Diphoton Excess at 750 GeV in leptophobic U(1)$^\\prime$ model inspired by $E_6$ GUT
Ko, P; Yu, Chaehyun
2016-01-01
We discuss the 750 GeV diphoton excess at the LHC@13TeV in the framework of leptophobic U(1)$^\\prime$ model inspired by the $E_6$ grand unified theory (GUT). In this model, the Standard Model (SM) chiral fermions carry charges under extra U(1)$^\\prime$ gauge symmetry which is spontaneously broken by a U(1)$^\\prime$-charged singlet scalar ($\\Phi$). In addition, extra quarks and leptons are introduced to achieve the anomaly-free conditions, which is a natural consequence of the assumed $E_6$ GUT. These new fermions are vectorlike under the SM gauge group but chiral under new U(1)$^\\prime$, and their masses come entirely from the nonzero vacuum expectation value of $\\Phi$ through the Yukawa interactions. Then, the CP-even scalar $h_\\Phi$ from $\\Phi$ can be produced at the LHC by the gluon fusion and decay to the diphoton via the one-loop diagram involving the extra quarks and leptons, and can be identified as the origin of diphoton excess at 750 GeV. In this model, $h_\\Phi$ can decay into a pair of dark matter p...
U(1) prime dark matter and R-parity violation
Brahm, D.E.
1990-04-01
Attempts to understand physics beyond the Standard Model must face many phenomenological constraint, from recent Z{sup {degree}} data, neutral current measurements, cosmology and astrophysics, neutrino experiments, tests of lepton-and baryon-number conservation and CP violation, and many other ongoing experiments. The most interesting models are those which are allowed by current data, but offer predictions which can soon be experimentally confirmed or refuted. Two classes of such models are explored in this dissertation. The first, containing an extra U(1){prime} gauge group, has a dark matter candidate which could soon be detected. The second, incorporating supersymmetry with R-parity violation, predicts rare Z{sup {degree}} decays at LEP; some of these models can already be ruled out by LEP data and gluino searches at the Tevatron. 54 refs., 31 figs.
Batra, P; Spivak, D; Batra, Puneet; Dobrescu, Bogdan A.; Spivak, David
2006-01-01
We present new techniques for finding anomaly-free sets of fermions. Although the anomaly cancellation conditions typically include cubic equations with integer variables that cannot be solved in general, we prove by construction that any chiral set of fermions can be embedded in a larger set of fermions which is chiral and anomaly-free. Applying these techniques to extensions of the Standard Model, we find anomaly-free models that have arbitrary quark and lepton charges under an additional U(1) gauge group.
Batra, Puneet; /Argonne; Dobrescu, Bogdan A.; /Fermilab; Spivak, David; /UC, Berkeley, Math. Dept.
2005-10-01
We present new techniques for finding anomaly-free sets of fermions. Although the anomaly cancellation conditions typically include cubic equations with integer variables that cannot be solved in general, we prove by construction that any chiral set of fermions can be embedded in a larger set of fermions which is chiral and anomaly-free. Applying these techniques to extensions of the Standard Model, we find anomaly-free models that have arbitrary quark and lepton charges under an additional U(1) gauge group.
A new anomaly-free gauged supergravity in six dimensions
We present a new anomaly-free gauged N = 1 supergravity model in six dimensions. The gauge group is E7 - G2 x U(1)R, with all hyperinos transforming in the product representation (56, 14). The theory admits monopole compactifications to R4 x S2, leading to D = 4 effective theories with broken supersymmetry and massless fermions. (author)
A New Anomaly-Free Gauged Supergravity in Six Dimensions
Avramis, S D; Randjbar-Daemi, S; Avramis, Spyros D.; Kehagias, Alex
2005-01-01
We present a new anomaly-free gauged N=1 supergravity model in six dimensions. The gauge group is $E_7 \\times G_2 \\times U(1)_R$, with all hyperinos transforming in the product representation {56,14). The theory admits monopole compactifications to $R^4 \\times S^2$, leading to D=4 effective theories with broken supersymmetry and massless fermions.
Anomaly-free discrete gauge symmetries in Froggatt-Nielsen models
Discrete symmetries (DS) can forbid dangerous B- and L-violating operators in the supersymmetric Lagrangian. Due to the violation of global DSs by quantum gravity effects, the introduced DS should be a remnant of a spontaneously broken local gauge symmetry. Demanding anomaly freedom of the high-energy gauge theory, we determine all family-independent anomaly-free ZN symmetries which are consistent with the trilinear MSSM superpotential terms in Part I. We find one outstanding Z6 symmetry, proton hexality P6, which prohibits all B- and L-violating operators up to dimension five, except for the Majorana neutrino mass terms LHuLHu. In Part II, we combine the idea that a DS should have a gauge origin with the scenario of Froggatt and Nielsen (FN). We construct concise U(1)X FN models in which the Z3 symmetry baryon triality, B3, arises from U(1)X breaking. We choose this specific DGS because it allows for R-parity violating interactions; thus neutrino masses can be explained without introducing right-handed neutrinos. We find six phenomenologically viable B3-conserving FN models. (orig.)
Anomaly-free discrete gauge symmetries in Froggatt-Nielsen models
Luhn, C.
2006-05-15
Discrete symmetries (DS) can forbid dangerous B- and L-violating operators in the supersymmetric Lagrangian. Due to the violation of global DSs by quantum gravity effects, the introduced DS should be a remnant of a spontaneously broken local gauge symmetry. Demanding anomaly freedom of the high-energy gauge theory, we determine all family-independent anomaly-free Z{sub N} symmetries which are consistent with the trilinear MSSM superpotential terms in Part I. We find one outstanding Z{sub 6} symmetry, proton hexality P{sub 6}, which prohibits all B- and L-violating operators up to dimension five, except for the Majorana neutrino mass terms LH{sub u}LH{sub u}. In Part II, we combine the idea that a DS should have a gauge origin with the scenario of Froggatt and Nielsen (FN). We construct concise U(1){sub X} FN models in which the Z{sub 3} symmetry baryon triality, B{sub 3}, arises from U(1){sub X} breaking. We choose this specific DGS because it allows for R-parity violating interactions; thus neutrino masses can be explained without introducing right-handed neutrinos. We find six phenomenologically viable B{sub 3}-conserving FN models. (orig.)
Utilitarian Supersymmetric Gauge Model of Particle Interactions
Ma, Ernest
2010-01-01
A remarkable U(1) gauge extension of the supersymmetric standard model was proposed eight years ago. It is anomaly-free, has no mu term, and conserves baryon and lepton numbers automatically. The phenomenology of a specific version of this model is discussed. In particular, leptoquarks are predicted, with couplings to the heavy singlet neutrinos, the scalar partners of which may be components of dark matter. The Majorana neutrino mass matrix itself may have two zero subdeterminants.
Utilitarian supersymmetric gauge model of particle interactions
A remarkabale U(1) gauge extension of the supersymmetric standard model was proposed 8 years ago. It is anomaly free, has no μ term, and conserves baryon and lepton numbers automatically. The phenomenology of a specific version of this model is discussed. In particular, leptoquarks are predicted, with couplings to the heavy singlet neutrinos, the scalar partners of which may be components of dark matter. The Majorana neutrino mass matrix itself may have two zero subdeterminants.
Comment on anomaly matching in N=1 supersymmetric QCD
Fujikawa, Kazuo
1998-01-01
An attempt is made at a systematic approach to anomaly matching problem in non-Abelian electric-magnetic duality in N=1 supersymmetric QCD. A strategy we employ is somewhat analogous to anomaly analyses in grand unified models where the anomaly cancellation becomes more transparent if one embeds SU(5) multiplets into a multiplet of (anomaly-free) SO(10). A complication arises in the treatment of $U^{AF}_{R}(1)^{3}$ matching where $U^{AF}_{R}(1)$ is anomaly-free $R$ symmetry. It is noted that ...
The Anomaly-Free Quantum Einstein Constraints and the Minkowski Theorem
Lewandowski, Jerzy
2016-01-01
We explicitly solved the anomaly-free quantum constraints proposed by Tomlin and Varadarajan for the weak Euclidean model of canonical loop quantum gravity. In doing so, we explicitly evaluated the actions of these quantum constraints on a large suitable state space. Remarkably, our analysis shows that the Minkowski condition, arising in other contexts of loop quantum gravity, also plays an important role in the actions and solutions of the anomaly-free quantum constraints.
What we learn on the heterotic string vacua from anomaly-free supergravity
The recently constructed D=10 anomaly-free supergravity (AFS) has been argued to contain the full effective theory of the heterotic string. The solutions of the effective theory must be solutions of AFS, while the converse is not necessarily true since string theory might specify the boundary conditions for the AFS torsion equation. We show that Calabi-Yau spaces are exact solutions of AFS, while compact group and coset manifolds are not. This is due to a positivity argument, which is the extension to anomaly-free supergravity of the ''ten into four won't go'' theorem of Freedman, Gibbons and West for the Chapline-Manton theory. (orig.)
