database (Denmark)
Simon Steen-Andersen is one of the most performed Danish composers of his generation, not only in Denmark but also internationally. His proliferating performance success has been followed by several honours, e.g. The Carl Nielsen Prize and Kunstpreis Musik from Akademie der Künste in Berlin (both...... 2013), the prize for the best orchestral work at the recently held Doneueschinger Musiktage and The Nordic Council Music Prize in 2014. Seismograf/DMT wishes to celebrate the composer Simon Steen-Andersen. We present and reflect on parts of his comprehensive career, in a Danish and an international...... Rasmus Holmboe; a reflection on the importance of the unrepeatable in Steen-Andersen’s music by composer and PhD Rune Søchting, and a contextualisation of central works by Norwegian editor and writer Ida Habbestad. Our Swedish colleague Andreas Engström writes about the new piano concerto (english...
Instanton effects in ABJM theory from Fermi gas approach
Energy Technology Data Exchange (ETDEWEB)
Hatsuda, Yasuyuki [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie; Tokyo Institute of Technology (Japan). Dept. of Physics; Moriyama, Sanefumi [Nagoya Univ. (Japan). Kobayashi Maskawa Inst.; Nagoya Univ. (Japan). Graduate School of Mathematics; Okuyama, Kazumi [Shinshu Univ., Matsumoto, Nagano (Japan). Dept. of Physics
2012-11-19
We study the instanton effects of the ABJM partition function using the Fermi gas formalism. We compute the exact values of the partition function at the Chern-Simons levels k=1, 2, 3, 4, 6 up to N=44, 20, 18, 16, 14 respectively, and extract non-perturbative corrections from these exact results. Fitting the resulting non-perturbative corrections by their expected forms from the Fermi gas, we determine unknown parameters in them. After separating the oscillating behavior of the grand potential, which originates in the periodicity of the grand partition function, and the worldsheet instanton contribution, which is computed from the topological string theory, we succeed in proposing an analytical expression for the leading D2-instanton correction. Just as the perturbative result, the instanton corrections to the partition function are expressed in terms of the Airy function.
Vacuum static compactified wormholes in eight-dimensional Lovelock theory
International Nuclear Information System (INIS)
In this paper, new exact solutions in eight-dimensional Lovelock theory will be presented. These solutions are the vacuum static wormhole, the black hole, and generalized Bertotti-Robinson space-times with nontrivial torsion. All of the solutions have a cross product structure of the type M5xΣ3, where M5 is a five-dimensional manifold and Σ3 a compact constant curvature manifold. The wormhole is the first example of a smooth vacuum static Lovelock wormhole which is neither Chern-Simons nor Born-Infeld. It will be also discussed how the presence of torsion affects the 'navigableness' of the wormhole for scalar and spinning particles. It will be shown that the wormhole with torsion may act as 'geometrical filter': A very large torsion may 'increase the traversability' for scalars while acting as a 'polarizator' on spinning particles. This may have interesting phenomenological consequences.
Simon Velez: rebel and engineer
Kolakowski, Marcin Mateusz
2001-01-01
Simon Velez—a rebel and an engineer He seems to feel better among young people than in any official ambiance, better yet: on the construction site. Despite his complete architectural education and considerable experience, he does not have an office. Much like the medieval masters, he is always on site. He makes structural drawings for the characteristic roofs, emphasising individuality without the unnecessary stress on loftiness. Due to the impressive, sophisticated gracefulness of structu...
Berthomieu, Alain
2007-01-01
This is the sequel of the first part math.DG/0611281. Here, the procedure of transgressing the families index theorem (the so-called $\\eta$-form) is adapted to take in account the case of Dirac type operators with kernels of varying dimension. The constructed form is then used to define the direct image under proper submersions of the ``free multiplicative'' $K$-theory which was defined in the first part, the behaviour of the characteristic classes on free multiplicative $K$-theory under submersion is studied. Some universal caracterisation of the forms is provided. Finally, combining our result with Bismut and Lott's results on direct images of flat vector bundles yields a ``Grothendieck-Riemann-Roch'' theorem for Nadel-Chern-Simons classes on relative $K$-theory for flat vector bundles which was defined in the first part.