A systematic search for anomaly-free supergravities in six dimensions
Avramis, S D
2005-01-01
We conduct a systematic search for anomaly-free six-dimensional N=1 chiral supergravity theories. Under a certain set of restrictions on the allowed gauge groups and the representations of the hypermultiplets, we enumerate all possible Poincare and gauged supergravities with one tensor multiplet satisfying the 6D anomaly cancellation criteria.
The Diphoton Excess from an Exceptional Supersymmetric Standard Model
Chao, Wei
2016-01-01
In this paper we explain the diphoton excess in the invariant mass M $\\approx$ 750 GeV , claimed by the ATLAS and CMS collaborations at the run-2 LHC, as the signal of a scalar singlet in a string inspired exceptional supersymmetric standard model (ESSM). The scalar singlet might play a rule in the spontaneous breaking of the $U(1)^\\prime$ gauge symmetry of the ESSM and couples to diphoton and/or gluon pair with the help of exotic quarks and Higgs-like supermultiplets, which are contained in the fundamental representation of the $E_6$ group. The model might give rise to a large enough production cross section at the LHC but can hardly fit with the wide width of the resonance except in the strong couple regime.
We study leptogenesis in the supersymmetric standard model plus the seesaw. We identify important qualitative differences that characterize supersymmetric leptogenesis with respect to the non-supersymmetric case. The lepton number asymmetries in fermions and scalars do not equilibrate, and are related via a non-vanishing gaugino chemical potential. Due to the presence of new anomalous symmetries, electroweak sphalerons couple to winos and higgsinos, and QCD sphalerons couple to gluinos, thus modifying the corresponding chemical equilibrium conditions. A new constraint on particles chemical potentials corresponding to an exactly conserved R-charge, that also involves the number density asymmetry of the heavy sneutrinos, appears. These new ingredients determine the 3 × 4 matrices that mix up the density asymmetries of the lepton flavours and of the heavy sneutrinos. We explain why in all temperature ranges the particle thermodynamic system is characterized by the same number of independent quantities. Numerical differences with respect to usual treatment remain at the O(1) level
We propose a supersymmetric model of particle physics in which supersymmetry is broken dynamically by strong gauge forces. The model, as it stands, requires that one parameter be fine tuned; a grand unified version would not require any fine tuning. The model has no strong CP problem, and agrees with all known particle physics experiments. A variety of new particles, many of which weigh less than 100 GeV, are predicted. (orig.)
Ruling out minimal anomaly free $\\mathrm{U}(1)$ extensions of the Standard Model
Ekstedt, Andreas; Ingelman, Gunnar; Löfgren, Johan; Mandal, Tanumoy
2016-01-01
We consider minimal anomaly free $\\mathrm{U}(1)$ extensions of the Standard Model with three generations of right-handed neutrinos and a complex scalar. Assuming all fields are charged under the new $\\mathrm{U}(1)$ group, we find that in a wide class of such models the only free parameter in the gauge sector is $M_{Z'}$, the mass of the new gauge boson $Z'$. Interestingly, we find that the production cross section of $Z'$ is independent of the $\\mathrm{U}(1)$ gauge coupling $g_z$. Assuming the right-handed neutrinos are Majorana fermions, we arrive at a peculiar relation where $g_z$ becomes a function of $M_{Z'}$. Using perturbativity requirements and the 13 TeV LHC dijet and dilepton data, we show that minimal anomaly free $\\mathrm{U}(1)$ models are strongly disfavored, with the exception of $B-L$ models. We discuss different aspects of these models and indicate possible extensions that can alleviate some restrictions and bypass the constraints.
This lecture was given at the KEK Summer School on August 3-6, 1993 by Professor N. Sakai. All the available experimental data at low energy can be adequately described by the standard model with SU(3) x SU(2) x U(1) gauge group. The three different gauge coupling constants originate from the three different interactions, namely, strong, weak and electromagnetic interactions. The three interactions described by the three different gauge groups can be truly unified into a single gauge group if a simple gauge group to describe all three interactions is chosen. Even if the grand unified theory is not accepted, the existence of gravitational interaction is sure. There are only two options to explain the gauge hierarchy, that is, technicolor model and supersymmetry. As the introduction to supersymmetry, Spinors and Grassmann number, Supertransformation, unitary representation, chiral scalar superfield and supersymmetric Lagrangian field theory are explained. Regarding the supersymmetric SU(3) x SU(2) x U(1) model, Yukawa coupling and particle content are described. It should be noted that the Higgsino (chiral fermions associated with Higgs scalar) in general introduces anomaly in gauge currents. The simplest way out of such anomaly problem is to introduce Higgsino doublet in pair. (K.I.)
Minimal anomaly-free chiral fermion sets and gauge coupling unification
Cebola, Luis M; Felipe, R Gonzalez; Simoes, C
2014-01-01
We look for minimal chiral sets of fermions beyond the Standard Model that are anomaly-free and, simultaneously, vector-like particles with respect to colour SU(3) and electromagnetic U(1). We then study whether the addition of such particles to the Standard Model particle content allows for the unification of gauge couplings at a high energy scale, above $5.0 \\times 10^{15}$ GeV so as to be safely consistent with proton decay bounds. The possibility to have unification at the string scale is also considered. Inspired in grand unified theories, we also search for minimal chiral fermion sets that belong to SU(5) multiplets. Restricting to representations up to dimension 50, we show that some of these sets can lead to gauge unification at the GUT and/or string scales.
Anomaly-free U(1) gauge symmetries in neutrino seesaw flavor models
Cebola, Luis M; Felipe, Ricardo Gonzalez
2013-01-01
Adding right-handed neutrino singlets and/or fermion triplets to the particle content of the Standard Model allows for the implementation of the seesaw mechanism to give mass to neutrinos and, simultaneously, for the construction of anomaly-free gauge group extensions of the theory. We consider Abelian extensions based on an extra U(1)_X gauge symmetry, where X is an arbitrary linear combination of the baryon number B and the individual lepton numbers L_{e,mu,tau}. By requiring cancellation of gauge anomalies, we perform a detailed analysis in order to identify the charge assignments under the new gauge symmetry that lead to neutrino phenomenology compatible with current experiments. In particular, we study how the new symmetry can constrain the flavor structure of the Majorana neutrino mass matrix, leading to two-zero textures with a minimal extra fermion and scalar content. The possibility of distinguishing different gauge symmetries and seesaw realizations at colliders is also briefly discussed.
Ilinskii, K N; Melezhik, V S; Ilinski, K N; Kalinin, G V; Melezhik, V V
1994-01-01
We revise the sequences of SUSY for a cyclic adiabatic evolution governed by the supersymmetric quantum mechanical Hamiltonian. The condition (supersymmetric adiabatic evolution) under which the supersymmetric reductions of Berry (nondegenerated case) or Wilczek-Zee (degenerated case) phases of superpartners are taking place is pointed out. The analogue of Witten index (supersymmetric Berry index) is determined. As the examples of suggested concept of supersymmetric adiabatic evolution the Holomorphic quantum mechanics on complex plane and Meromorphic quantum mechanics on Riemann surface are considered. The supersymmetric Berry indexes for the models are calculated.
Supersymmetric dimensional regularization
A generalized scheme of dimensional regularization which preserves supersymmetry is proposed. The scheme is applicable to all supersymmetric theories. Two models with extended supersymmetry are considered. The Slavnov naive supersymmetric identities are shown to hold at a dimensional regularized level
What is the discrete gauge symmetry of the minimal supersymmetric standard model
We systematically study the extension of the supersymmetric standard model (SSM) by an anomaly-free discrete gauge symmetry ZN. We extend the work of Ibanez and Ross with N=2, 3 to arbitrary values of N. As new fundamental symmetries, we find four Z6, nine Z9, and nine Z18. We then place three phenomenological demands upon the low-energy effective SSM: (i) the presence of the μ term in the superpotential, (ii) baryon-number conservation up to dimension-five operators, and (iii) the presence of the seesaw neutrino mass term LHuLHu. We are then left with only two anomaly-free discrete gauge symmetries: baryon triality, B3, and a new Z6, which we call proton hexality, P6. Unlike B3, P6 prohibits the dimension-four lepton-number violating operators. This we propose as the discrete gauge symmetry of the minimal SSM, instead of R parity
Supersymmetric nonlinear sigma models
Supersymmetric nonlinear sigma models are formulated as gauge theories. Auxiliary chiral superfields are introduced to impose supersymmetric constraints of F-type. Target manifolds defined by F-type constraints are always non-compact. In order to obtain nonlinear sigma models on compact manifolds, we have to introduce gauge symmetry to eliminate the degrees of freedom in non-compact directions. All supersymmetric nonlinear sigma models defined on the hermitian symmetric spaces are successfully formulated as gauge theories. (author)
Supersymmetric particles at LEP
The authors examine whether the supersymmetrization of nature at a mass scale up to 100 GeV can be confirmed or excluded by experiments with LEP. They review the qualitative features of the spectroscopy suggested by supersymmetric theories. Then they discuss possible production rates and means of detection of these particles at LEP. In this framework they make some remarks about other projects for future high energy physics machines which can be used for the study of supersymmetric phenomena. (HSI)
Supersymmetric Open Wilson Lines
Baker, Edward B
2011-01-01
In this paper we study Open Wilson Lines (OWL's) in the context of two Supersymmetric Yang Mills theories. First we consider four dimensional N=2 Supersymmetric Yang Mills Theory with hypermultiplets transforming in the fundamental representation of the gauge group, and find supersymmetric OWL's only in the superconformal versions of these theories. We then consider four dimensional N=4 SYM coupled to a three dimensional defect hypermultiplet. Here there is a semi-circular supersymmetric OWL, which is related to the ray by a conformal transformation. We perform a perturbative calculation of the operators in both theories, and discuss using localization to compute them non-perturbatively.