Simon Newcomb: America's Unofficial Astronomer Royal
Graham, John
2007-10-01
Bill Carter and Merri Sue Carter Mantazas; xiii + 213 pp.; ISBN 1-59113-803-5 2006; $26.95 This book introduced me to a commanding figure in American science from the late nineteenth century: Simon Newcomb. Newcomb has been called the nineteenth-century equivalent of Carl Sagan and Albert Einstein. He rose from humble beginnings to be the preeminent American astronomer of his generation. He made basic, far-reaching, and enduring contributions to positional astronomy and planetary dynamics. On the more practical side, he determined a remarkably accurate value for the velocity of light, one within 0.01% of the value accepted today. His work provided an experimental grounding for the special and general theories of relativity to be formulated by Einstein in the coming twentieth century.
Directory of Open Access Journals (Sweden)
Mirjam Dierkes
2013-10-01
Full Text Available Können die akademischen Disziplinen Gender Studies und Philosophie voneinander profitieren? Die am vorliegenden Sammelband Beteiligten bejahen diese Frage eindeutig und sind der Überzeugung, dass hier ein erhebliches – größtenteils noch unausgeschöpftes – Potential liegt, dessen Facettenreichtum bei der Lektüre des Buches tatsächlich sehr anschaulich wird. Gerade aufgrund der Fülle der bearbeiteten Fragestellungen hätte allerdings eine deutlicher inhaltlich-systematisch angelegte Struktur dem Band gutgetan. Doch liefert er durch Anregungen zu vielfältigen Reflexionen über konkret-inhaltliche und wissenschaftstheoretische Fragen und deutliche Akzentsetzungen für die Weiterentwicklung feministischer Theorie nicht nur den Beweis des Potentials der Gender Studies für die Philosophie, vielmehr wird die Inspirationskraft auch in umgekehrter Richtung deutlich.Can the academic disciplines of gender studies and philosophy benefit from one another? The participants of this anthology definitely affirm this question and believe that the collaboration offers considerable – mainly still unexploited – potential, whose multifacetedness the book indeed illustrates nicely. However, particularly due to the abundance of discussed questions, the book would have profited from a clearer content-systematic structure. Nevertheless, due to stimuli for various contemplations about specific content-related and epistemological questions and a distinct accentuation for the development of feminist theory, it not only provides evidence for the potential of gender studies for philosophy, but it also reveals the potential for inspiration in the reverse direction.
Measuring the Second Chern Number from Nonadiabatic Effects
Kolodrubetz, Michael
2016-07-01
The geometry and topology of quantum systems have deep connections to quantum dynamics. In this Letter, I show how to measure the non-Abelian Berry curvature and its related topological invariant, the second Chern number, using dynamical techniques. The second Chern number is the defining topological characteristic of the four-dimensional generalization of the quantum Hall effect and has relevance in systems from three-dimensional topological insulators to Yang-Mills field theory. I illustrate its measurement using the simple example of a spin-3 /2 particle in an electric quadrupole field. I show how one can dynamically measure diagonal components of the Berry curvature in an overcomplete basis of the degenerate ground state space and use this to extract the full non-Abelian Berry curvature. I also show that one can accomplish the same ideas by stochastically averaging over random initial states in the degenerate ground state manifold. Finally, I show how this system can be manufactured and the topological invariant measured in a variety of realistic systems, from superconducting qubits to trapped ions and cold atoms.
On Higher Derivatives in 3D Gravity and Higher Spin Gauge Theories
Bergshoeff, Eric A; Townsend, Paul K
2009-01-01
The general second-order massive field equations for arbitrary positive integer spin in three spacetime dimensions, and their "self-dual" limit to first-order equations, are shown to be equivalent to gauge-invariant higher-derivative field equations. We recover most known equivalences for spins 1 and 2, and find some new ones. In particular, we find a non-unitary massive 3D gravity theory with a 5th order term obtained by contraction of the Ricci and Cotton tensors; this term is part of an N=2 super-invariant that includes the "extended Chern-Simons" term of 3D electrodynamics. We also find a new unitary 6th order gauge theory for "self-dual" spin 3.
Mapping class groups for D=2+1 quantum gravity and topological quantum field theories
International Nuclear Information System (INIS)
A series of disjunctional techniques combining Cerf's original work on diffeomorphism extensions and the Smale-Hatcher Conjecture are used to determine the mapping class groups or homeotopy groups of three-manifolds in which Chern-Simons-Witten and 3-dimensional quantum gravity theories live. Four cases of interest are being considered, two of which focus on three-manifolds with topology M=ΣgxR (g≥2). We show that when the 3-manifold Mg is endowed with only one boundary component, its mapping class group is trivial; whereas the mapping class group is non-zero when Mg has two boundary components. As for proper 3-manifolds such as handlebody Hg (g≥2), we prove that the mapping class group is trivial when Hg possesses one boundary component. In contrast, when endowed with no boundary component at all, Hg has a highly non-trivial mapping class group. The original impetus for the present work draws on recent developments in 3-dimensional physics, most notably on Chern-Simons-Witten theories and their quantum gravity incarnations. In these theories, mapping class groups have been at the forefront of determining suitable quantizations, solving operator ordering problems, finding a suitable set of diffeomorphism-invariant observables, and detecting and cancelling global gravitational anomalies. The problem of finding a suitable set of mapping class group induced observables is singled out. We provide a generalization of the Nelson-Regge construction of diffeomorphism-invariant observables for 2+1 quantum gravity by showing that the set of mapping class group induced observables corresponds to the centralizer of non-trivial mapping class groups. For proper 3-handlebodies with non-trivial homeotopy groups, it is argued that the lack of a global time direction is a significant obstacle in the physical description of topological quantum field theories, including their quantum gravity incarnation
Topological flat band models with arbitrary Chern numbers
Yang, Shuo; Gu, Zheng-Cheng; Sun, Kai; Das Sarma, S.
2012-12-01
We report the theoretical discovery of a systematic scheme to produce topological flat bands (TFBs) with arbitrary Chern numbers. We find that generically a multiorbital high Chern number TFB model can be constructed by considering multilayer Chern number C=1 TFB models with enhanced translational symmetry. A series of models are presented as examples, including a two-band model on a triangular lattice with a Chern number C=3 and an N-band square lattice model with C=N for an arbitrary integer N. In all these models, the flatness ratio for the TFBs is larger than 30 and increases with increasing Chern number. In the presence of appropriate interparticle interactions, these models are likely to lead to the formation of Abelian and non-Abelian fractional Chern insulators. As a simple example, we test the C=2 model with hardcore bosons at 1/3 filling, and an intriguing fractional quantum Hall state is observed.