Supersymmetric Hybrid Inflation
Lazarides, G
2001-01-01
The non-supersymmetric and supersymmetric versions of hybrid inflation are summarized. It is emphasized that supersymmetric hybrid inflation (with its extensions) is an extremely "natural" inflationary scenario since it does not require "tiny" parameters, its superpotential has the most general form allowed by the symmetries, and it can be protected against radiative or supergravity corrections. A concrete supersymmetric grand unified theory which leads to hybrid inflation, solves the mu problem and generates seesaw masses for the light neutrinos is constructed. The "reheating" which follows hybrid inflation is studied in this theory. It is shown that the gravitino constraint on the "reheat" temperature can be "naturally" satisfied. Also, the observed baryon asymmetry of the universe can be generated via a primordial leptogenesis consistently with the requirements from solar and atmospheric neutrino oscillations. Extensions of the standard supersymmetric hybrid inflationary scenario which are still consistent...
Supersymmetric top quark decays
The supersymmetric decays of the top quark into charged Higgs plus bottom, t → H+b, and into the supersymmetric partner of the top (u1) plus the lightest neutralino (χ10), t → u1χ10, are discussed within the framework of the Minimal Supersymmetric Standard Model with radiatively induced breaking of the gauge group SU(2) x U(1). The possibility of detecting these decays at present, i.e. given the available bounds on supersymmetric parameters, is compared with the situation a Next e+e- Linear Collider would face if supersymmetric particles were still undiscovered at LEP II. The indirect implications for t → H+b and t → u1χ10 of a measurement of the bottom quark decay b → sγ at the Standard Model level are taken into account. (orig.)
Connection between generation number and anomaly-cancellation in supersymmetric models
Supersymmetric theories in which the number of generations of quarks and leptons is related by gauge anomaly-cancellations to the spectrum of Higgs fields are constructed. Models yielding at least three generations with the minimal Higgs spectrum assumed are discussed in detail. This mechanism requires an extension of the Standard Model gauge group such that an ordinary quark-lepton generation is not anomaly-free. Models of SU(3) weak isospin, separate isospin groups for quarks and leptons, and chiral colour are also discussed
We begin to construct the most general supersymmetric Lagrangians in one, two and four dimensions. We find that the matter couplings have a natural interpretation in the language of the nonlinear sigma model
Supersymmetric Radiative Flavour
Conlon, Joseph P.; Pedro, Francisco G.
2011-01-01
We examine possibilities for the radiative generation of the Yukawa couplings and flavour structure in supersymmetric models in the supersymmetric phase. Not withstanding the non-renormalisation of the Wilsonian superpotential, this can occur through the 2-loop vertex renormalisation of the physical 1PI couplings. We describe this effect and construct models in which this occurs. For models attempting to reproduce the full flavour structure of the Standard Model, we analyse the tension betwee...
Achour, Jibril Ben; Marciano, Antonino
2016-01-01
Using self dual Ashtekar variables, we investigate (at the effective level) the spherically symmetry reduced model of loop quantum gravity, both in vacuum and when coupled to a scalar field. Within the real Ashtekar-Barbero formulation, the system scalar field coupled to spherically symmetric gravity is known to possess a non closed (quantum) algebra of constraints once the holonomy corrections are introduced, which forbids the loop quantization of the model. Moreover, the vacuum case, while not anomalous, introduces modifications which are usually interpreted as a signature change of the metric in the deep quantum region. We show in this paper that both those difficulties disappear when working with self dual Ashtekar variables, both in the vacuum case and in the case of gravity minimally coupled to a scalar field. In this framework, the algebra of the holonomy corrected constraints is anomaly free and reproduces the classical hypersurface deformation algebra without any deformations. A possible path towards...
Supersymmetric color superconductivity
Harnik, Roni; Larson, Daniel T.; Murayama, Hitoshi
2003-09-18
Recent interest in novel phases in high density QCD motivates the study of high density supersymmetric QCD (SQCD), where powerful exact results for supersymmetric gauge theories can be brought to bear in the strongly coupled regime. We begin by describing how a chemical potential can be incorporated into a supersymmetric theory as a spurion vector superfield. We then study supersymmetric SU(N{sub c}) gauge theories with N{sub f} flavors of quarks in the presence of a baryon chemical potential {mu}, and describe the global symmetry breaking patterns at low energy. Our analysis requires {mu} < {Lambda} and is thus complementary to the variational approach that has been successful for {mu} >> {Lambda}. We find that for N{sub F} < N{sub c} a modified U(1){sub B} symmetry is preserved, analogous to the non-supersymmetric 2SC phase, whereas for N{sub f} = N{sub c} there is a critical chemical potential above which the U(1){sub B} is broken, as it is in the non-supersymmetric CFL phase. We further analyze the cases with N{sub c} + 1 {le} N{sub f} < 3/2 N{sub c} and find that baryon number is broken dynamically for {mu} > {mu}{sub c}. We also give a qualitative description of the phases in the ''conformal window'', 3/2 N{sub c} < N{sub f} < 3N{sub c}, at finite density.
Supersymmetric Baryonic Branes
Gomis, J P; Simón, J; Townsend, P K; Gomis, Joaquim; Ramallo, Alfonso V.; Simon, Joan; Townsend, Paul K.
1999-01-01
We derive an energy bound for a `baryonic' D5-brane probe in the $adS_5\\times S^5$ background near the horizon of $N$ D3-branes. Configurations saturating the bound are shown to be 1/4 supersymmetric $S^5$-wrapped D5-branes with $N$ singularities at arbitrary positions. Previous results for $N$ coincident singularities are recovered as a special case. We derive a similar energy bound for a `baryonic' M5-brane probe in the background of $N$ M5-branes. Configurations saturating the bound are again 1/4 supersymmetric and, in the $adS_7\\times S^4$ near-horizon limit, provide a worldvolume realization of the `baryon string' vertex of the (2,0)-supersymmetric six-dimensional conformal field theory on coincident M5-branes. For the full M5-background we find a worldvolume realization of the Hannany-Witten effect in M-theory.
Ellis, Jonathan Richard
2003-01-01
These lectures provide a phenomenological introduction to supersymmetry, concentrating on the minimal supersymmetric extension of the Standard Model (MSSM). Motivations are provided for thinking that supersymmetry might appear at the TeV scale, including the naturalness of the mass hierarchy, gauge unification and the probable mass of the Higgs boson. Then simple globally supersymmetric field theories are introduced, with the emphasis on features important for model-building. Supersymmetry breaking and local supersymmetry (supergravity) are then introduced, and the structure of sparticle mass matrices and mixing are reviewed. The available experimental and cosmological constraints on MSSM parameters are discussed and combined, and the prospects for discovering supersymmetry in future experiments are previewed. Finally, the observability of leptonic processes violating flavour and CP are discussed, on the basis of the minimal supersymmetric seesaw model of neutrino masses.
Renormalization in supersymmetric models
Fonseca, Renato M
2013-01-01
There are reasons to believe that the Standard Model is only an effective theory, with new Physics lying beyond it. Supersymmetric extensions are one possibility: they address some of the Standard Model's shortcomings, such as the instability of the Higgs boson mass under radiative corrections. In this thesis, some topics related to the renormalization of supersymmetric models are analyzed. One of them is the automatic computation of the Lagrangian and the renormalization group equations of these models, which is a hard and error-prone process if carried out by hand. The generic renormalization group equations themselves are extended so as to include those models which have more than a single abelian gauge factor group. Such situations can occur in grand unified theories, for example. For a wide range of SO(10)-inspired supersymmetric models, we also show that the renormalization group imprints on sparticle masses some information on the higher energies behavior of the models. Finally, in some cases these the...
Naturalness of supersymmetric models
Strumia, Alessandro
2001-01-01
After presenting a simple procedure for testing naturalness (similar to Bayesian inference and not more subjective than it) we show that LEP2 experiments pose a naturalness problem for `conventional' supersymmetric models. About 95% of the parameter space of minimal supergravity MSSM is excluded by LEP2 experiments. Moreover in this model electroweak baryogenesis, or detectable supersymmetric corrections to mixing of K and B mesons, are possible only in very small corners of the parameter space. The naturalness problem is stronger in gauge mediation models, expecially with light messengers. We recall some possible explanations (different from an improbable numerical accident) of why supersymmetry has not (yet?) been found.