International Nuclear Information System (INIS)
We have described a theory of a single massive spin 2 field interacting with background gravitational, electromagnetic, and dilaton fields. By virtue of a gauge invariance of this massive spin 2 field, which is valid up to terms of higher order in the massive field, the theory is consistent up to terms of this higher order. The four dimensional Lagrangian and its gauge transformation have been explicitly exhibited. The Chern-Simons action for several versions anti de Sitter and de Sitter supergravity theories have been constructed. Gauge transformations of the supergroups are equivalent to diffeomorphisms on shell. The partition function for two level systems obeying parastatistics of an arbitrary order Q were obtained without making use of a particular ansatz. These results for the first time illuminate the statistical behavior of parastatistical systems and rule out a number of speculations made in the literature. We have analyzed the quark lepton mass generation in technicolor theories. In our computations we have taken into account the extended technicolor contributions to technifermion chiral symmetry breaking. We found that top mass masses of the order of 80 GeV can be generated without violations of the rho parameter bound. The generalized parafermionic theories of Gepner have been bosonized. The energy momentum tensor was shown to appear in the non-leading terms of the operator product expansion of the parafermionic conformal fields, just like in the case of the original Zamolodchikov-Fateev parafermionic theories. The question of modular invariance was also investigated in the framework of bosonized parafermionic theories. 38 refs
On maximally supersymmetric Yang-Mills theories
Movshev, M
2004-01-01
We consider ten-dimensional supersymmetric Yang-Mills theory (10D SUSY YM theory) and its dimensional reductions, in particular, BFSS and IKKT models. We formulate these theories using algebraic techniques based on application of differential graded Lie algebras and associative algebras as well as of more general objects, L_{\\infty}- and A_{\\infty}- algebras. We show that using pure spinor formulation of 10D SUSY YM theory equations of motion and isotwistor formalism one can interpret these equations as Maurer-Cartan equations for some differential Lie algebra. This statement can be used to write BV action functional of 10D SUSY YM theory in Chern-Simons form. The differential Lie algebra we constructed is closely related to differential associative algebra Omega of (0, k)-forms on some supermanifold; the Lie algebra is tensor product of Omega and matrix algebra . We construct several other algebras that are quasiisomorphic to Omega and, therefore, also can be used to give BV formulation of 10D SUSY YM theory...
Berry Phases, Quantum Phase Transitions and Chern Numbers
Contreras, H. A.; Reyes-Lega, A. F.
2007-01-01
We study the relation between Chern numbers and Quantum Phase Transitions (QPT) in the XY spin-chain model. By coupling the spin chain to a single spin, it is possible to study topological invariants associated to the coupling Hamiltonian. These invariants contain global information, in addition to the usual one (obtained by integrating the Berry connection around a closed loop). We compute these invariants (Chern numbers) and discuss their relation to QPT. In particular we show that Chern nu...
Calculating the partition function of N=2 Gauge theories on $S^3$ and AdS/CFT correspondence
Cheon, Sangmo; Kim, Nakwoo
2011-01-01
We test the AdS/CFT correspondence by computing the partition function of some $\\cN=2$ quiver Chern-Simons-matter theories on three-sphere. The M-theory backgrounds are of the Freund-Rubin type with the seven-dimensional internal space given as Sasaki-Einstein manifolds $Q^{1,1,1}$ or $V^{5,2}$. Localization technique reduces the exact path integral to a matrix model, and we study the large-N behavior of the partition function. For simplicity we consider only non-chiral models which have a real-valued partition function. The result is in full agreement with the prediction of the gravity duals, i.e. the free energy is proportional to $N^{3/2}$ and the coefficient matches correctly the volume of $Q^{1,1,1}$ and $V^{5,2}$.
Anomaly cancelation in field theory and F-theory on a circle
Grimm, Thomas W.; Kapfer, Andreas
2016-05-01
We study the manifestation of local gauge anomalies of four- and six-dimensional field theories in the lower-dimensional Kaluza-Klein theory obtained after circle compactification. We identify a convenient set of transformations acting on the whole tower of massless and massive states and investigate their action on the low-energy effective theories in the Coulomb branch. The maps employ higher-dimensional large gauge transformations and precisely yield the anomaly cancelation conditions when acting on the one-loop induced Chern-Simons terms in the three- and five-dimensional effective theory. The arising symmetries are argued to play a key role in the study of the M-theory to F-theory limit on Calabi-Yau manifolds. For example, using the fact that all fully resolved F-theory geometries inducing multiple Abelian gauge groups or non-Abelian groups admit a certain set of symmetries, we are able to generally show the cancelation of pure Abelian or pure non-Abelian anomalies in these models.
Observations on the SIMON Block Cipher Family
DEFF Research Database (Denmark)
Kölbl, Stefan; Leander, Gregor; Tiessen, Tyge
2015-01-01
In this paper we analyse the general class of functions underlying the Simon block cipher. In particular, we derive efficiently computable and easily implementable expressions for the exact differential and linear behaviour of Simon-like round functions. Following up on this, we use those express...