Planarizable Supersymmetric Quantum Toboggans
Miloslav Znojil
2011-02-01
Full Text Available In supersymmetric quantum mechanics the emergence of a singularity may lead to the breakdown of isospectrality between partner potentials. One of the regularization recipes is based on a topologically nontrivial, multisheeted complex deformations of the line of coordinate x giving the so called quantum toboggan models (QTM. The consistent theoretical background of this recipe is briefly reviewed. Then, certain supersymmetric QTM pairs are shown exceptional and reducible to doublets of non-singular ordinary differential equations a.k.a. Sturm-Schrödinger equations containing a weighted energy E→EW(x and living in single complex plane.
Koehn, Michael; Trodden, Mark
2016-04-01
In supersymmetric theories, topological defects can have nontrivial behaviors determined purely by whether or not supersymmetry is restored in the defect core. A well-known example of this is that some supersymmetric cosmic strings are automatically superconducting, leading to important cosmological effects and constraints. We investigate the impact of nontrivial kinetic interactions, present in a number of particle physics models of interest in cosmology, on the relationship between supersymmetry and supercurrents on strings. We find that in some cases it is possible for superconductivity to be disrupted by the extra interactions.
Gudnason, Sven Bjarke; Sasaki, Shin
2015-01-01
Construction of a supersymmetric extension of the Skyrme term was a long-standing problem because of the auxiliary field problem; that is, the auxiliary field may propagate and cannot be eliminated, and the problem of having fourth-order time derivative terms. In this paper, we construct for the first time a supersymmetric extension of the Skyrme term in four spacetime dimensions, in the manifestly supersymmetric superfield formalism that does not suffer from the auxiliary field problem. Chiral symmetry breaking in supersymmetric theories results not only in Nambu-Goldstone (NG) bosons (pions) but also in the same number of quasi-NG bosons so that the low-energy theory is described by an SL(N,C)-valued matrix field instead of SU(N) for NG bosons. The solution of auxiliary fields is trivial on the canonical branch of the auxiliary field equation, in which case our model results in a fourth-order derivative term that is not the Skyrme term. For the case of SL(2,C), we find explicitly a nontrivial solution to th...
We discuss a supersymmetric version of DBI (Dirac-Born-Infeld) inflation, which is a typical inflation model in string cosmology. The supersymmetric DBI action together with a superpotential always leads to correction terms associated with the potential into the kinetic term, which drastically change the dynamics of DBI inflation. We find two significant features of supersymmetric DBI inflation. The first one is that ultra-relativistic motion is prohibited to cause inflation, which leads to order of unity sound velocity squared and hence small non-Gaussianities of primordial curvature perturbations. The second one is that the relation between the tensor-to-scalar ratio and the field variation is modified. Then, significant tensor-to-scalar ratio r≥0.01 is possible because the variation of the canonically normalized inflaton can be beyond the reduced Planck scale. These new features are in sharp contrast with those of the standard non-supersymmetric DBI inflation and hence have a lot of interest implications on upcoming observations of cosmic microwave background (CMB) anisotropies by the Planck satellite as well as direct detection experiments of gravitational waves like DECIGO and BBO.
Supersymmetrization: AKSZ and beyond?
Salnikov, Vladimir
2016-01-01
In this paper we describe multigraded generalizations of some constructions useful for mathematical understanding of gauge theories: we perform a near-at-hand generalization of the Aleksandrov--Kontsevich--Schwarz--Zaboronsky procedure, we also extend the formalism of $Q$-bundles introduced first by A. Kotov and T. Strobl. We compare these approaches studying some supersymmetric sigma models important in theoretical physics.
Sasaki, Shin; Yokoyama, Daisuke
2012-01-01
We discuss a supersymmetric version of DBI (Dirac-Born-Infeld) inflation, which is a typical inflation model in string cosmology. The supersymmetric DBI action together with a superpotential always leads to correction terms associated with the potential into the kinetic term, which drastically change the dynamics of DBI inflation. We find two significant features of supersymmetric DBI inflation. The first one is that ultra-relativistic motion is prohibited to cause inflation, which leads to order of unity sound velocity squared and hence small non-Gaussianities of primordial curvature perturbations. The second one is that the relation between the tensor-to-scalar ratio and the field variation is modified. Then, significant tensor-to-scalar ratio $r \\gtrsim 0.01$ is possible even for sub-Planck variation of the field. These new features are in sharp contrast with those of the standard non-supersymmetric DBI inflation and hence have a lot of interest implications on upcoming observations of cosmic microwave bac...
Semiclassical Supersymmetric Quantum Gravity
Kiefer, Claus; Lück, Tobias; Vargas Moniz, Paulo
2008-09-01
We develop a semiclassical approximation scheme for the constraint equations of supersymmetric canonical quantum gravity. This is achieved by a Born-Oppenheimer type of expansion, in analogy to the case of the usual Wheeler-DeWitt equation. We recover at consecutive orders the Hamilton-Jacobi equation, the functional Schrödinger equation, and quantum gravitational correction terms to this Schrödinger equation. In particular, our work has the following implications: (i) the Hamilton-Jacobi equation and therefore the background spacetime must involve the gravitino, (ii) a (many fingered) local time parameter has to be present on Super Riem Σ (the space of all possible tetrad and gravitino fields), (iii) quantum supersymmetric gravitational corrections affect the evolution of the very early universe.
Nearly Supersymmetric Dark Atoms
Siavosh R. Behbahani
2011-01-01
Full Text Available Theories of dark matter that support bound states are an intriguing possibility for the identity of the missing mass of the Universe. This article proposes a class of models of supersymmetric composite dark matter where the interactions with the Standard Model communicate supersymmetry breaking to the dark sector. In these models, supersymmetry breaking can be treated as a perturbation on the spectrum of bound states. Using a general formalism, the spectrum with leading supersymmetry effects is computed without specifying the details of the binding dynamics. The interactions of the composite states with the Standard Model are computed, and several benchmark models are described. General features of nonrelativistic supersymmetric bound states are emphasized.
Nearly Supersymmetric Dark Atoms
Behbahani, Siavosh R.; Jankowiak, Martin; /SLAC /Stanford U., ITP; Rube, Tomas; /Stanford U., ITP; Wacker, Jay G.; /SLAC /Stanford U., ITP
2011-08-12
Theories of dark matter that support bound states are an intriguing possibility for the identity of the missing mass of the Universe. This article proposes a class of models of supersymmetric composite dark matter where the interactions with the Standard Model communicate supersymmetry breaking to the dark sector. In these models supersymmetry breaking can be treated as a perturbation on the spectrum of bound states. Using a general formalism, the spectrum with leading supersymmetry effects is computed without specifying the details of the binding dynamics. The interactions of the composite states with the Standard Model are computed and several benchmark models are described. General features of non-relativistic supersymmetric bound states are emphasized.
Planarizable Supersymmetric Quantum Toboggans
Znojil, Miloslav
2011-01-01
Roč. 7, - (2011), 018/1-018/23. ISSN 1815-0659. [Workshop on Supersymmetric Quantum Mechanics and Spectral Design. Benasque, 18.07.2010-30.07. 2010] R&D Projects: GA ČR GAP203/11/1433 Institutional research plan: CEZ:AV0Z10480505 Keywords : supersymmetry * Schrodinger equation * complexified coordinates Subject RIV: BE - Theoretical Physics Impact factor: 1.071, year: 2011
Dynamics of supersymmetric chameleons
Brax, Philippe [Institut de Physique Theorique, CEA, IPhT, CNRS, URA 2306, F-91191Gif/Yvette Cedex (France); Davis, Anne-Christine; Sakstein, Jeremy, E-mail: Philippe.Brax@cea.fr, E-mail: A.C.Davis@damtp.cam.ac.uk, E-mail: J.A.Sakstein@damtp.cam.ac.uk [DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2013-10-01
We investigate the cosmological dynamics of a class of supersymmetric chameleon models coupled to cold dark matter fermions. The model includes a cosmological constant in the form of a Fayet-Illiopoulos term, which emerges at late times due to the coupling of the chameleon to two charged scalars. Supergravity corrections ensure that the supersymmetric chameleons are efficiently screened in all astrophysical objects of interest, however this does not preclude the enhancement of gravity on linear cosmological scales. We solve the modified equations for the growth of cold dark matter density perturbations in closed form in the matter era. Using this, we go on to derive the modified linear power spectrum which is characterised by two scales, the horizon size at matter-radiation equality and at the redshift when the chameleon reaches the minimum of its effective potential. We analyse the deviations from the ΛCDM predictions in the linear regime. We find that there is generically a region in the model's parameter space where the model's background cosmology coincides with that of the ΛCDM model. Furthermore, we find that characteristic deviations from ΛCDM are present on the matter power spectrum providing a clear signature of supersymmetric chameleons.
The supersymmetric (SUSY) structure of coupled-mode equations that describe scattering of optical waves in one-dimensional Bragg gratings is highlighted. This property can find applications to the synthesis of special Bragg filters and distributed-feedback (DFB) optical cavities. In particular, multiple SUSY (Darboux–Crum) transformations can be used to synthesize DFB filters with any desired number of resonances at target frequencies. As an example, we describe the design of a DFB structure with a set of equally-spaced resonances, i.e. a frequency comb transmission filter. (paper)
Generalized Supersymmetric Perturbation Theory
B. G(o)n(ǖ)l
2004-01-01
@@ Using the basic ingredient of supersymmetry, a simple alternative approach is developed to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wavefunctions do not involve tedious calculations which appear in the available perturbation theories. The model applicable in the same form to both the ground state and excited bound states, unlike the recently introduced supersymmetric perturbation technique which, together with other approaches based on logarithmic perturbation theory, are involved within the more general framework of the present formalism.
Mikhailov, Andrei
2004-01-01
Single trace operators with the large R-charge in supersymmetric Yang-Mills theory correspond to the null-surfaces in $AdS_5\\times S^5$. We argue that the moduli space of the null-surfaces is the space of contours in the super-Grassmanian parametrizing the complex $(2|2)$-dimensional subspaces of the complex $(4|4)$-dimensional space. The odd coordinates on this super-Grassmanian correspond to the fermionic degrees of freedom of the superstring.
Supersymmetric gauge invariant interaction revisited
A supersymmetric Lagrangian invariant under local U(1) gauge transformations is written in terms of a non-chiral superfield which substitute the usual vector supermultiplet together with chiral and anti-chiral superfields. The Euler equations allow us to obtain the off-shell version of the usual Lagrangian for supersymmetric quantum-electrodynamics (SQED). (Author)
Supersymmetric seesaw inflection
We showed that Supersymmetric Unified theories which explain small neutrino masses via renormalizable Type-I-see-saw mechanism can also support slow roll inflection point inflation. In such a scenario inflation occurs along a MSSM D-flat direction associated with gauge invariant combination of Higgs, slepton and right handed sneutrino. The scale of inflation is set by right handed neutrino mass Mυc ∼1061012 GeV and inflation parameters are determined in terms of Dirac and Majorana couplings responsible for neutrino masses. The fine tuning conditions to have effective slow roll inflation are determined in terms of superpotential parameters (Dirac and Majorana couplings). This is in contrast to MSSM or Dirac neutrino inflection scenarios where fine tuning conditions are on soft Susy breaking parameters. In our case Mυc ≫ MSusy, so soft Susy breaking parameters have hardly any role to play in fine tuning. The fine tuning conditions are thus radiatively stable due to nonrenormalization theorems. Reheating occurs via instant preheating which dumps all the inflation energy into MSSM degrees of freedom giving a high reheat temperature Trh ≅ Mυc106 GeV ∼ 101l1015 GeV. We also examined how this scenario can be embedded in realistic New Minimal Supersymmetric SO(10) Grand Unified Theory. (author)
Supersymmetrizing massive gravity
Malaeb, O.
2013-07-01
When four scalar fields with global Lorentz symmetry are coupled to gravity and take a vacuum expectation value, breaking diffeomorphism invariance spontaneously, the graviton becomes massive. This model is supersymmetrized by considering four N=1 chiral superfields with global Lorentz symmetry. The global supersymmetry is promoted to a local one using the rules of tensor calculus of coupling the N=1 supergravity Lagrangian to the four chiral multiplets. When the scalar components of the chiral multiplets zA acquire a vacuum expectation value, both diffeomorphism invariance and local supersymmetry are broken spontaneously. The global Lorentz index A becomes identified with the space-time Lorentz index, making the scalar fields zA vectors and the chiral spinors ψA spin-3/2 Rarita-Schwinger fields. We show that the spectrum of the model in the broken phase consists of a massive spin-2 field, two massive spin-3/2 fields with different mass and a massive vector.
We propose a grand unified supersymmetric theory based on SU(5) with spontaneously broken supersymmetry. The theory (really a class of theories) is completely realistic. In particular, supersymmetry partners of ordinary fermions and bosons are heavy. The model requires one fine-tuning in order to render the color triplet partners of the Higgs fields (which mediate proton decay) superheavy. This fine-tuning is stable against radiative corrections. At the tree level, the model contains two scales, the unification scale, of order 1016 GeV, and the supersymmetry breaking scale, of order 1010 GeV. The breaking of SU(2) x U(1) invariance arises as a radiative effect. The lightest of the new particles implied by supersymmetry are expected to have masses of order tens of GeV. (orig.)
Deformed supersymmetric mechanics
Motivated by a recent interest in curved rigid supersymmetries, we construct a new type of N = 4, d = 1 supersymmetric systems by employing superfields defined on the cosets of the supergroup SU(2|1). The relevant worldline supersymmetry is a deformation of the standard N = 4, d = 1 supersymmetry by a mass parameter m. As instructive examples we consider at the classical and quantum levels the models associated with the supermultiplets (1,4,3) and (2,4,2) and find out interesting interrelations with some previous works on nonstandard d = 1 supersymmetry. In particular, the d = 1 systems with 'weak supersymmetry' are naturally reproduced within our SU(2|1) superfield approach as a subclass of the (1,4,3) models. A generalization to the N = 8, d = 1 case implies the supergroup SU(2|2) as a candidate deformed worldline supersymmetry
Supersymmetric mode converters
Heinrich, Matthias; Miri, Mohammad-Ali; Stützer, Simon; Nolte, Stefan; Szameit, Alexander; Christodoulides, Demetrios N.
2015-08-01
In recent years, the ever-increasing demand for high-capacity transmission systems has driven remarkable advances in technologies that encode information on an optical signal. Mode-division multiplexing makes use of individual modes supported by an optical waveguide as mutually orthogonal channels. The key requirement in this approach is the capability to selectively populate and extract specific modes. Optical supersymmetry (SUSY) has recently been proposed as a particularly elegant way to resolve this design challenge in a manner that is inherently scalable, and at the same time maintains compatibility with existing multiplexing strategies. Supersymmetric partners of multimode waveguides are characterized by the fact that they share all of their effective indices with the original waveguide. The crucial exception is the fundamental mode, which is absent from the spectrum of the partner waveguide. Here, we demonstrate experimentally how this global phase-matching property can be exploited for efficient mode conversion. Multimode structures and their superpartners are experimentally realized in coupled networks of femtosecond laser-written waveguides, and the corresponding light dynamics are directly observed by means of fluorescence microscopy. We show that SUSY transformations can readily facilitate the removal of the fundamental mode from multimode optical structures. In turn, hierarchical sequences of such SUSY partners naturally implement the conversion between modes of adjacent order. Our experiments illustrate just one of the many possibilities of how SUSY may serve as a building block for integrated mode-division multiplexing arrangements. Supersymmetric notions may enrich and expand integrated photonics by versatile optical components and desirable, yet previously unattainable, functionalities.
Supersymmetric Quantum Mechanics and Topology
Muhammad Abdul Wasay
2016-01-01
Full Text Available Supersymmetric quantum mechanical models are computed by the path integral approach. In the β→0 limit, the integrals localize to the zero modes. This allows us to perform the index computations exactly because of supersymmetric localization, and we will show how the geometry of target space enters the physics of sigma models resulting in the relationship between the supersymmetric model and the geometry of the target space in the form of topological invariants. Explicit computation details are given for the Euler characteristics of the target manifold and the index of Dirac operator for the model on a spin manifold.
Supersymmetric quantum mechanics and topology
Wasay, Muhammad Abdul
2016-01-01
Supersymmetric quantum mechanical models are computed by the Path integral approach. In the $\\beta\\rightarrow0$ limit, the integrals localize to the zero modes. This allows us to perform the index computations exactly because of supersymmetric localization, and we will show how the geometry of target space enters the physics of sigma models resulting in the relationship between the supersymmetric model and the geometry of the target space in the form of topological invariants. Explicit computation details are given for the Euler characteristics of the target manifold, and the index of Dirac operator for the model on a spin manifold.
Properties of supersymmetric particles and processes
The motivations for experimental searches for supersymmetric particles are discussed. The role of R-parity in these searches is described. The production and decay characteristics of each class of supersymmetric particles are investigated in the context of both e+e- and hadron machines. There is a detailed presentation of a sample calculation of a supersymmetric process. Emphasis is given to the signatures for detection of supersymmetric particles and processes. The current limits for supersymmetric particles are given. 125 refs., 50 figs
Properties of supersymmetric particles and processes
In these lectures the author discuss the motivations for experimental searches for supersymmetric particles. The role of R-parity in these searches is described. The production and decay characteristics of each class of supersymmetric particles are investigated in the context of both e+e- and hadron machines. There is a detailed presentation of a sample calculation of a supersymmetric process. Emphasis is given to the signatures for detection of supersymmetric particles and processes. The current limits for supersymmetric particles are given
Rare supersymmetric top quark decays
Two supersymmetric decays of the top quark, t → H+b and t → u1χ0, are discussed within the framework of the Minimal Supersymmetric Standard Model with radiatively induced breaking of SU(2) x U(1). The present possibility of detecting these decays, given the available bounds on supersymmetric parameters, is compared with the situation a Next e+e- Linear Collider would face if supersymmetric particles were still undiscovered after LEP II. The indirect implications for t → H+b and t → u1χ0 of a possible detection of the bottom quark decay b → sγ at the Standard Model level are taken into account. (orig.)