Bidirectional Priming Processes in the Simon Task
Metzker, Manja; Dreisbach, Gesine
2009-01-01
The Simon effect is mostly explained in terms of dual-route models, which imply unidirectional activation processes from stimulus features to response features. However, there is also evidence that these preactivated response features themselves prime corresponding stimulus features. From this perspective, the Simon effect should only occur…
Topological flat band models with arbitrary Chern numbers
Yang, Shuo; Gu, Zheng-Cheng; Sun, Kai; Sarma, S. Das
2012-01-01
We report the theoretical discovery of a systematic scheme to produce topological flat bands (TFBs) with arbitrary Chern numbers. We find that generically a multi-orbital high Chern number TFB model can be constructed by considering multi-layer Chern number C=1 TFB models with enhanced translational symmetry. A series of models are presented as examples, including a two-band model on a triangular lattice with a Chern number C=3 and an $N$-band square lattice model with $C=N$ for an arbitrary ...
Chen, Li; Mazaheri, Tahereh; Seidel, Alexander; Tang, Xiang
2014-04-01
We investigate the possibility of exactly flat non-trivial Chern bands in tight binding models with local (strictly short-ranged) hopping parameters. We demonstrate that while any two of the three criteria can be simultaneously realized (exactly flat band, non-zero Chern number, local hopping), it is not possible to simultaneously satisfy all three. Our theorem covers both the case of a single flat band, for which we give a rather elementary proof, as well as the case of multiple degenerate flat bands. In the latter case, our result is obtained as an application of K-theory. We also introduce a class of models on the Lieb lattice with nearest and next-nearest neighbor hopping parameters, which have an isolated exactly flat band of a zero Chern number but, in general, non-zero Berry curvature.
The Domain Geometry and the Bubbling Phenomenon of Rank Two Gauge Theory
Huang, Hsin-Yuan; Zhang, Lei
2016-06-01
Let {Ω} be a flat torus and {G} be the Green's function of {-Δ} on {Ω} . One intriguing mystery of {G} is how the number of its critical points is related to blowup solutions of certain PDEs. In this article we prove that for the following equation that describes a Chern-Simons model in Gauge theory: Δ u_1+1/ɛ^2e^{u_2}(1-e^{u_1})=8πδ_{p1} Δ u_2+1/ɛ^2e^{u_1}(1-e^{u_2})=8πδ_{p2} in quad Ω, quad p_1-p_2 is a half period, if fully bubbling solutions of Liouville type exist, {G} has exactly three critical points. In addition we establish necessary conditions for the existence of fully bubbling solutions with multiple bubbles.
Comments on the origin of dual superconformal symmetry in ABJM theory
Colgáin, E Ó
2016-01-01
Strong evidence for dual superconformal symmetry in $\\mathcal{N} = 6$ superconformal Chern-Simons theory has fueled expectations that the AdS/CFT dual geometry $AdS_4 \\times \\mathbb{C} P^3$ is self-dual under T-duality. We revisit the problem to identify commuting bosonic and fermionic isometries in a systematic fashion and show that fermionic T-duality, a symmetry originally proposed by Berkovits & Maldacena, inevitably leads to a singularity in the dilaton transformation. We show that TsT deformations commute with fermionic T-duality and comment on T-duality in the corresponding sigma model. Our results rule out self-duality based on fermionic T-duality for $AdS_4 \\times \\mathbb{C} P^3$ or its TsT deformations, but leave the door open for new possibilities.
Exploring Lovelock theory moduli space for Schrödinger solutions
Jatkar, Dileep P.; Kundu, Nilay
2016-09-01
We look for Schrödinger solutions in Lovelock gravity in D > 4. We span the entire parameter space and determine parametric relations under which the Schrödinger solution exists. We find that in arbitrary dimensions pure Lovelock theories have Schrödinger solutions of arbitrary radius, on a co-dimension one locus in the Lovelock parameter space. This co-dimension one locus contains the subspace over which the Lovelock gravity can be written in the Chern-Simons form. Schrödinger solutions do not exist outside this locus and on this locus they exist for arbitrary dynamical exponent z. This freedom in z is due to the degeneracy in the configuration space. We show that this degeneracy survives certain deformation away from the Lovelock moduli space.