Basic hypergeometry of supersymmetric dualities
Gahramanov, Ilmar
2016-01-01
We introduce several new identities combining basic hypergeometric sums and integrals. Such identities appear in the context of superconformal index computations for three-dimensional supersymmetric dual theories. We give both analytic proofs and physical interpretations of the presented identities.
Supersymmetric Dark Matter or Not
Olive, Keith A.
2016-01-01
The lack of evidence for low energy supersymmetry at the LHC implies a supersymmetry scale in excess a TeV. While this is consistent (and even helpful) with a Higgs boson mass at $\\approx$ 125 GeV, simple supersymmetric models with scalar and gaugino mass universality are being pushed into strips of parameter space. These often require coannihilations to obtain an acceptable relic density and the extent of these coannihilation strips will be discussed. In contrast, non-supersymmetric grand un...
Supersymmetric Valence Bond Solid States
Arovas, Daniel P.; Hasebe, Kazuki; Qi, Xiao-Liang; Zhang, Shou-Cheng
2009-01-01
In this work we investigate the supersymmetric version of the valence bond solid (SVBS) state. In one dimension, the SVBS states continuously interpolate between the valence bond states for integer and half-integer spin chains, and they generally describe superconducting valence bond liquid states. Spin and superconducting correlation functions can be computed exactly for these states, and their correlation lengths are equal at the supersymmetric point. In higher dimensions, the wave function...
Aspects of supersymmetric BRST cohomology
Brandt, Friedemann
2013-10-01
The application and extension of well-known BRST cohomological methods to supersymmetric field theories are discussed. The focus is on the emergence and particular features of supersymmetry algebra cohomology in this context. In particular it is discussed and demonstrated that supersymmetry algebra cohomology emerges within the cohomological analysis of standard supersymmetric field theories whether or not the commutator algebra of the symmetry transformations closes off-shell.
Supersymmetric exceptional gauge unification
Baaklini, N.S.
1980-12-15
We discuss the accommodation of quark-lepton generations, classified by SU(5), in the adjoint representations of simple Lie groups. We find SO(11), E/sub 6/, E/sub 7/, and E/sub 8/ as the only possible embedding groups, with the respective contents of one, one, three, and five conventional generations, together with their (V+A) conjugates and other particles. SU(4) supersymmetric unification models based on these gauge groups and which unify, via one coupling constant, the interactions of one vector boson, four spin-1/2 fermion, and six Higgs scalar multiplets, all being in the adjoint representation, are considered. Attention is focused on E/sub 7/ and E/sub 8/. The latter algebras are represented in the familiar SU(8) and SU(9) basis. We discuss quark-lepton assignments and propose patterns of symmetry breaking which can be triggered by the adjoint Higgs scalars, and which are compatible with the observed values of the strong and the weak couplings, as well as the weak mixing angle. Remarks are given with regard to the breaking of supersymmetry and the possible role of radiative corrections and renormalization effects in generating the gauge hierarchy.
Modified Supersymmetric Dark Sectors
Redino, Christopher
2015-01-01
SUSY models with a modified dark sector require constraints to be reinterpreted, which may allow for scenarios with low tuning. A modified dark sector can also change the phenomenology greatly. The addition of the QCD axion to the Minimal Supersymmetric Standard Model (MSSM) solves the strong CP problem and also modifies the dark sector with new dark matter candidates. While SUSY axion phenomenology is usually restricted to searches for the axion itself or searches for the ordinary SUSY particles, this work focuses on scenarios where the axion's superpartner, the axino may be detectable at the Large Hadron Collider (LHC) in the decays of neutralinos displaced from the primary vertex. In particular this work focuses on the KSVZ axino. The decay length of neutralinos in this scenario easily fits the ATLAS detector for SUSY spectra expected to be testable at the 14 TeV LHC. This signature of displaced decays to axinos is compared to other well motivated scenarios containing a long lived neutralino which decays i...
A new N=1 supersymmetric Harry Dym equation is constructed by applying supersymmetric reciprocal transformation to a trivial supersymmetric Harry Dym equation, and its recursion operator and Lax formulation are also obtained. Within the framework of symmetry approach, a class of 3rd order supersymmetric equations of Harry Dym type are considered. In addition to five known integrable equations, a new supersymmetric equation, admitting 5th order generalized symmetry, is shown to be linearizable through supersymmetric reciprocal transformation. Furthermore, its Lax representation and recursion operator are given so that the integrability of this new equation is confirmed. -- Highlights: ► A new supersymmetric Harry Dym equation is constructed through supersymmetric reciprocal transformations. ► The recursion operator and Lax formulation are established for the new supersymmetric Harry Dym equation. ► A supersymmetric equation of Harry Dym type is shown to be linearized through supersymmetric reciprocal transformation.
Natural supersymmetric minimal dark matter
Fabbrichesi, Marco; Urbano, Alfredo
2016-03-01
We show how the Higgs boson mass is protected from the potentially large corrections due to the introduction of minimal dark matter if the new physics sector is made supersymmetric. The fermionic dark matter candidate (a 5-plet of S U (2 )L) is accompanied by a scalar state. The weak gauge sector is made supersymmetric, and the Higgs boson is embedded in a supersymmetric multiplet. The remaining standard model states are nonsupersymmetric. Nonvanishing corrections to the Higgs boson mass only appear at three-loop level, and the model is natural for dark matter masses up to 15 TeV—a value larger than the one required by the cosmological relic density. The construction presented stands as an example of a general approach to naturalness that solves the little hierarchy problem which arises when new physics is added beyond the standard model at an energy scale around 10 TeV.
Symmetry breaking in supersymmetric GUTs
This paper analyzes the first step of symmetry breaking in N=1 supersymmetric unified theories. The possible patterns of gauge symmetry breaking consistent with supersymmetry are characterized. Some well-known properties of the scalar potential in supersymmetric gauge theories are reviewed. Simple methods to discover which v.e.v.'s of a given multiplet of scalar fields are consistent with the conditions of given equations are introduced. The vanishing of the D2-term and of the F2-term is discussed and a simple lemma derived from the former. The results of these discussions are applied to some possible candidates for a supersymmetric gauge theory based on the gauge groups SU(5), 0(10), and E6
Quantum supersymmetric Fermi-solitons
We investigate the quantum field theory, which is given on Minkowski manifold Md with its number of dimensions d>4 and is invariant under the group of nonlinear supersymmetric transformations proposed by Volkov and Akulov. It is shown that the vacuum state of this field theory, after such a compactification of the additional dimensions as Md → M4 centre dot Vd-4, is a particle-like Fermi-soliton. Its characteristic radius coincides with that of the compactified manifold Vd-4, and such an object is defined as a quantum supersymmetric Fermi-soliton
Ghost-free Supersymmetric Galileons
Farakos, Fotis; Kehagias, Alex
2013-01-01
We present consistent supersymmetric theories invariant under the generalization of the Galilean shift symmetry to ${\\cal{N}}=1$ superspace. These theories are constructed via the decoupling limit of certain non-minimally derivative coupled supergravities, thus they correspond to the supersymmetrization of the so-called covariant Galileon. Specifically, these theories are constructed in the linearized ${\\cal{N}}=1$ new-minimal supergravity set-up where the chiral supermultiplet is minimally coupled to gravity via the standard R-current contact term, and, at the same time, non-minimally derivatively coupled to the Einstein superfield.
Supersymmetric phase-space operators
A symmetric extension of the phase-space creation-annihilation operators and of the relevant formalism is considered. The symmetric phase-space partner potentials can be introduced and the concepts of supersymmetric quantum mechanics can be almost naturally extended to the phase-space case
Supersymmetric Ruijsenaars-Schneider Model
Blondeau-Fournier, O.; Desrosiers, P.; Mathieu, P.
2015-03-01
An integrable supersymmetric generalization of the trigonometric Ruijsenaars-Schneider model is presented whose symmetry algebra includes the super Poincaré algebra. Moreover, its Hamiltonian is shown to be diagonalized by the recently introduced Macdonald superpolynomials. Somewhat surprisingly, the consistency of the scalar product forces the discreteness of the Hilbert space.
Invariants in Supersymmetric Classical Mechanics
Alonso Izquierdo, Alberto; González León, Miguel Ángel; Mateos Guilarte, Juan
2000-01-01
[EN] The bosonic second invariant of SuperLiouville models in supersymmetric classical mechanics is described. [ES] El segundo campo cuántico de bosones invariante del modelo SuperLiouville es descrito en la mecanica clasica supersimétrica.
Supersymmetric classical mechanics: free case
We present a review work on Supersymmetric Classical Mechanics in the context of a Lagrangian formalism, with N = 1-supersymmetry. We show that the N = 1 supersymmetry does not allow the introduction of a potencial energy term depending on a single commuting supercoordinate, φ(t;Θ). (author)
Natural ranges of supersymmetric signals
Giusti, Leonardo; Strumia, A
1999-01-01
The LEP2 experiments pose a serious naturalness problem for supersymmetric models. The problem is stronger in gauge mediation than in supergravity models. Particular scenarios, like electroweak baryogenesis or gauge mediation with light messengers, are strongly disfavoured. Searching a theoretical reason that naturally explains why supersymmetry has not been found poses strong requests on model building. If instead an unlikely (p\\approx 5%) numerical accident has hidden supersymmetry to LEP2, we compute the naturalness distribution of values of allowed sparticle masses and supersymmetric loop effects. We find that b to s gamma remains a very promising signal of minimal supersymmetry even if there is now a 20% (4%) probability that coloured particles are heavier than 1 TeV (3 TeV). We study how much other effects are expected to be detectable.
Exploring the Supersymmetric $\\sigma$ Model
De Oliveira-Imbiriba, B C
1999-01-01
The purpose of this work is to present some basic concepts about the non-linear sigma model in a simple and direct way. We start with showing the bosonic model and the Wess-Zumino-Witten term, making some comments about its topological nature, and its association with the torsion. It is also shown that to cancel the quantum conformal anomaly the model should obey the Einstein equations. We provide a quick introduction about supersymmetry in chapter 2 to help the understanding the supersymmetric extension of the model. In the last chapter we present the supersymmetric model and its equations of motion. Finally we work-out the two-supersymmetry case, introducing the chiral as well as the twisted chiral fields, expliciting the very specific $SU(2)\\otimes U(1)$ case.
Supersymmetric Dark Matter or Not
Olive, Keith A
2016-01-01
The lack of evidence for low energy supersymmetry at the LHC implies a supersymmetry scale in excess a TeV. While this is consistent (and even helpful) with a Higgs boson mass at $\\approx$ 125 GeV, simple supersymmetric models with scalar and gaugino mass universality are being pushed into strips of parameter space. These often require coannihilations to obtain an acceptable relic density and the extent of these coannihilation strips will be discussed. In contrast, non-supersymmetric grand unified theories such as SO(10) may also provide a dark matter candidate. Because of the presence of an intermediate scale, these theories may unify gauge couplings, provide for neutrino masses and a suitably long lived proton.
Signals of Supersymmetric Dark Matter
Abbas, A
2000-01-01
The Lightest Supersymmetric Particle predicted in most of the supersymmetric scenarios is an ideal candidate for the dark matter of cosmology. Their detection is of extreme significance today. Recently there have been intriguing signals of a 59 Gev neutralino dark matter at DAMA in Gran Sasso. We look at other possible signatures of dark matter in astrophysical and geological frameworks. The passage of the earth through dense clumps of dark matter would produce large quantities of heat in the interior of this planet through the capture and subsequent annihilation of dark matter particles. This heat would lead to large-scale volcanism which could in turn have caused mass extinctions. The periodicity of such volcanic outbursts agrees with the frequency of palaeontological mass extinctions as well as the observed periodicity in the occurrence of the largest flood basalt provinces on the globe. Binary character of these extinctions is another unique aspect of this signature of dark matter. In addition dark matter...
Fun with supersymmetric quantum mechanics
One reason for studying supersymmetric quantum mechanics is that there are a class of superpotentials W(x) which behave at large x as x/sup α/ for which we know from general arguments whether SUSY is broken or unbroken. Thus one can use these superpotentials to test various ideas about how to see if supersymmetry is broken in an arbitrary model. Recently, Witten proposed a topological invariant, the Witten index Δ which counts the number of bosons minus the number of fermions having ground state energy zero. Since if supersymmetry is broken, the ground state energy cannot be zero, one expects if Δ is not zero, SUSY is preserved and the theory is not a good candidate for a realistic model. In this study we evaluate Δ for several examples, and show some unexpected peculiarities of the Witten index for certain choice of superpotentials W(x). We also discuss two other nonperturbative methods of studying supersymmetry breakdown. One involves relating supersymmetric quantum mechanics to a stochastic classical problem and the other involves considering a discrete (but not supersymmetric) version of the theory and studying its behavior as one removes the lattice cuttoff. In this survey we review the Hamiltonian and path integral approaches to supersymmetric quantum mechanics. We then discuss the related path integrals for the Witten Index and for stochastic processes and show how they are indications for supersymmetry breakdown. We then discuss a system where the superpotential W(x) has assymetrical values at +-infinity. We finally discuss nonperturbative strategies for studying supersymmetry breakdown based on introducing a lattice and studying the behavior of the ground state energy as the lattice cutoff is removed. 17 references
Hiller, Gudrun; Hochberg, Yonit; Nir, Yosef
2012-01-01
There is experimental evidence for a direct CP asymmetry in singly Cabibbo suppressed D decays, \\Delta A_{CP} \\sim 0.006. Naive expectations are that the Standard Model contribution to \\Delta A_{CP} is an order of magnitude smaller. We explore the possibility that a major part of the symmetry comes from supersymmetric contributions. The leading candidates are models where the flavor structure of the trilinear scalar couplings is related to the structure of the Yukawa couplings via approximate...
Solvable two-dimensional supersymmetric models and the supersymmetric Virasoro algebra
The simplest extension of a variety of solvable 2 dimensional models to supersymmetric models is obtained and classical solutions are discussed. It is found that these supersymmetric models are closely related. 11 refs
Supersymmetric Quantum Hall Effect on Fuzzy Supersphere
Hasebe, Kazuki
2004-01-01
Supersymmetric quantum Hall liquids are constructed on a supersphere in a supermonopole background. We derive a supersymmetric generalization of the Laughlin wavefunction, which is a ground state of a hard-core $OSp(1|2)$ invariant Hamiltonian. We also present excited topological objects, which are fractionally charged deficits made by super Hall currents. Several relations between quantum Hall systems and their supersymmetric extensions are discussed.
Dyon-dynamics in supersymmetric theory
Supersymmetrized Schroedinger Equation for dyon-dyon system has been obtained by dimensional reduction of supersymmetrized four-dimensional harmonic oscillator and it has been interpreted as an ensemble of two Schroedinger and one Pauli Equation. The supersymmetrized solutions of Schroedinger Equation of a dyon moving in the field of another dyon are shown to be modified from the corresponding bound state solutions of two dyons. (author)
Supersymmetric Decays of the Z' Boson
Chang, Chun-Fu; Cheung, Kingman; Yuan, Tzu-Chiang
2011-01-01
The decay of the Z' boson into supersymmetric particles is studied. We investigate how these supersymmetric modes affect the current limits from the Tevatron and project the expected sensitivities at the LHC. Employing three representative supersymmetric Z' models, namely, E_6, U(1)_{B-L}, and the sequential model, we show that the current limits of the Z' mass from the Tevatron could be reduced substantially due to the weakening of the branching ratio into leptonic pairs. The mass reach for ...
Supersymmetric theories on squashed five-sphere
Imamura, Yosuke
2012-01-01
We construct supersymmetric theories on the SU(3)xU(1) symmetric squashed five-sphere with 2, 4, 6, and 12 supercharges. We first determine the Killing equation by dimensional reduction from 6d, and use Noether procedure to construct actions. The supersymmetric Yang-Mills action is straightforwardly obtained from the supersymmetric Chern-Simons action by using a supersymmetry preserving constant vector multiplet.
Duality in supersymmetric Yang-Mills theory
Peskin, M.E.
1997-02-01
These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, the author analyzes the qualitative behavior of the simplest illustrative models. These include supersymmetric QCD for N{sub f} < N{sub c}, in which the superpotential is generated nonperturbatively, N = 2 SU(2) Yang-Mills theory (the Seiberg-Witten model), in which the nonperturbative behavior of the effect coupling is described geometrically, and supersymmetric QCD for N{sub f} large, in which the theory illustrates a non-Abelian generalization of electric-magnetic duality. 75 refs., 12 figs.
Geloun, Joseph Ben; Scholtz, Frederik G
2009-01-01
The N=1 supersymmetric invariant Landau problem is constructed and solved. By considering Landau level projections remaining non trivial under N=1 supersymmetry transformations, the algebraic structures of the N=1 supersymmetric covariant non(anti)commutative superplane analogue of the ordinary N=0 noncommutative Moyal-Voros plane are identified.
In the supersymmetric standard model operators of dimension 4 and 5 generically violate B and L number. One usually assumes the presence of some discrete symmetry ('matter parities') in order to forbid dangerous operators which may lead otherwise to unacceptable violations of B and L. We give a general classification of such discrete ZN symmetries (and R-symmetries) and show that the number of independent possibilities is substantially reduced by equivalences. We argue that normal discrete symmetries may be expected to be violated by quantum gravity effects and hence are not enough to inhibit nucleon decay. On the other hand, gauge (either discrete or continuous) symmetries are stable under quantum gravity effects and we discuss how such symmetries may eliminate the dangeous B- or L-violating operators. We find that the massless fermion content of models with discrete 'gauge' symmetries is strongly constrained by the cancellation of 'discrete gauge anomalies'. We show that there are two preferred ZN symmetries which are discrete anomaly free with the minimal light matter content. One of them is the standard R-parity whereas the other is a unique Z3 symmetry allowing for lepton number violation. We argue that from the point of view of arranging for proton stability without fine-tuning the second option should be preferred. The differences in the phenomenology of the various supersymmetric models dictated by the different symmetries are discussed. (orig.)