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...
Characterization of Lattice Chern Insulators by Bulk Entanglement Spectrum
Chiou, Dah-Wei; Lin, Feng-Li
2016-01-01
We have studied extensively the band crossing patterns of the bulk entanglement spectrum (BES) for various lattice Chern insulators. We find that only partitions with dual symmetry can have either stable nodal-lines or nodal-points in the BES when the system is in the topological phase of a nonzero Chern number. By deforming the Hamiltonian to lift the accidental symmetry, one can see that only nodal points are robust. They thus should bear certain topological characteristics of the BES. By studying the band crossing patterns in details we conclude that the topological characteristics of the BES are inherited from the topological order of the underlying Chern insulators and the former can have more refined topological structures. We then propose the conjecture that the sum of the vorticities in the BES in a properly chosen reduced Brillouin zone equals the Chern number of the underlying Chern insulator.
Towards large-Chern-number topological phases by periodic quenching
Xiong, Tian-Shi; Gong, Jiangbin; An, Jun-Hong
2016-05-01
Topological phases with large Chern numbers have important implications. They were previously predicted to exist by considering fabricated long-range interactions or multilayered materials. Stimulated by recent wide interests in Floquet topological phases, here we propose a scheme to engineer large-Chern-number phases with ease by periodic quenching. Using a two-band system as an example, we theoretically show how a variety of topological phases with widely tunable Chern numbers can be generated by periodic quenching between two simple Hamiltonians that otherwise give low Chern numbers. The obtained large Chern numbers are explained through the emergence of multiple Dirac cones in the Floquet spectra. The transition lines between different topological phases in the two-band model are also explicitly found, thus establishing a class of easily solvable but very rich systems useful for further understandings and applications of topological phases in periodically driven systems.
Magneto-optical response in the arbitrary-Chern number topological phase on square lattice
Wang, Yi-Xiang
2016-07-01
In this work, we investigate the magneto-optical response in the arbitrary-Chern number topological phase. Based on the Dirac theory, we derive the analytic expressions for the magneto-optical response. More importantly, we construct the model on the possible square lattice and make the numerical calculations with the exact diagonalization method. We find the analytical and numerical results are in good agreement with each other. For the optical absorption spectrum, the low-energy absorptive peaks and the corresponding hopping processes are distinct in different Chern number phases, heavily depending on the filling factor of the system. While for the optical Hall conductivities, the physical mechanisms are revealed for the dichroism of the absorption peaks in response to the right- and left-circularly polarized light. We discuss the feasibility of these results in experiment.
Warped conformal field theory as lower spin gravity
Hofman, Diego M.; Rollier, Blaise
2015-08-01
Two dimensional Warped Conformal Field Theories (WCFTs) may represent the simplest examples of field theories without Lorentz invariance that can be described holographically. As such they constitute a natural window into holography in non-AdS space-times, including the near horizon geometry of generic extremal black holes. It is shown in this paper that WCFTs posses a type of boost symmetry. Using this insight, we discuss how to couple these theories to background geometry. This geometry is not Riemannian. We call it Warped Geometry and it turns out to be a variant of a Newton-Cartan structure with additional scaling symmetries. With this formalism the equivalent of Weyl invariance in these theories is presented and we write two explicit examples of WCFTs. These are free fermionic theories. Lastly we present a systematic description of the holographic duals of WCFTs. It is argued that the minimal setup is not Einstein gravity but an SL (2, R) × U (1) Chern-Simons Theory, which we call Lower Spin Gravity. This point of view makes manifest the definition of boundary for these non-AdS geometries. This case represents the first step towards understanding a fully invariant formalism for WN field theories and their holographic duals.