Supersymmetric localization in two dimensions
Benini, Francesco
2016-01-01
This is an introductory review to localization techniques in supersymmetric two-dimensional gauge theories. In particular we describe how to construct Lagrangians of N=(2,2) theories on curved spaces, and how to compute their partition functions and certain correlators on the sphere, the hemisphere and other curved backgrounds. We also describe how to evaluate the partition function of N=(0,2) theories on the torus, known as the elliptic genus. Finally we summarize some of the applications, in particular to probe mirror symmetry and other non-perturbative dualities.
Supersymmetric Adler Functions and Holography
Iwanaga, Masaya; Sakai, Tadakatsu
2016-01-01
We perform several tests on a recent proposal by Shifman and Stepanyantz for an exact expression for the current correlation functions in supersymmetric gauge theories. We clarify the meaning of the relation in superconformal theories. In particular we show that it automatically follows from known relations between the current correlation functions and anomalies. It therefore also automatically matches between different dual realizations of the same superconformal theory. We use holographic examples as well as calculations in free theories to show that the proposed relation fails in theories with mass terms.
Electroweak breaking in supersymmetric models
Ibáñez, L E
1992-01-01
We discuss the mechanism for electroweak symmetry breaking in supersymmetric versions of the standard model. After briefly reviewing the possible sources of supersymmetry breaking, we show how the required pattern of symmetry breaking can automatically result from the structure of quantum corrections in the theory. We demonstrate that this radiative breaking mechanism works well for a heavy top quark and can be combined in unified versions of the theory with excellent predictions for the running couplings of the model. (To be published in ``Perspectives in Higgs Physics'', G. Kane editor.)
Inflation in Supersymmetric Unified Theories
Jeannerot, R.
1997-01-01
We construct supersymmetric unified models which automatically lead to a period of inflation. The models all involve a U(1) symmetry which does not belong to the MSSM. We consider three different types of models depending on whether this extra U(1) is the subgroup of a non abelian gauge group, is a U(1) factor belonging to the visible sector or is a U(1) factor belonging to the hidden sector. Depending on the structure of the unified theory, on the spontaneous symmetry breaking pattern and on...
The holographic supersymmetric Casimir energy
Genolini, Pietro Benetti; Martelli, Dario; Sparks, James
2016-01-01
We consider a general class of asymptotically locally AdS_5 solutions of minimal gauged supergravity, that are dual to superconformal field theories on curved backgrounds S^1 x M_3 preserving two supercharges. We demonstrate that standard holographic renormalization corresponds to a scheme that breaks supersymmetry. We propose new boundary terms that restore supersymmetry, and show that for smooth solutions with topology S^1 x R^4 the improved on-shell action reproduces both the supersymmetric Casimir energy and the field theory BPS relation between charges.
Ultraviolet divergences and supersymmetric theories
This article is closely related to the one by Ferrara in these same Proceedings. It deals with what is perhaps the most fascinating property of supersymmetric theories, their improved ultraviolet behavior. My aim here is to present a survey of the state of the art as of August, 1984, and a somewhat more detailed discussion of the breakdown of the superspace power-counting beyond N = 2 superfields. A method is also described for simplifying divergence calculations that uses the locality of subtracted Feynman integrals. 74 references
Flow equations for supersymmetric field theories
A manifestly supersymmetric exact renormalization group flow is presented for the N=1 Wess-Zumino-Model in two dimensions. For that purpose, supersymmetric regulators are constructed in the off-shell formulation. The considered model allows for dynamical supersymmetry breaking. The phase diagramm is discussed as well as the fixed-point structure of the ERG-flow
Supersymmetric particle production at hadron colliders
Krämer, Michael
1998-01-01
The theoretical status of MSSM particle production at the hadron colliders Tevatron and LHC is reviewed, including next-to-leading order supersymmetric QCD corrections. The higher-order corrections significantly reduce the theoretical uncertainty and lead to a rise of the lower bounds on supersymmetric particle masses, as demonstrated for the case of top-squark and gaugino pair production at the Tevatron.
Fermion-dyon dynamics in supersymmetric theories
Supersymmetrized Schroedinger equation for fermion-dyon system has been obtained by dimensional reduction of supersymmetrized four dimensional harmonic oscillator and it has been interpreted as an ensemble of two Schroedinger and one Pauli equation each describing the motion of an electrically charged particle in the field of a dyon with different magnetic charge. (author)
Supersymmetric Kosterlitz-Thouless phase transition
Supersymmetry is introduced in the Coulomb gas, namely the statistical theory for a set of interacting vortices and antivortices. The equivalence of this theory to the supersymmetric Sine-Gordon model is established. Mean-field considerations applied to this supersymmetric Coulomb gas lead to a phase transition of the kind described by Kosterlitz and Thouless. 12 references
Supersymmetric methods in quantum and statistical physics
The author presents an introduction to supersymmetry. Starting from a historical review the basic definitions for supersymmetric quantum mechanics are given, and the fundamental properties following from these definitions are discussed. Then after a description of supersymmetric potentials supersymmetric classical mechanics are introduced, and the exact solution of a supersymmetric quantum eigenvalue problem is described. Thereafter the quasi-classical path-integral approach to the Witten model, the supersymmetric structure of the Fokker-Planck and the Langevin equation, the supersymmetry of Pauli's Hamiltonian in the connection with the paramagnetism of a non-interacting electron gas, and the supersymmetry in the Dirac equation with its application to semiconductor heterojunctions are considered. (HSI). 36 figs., 13 tabs
Supersymmetric decays of the top quark
The supersymmetric decays of the top quark into charged Higgs plus bottom, t → H+b, and into the supersymmetric partner of the top (u1) plus the lightest neutralino (χ10, t → u1χ10, are discussed within the framework of the Minimal Supersymmetric Standard Model with radiatively induced breaking of the gauge group SU(2) x U(1). The possibility of detecting these decays at present, i.e. given the available bounds on supersymmetric parameters, is compared with the situation a Next e+e- Linear Collider would face if supersymmetric particles were still undiscovered at LEP II. The indirect implications for t → H+b and t → u1 anti 0 of a measurement of the bottom quark decay b → sγat the Standard model level are taken into account. (orig.)
A Maximally Supersymmetric Kondo Model
Harrison, Sarah; Kachru, Shamit; Torroba, Gonzalo; /Stanford U., Phys. Dept. /SLAC
2012-02-17
We study the maximally supersymmetric Kondo model obtained by adding a fermionic impurity to N = 4 supersymmetric Yang-Mills theory. While the original Kondo problem describes a defect interacting with a free Fermi liquid of itinerant electrons, here the ambient theory is an interacting CFT, and this introduces qualitatively new features into the system. The model arises in string theory by considering the intersection of a stack of M D5-branes with a stack of N D3-branes, at a point in the D3 worldvolume. We analyze the theory holographically, and propose a dictionary between the Kondo problem and antisymmetric Wilson loops in N = 4 SYM. We perform an explicit calculation of the D5 fluctuations in the D3 geometry and determine the spectrum of defect operators. This establishes the stability of the Kondo fixed point together with its basic thermodynamic properties. Known supergravity solutions for Wilson loops allow us to go beyond the probe approximation: the D5s disappear and are replaced by three-form flux piercing a new topologically non-trivial S3 in the corrected geometry. This describes the Kondo model in terms of a geometric transition. A dual matrix model reflects the basic properties of the corrected gravity solution in its eigenvalue distribution.
Ultraviolet divergences and supersymmetric theories
I attempt to outline the present understanding of the ultraviolet behavior of supersymmetric theories. Two things emerge clearly from this discussion. We have at our disposal a class of completely finite renormalizable models with extended global supersymmetry, and we have a number of formal ways of proving their finiteness. However, at present the motivation for looking at such theories is not clear. More precisely, it is not clear why a finite model should be preferred to other infinite, but still renormalizable and predictive, ones. On the other hand, supergravity theories are a priori far more interesting, as they offer a perspective for unifying all interactions including gravity. However, their couplings are parametrized by Newton's constant, which is of negative mass dimension. Thus these theories are all potentially nonrenormalizable. At present it does not seem possible to prove that they are finite along the lines of what has been achieved for supersymmetric Yang-Mills theories. All the available arguments fail, in one way or another, due to the presence of a dimensional coupling. Moreover, the indications of the indirect analysis are rather discouraging, and suggest that divergences should really set in at the 'obvious' number of loops, three. Of course, explicit calculations in (super)gravity theories would be most illuminating. Hopefully, the integration technique mentioned in sect. 3, together with the development of a suitable computer software and, at least, the completion of the work, should make this nontrivial task accessible in the near future. (orig.)
Applications of supersymmetric quantum mechanics
The central subject of the thesis is the spinning particle model. It is a theory describing in a pseudoclassical way a Dirac particle which moves in an arbitrary d-dimensional space-time.In addition to space-time coordinates, the particle has spin which is described in terms of anti-commuting coordinates. Along the particles world line there is a super-symmetry between the fermionic spin variables and the bosonic position coordinates of the particle. It is straightforward to quantisize this model giving rise to supersymmetric quantum mechanics. The model does indeed describe a particle with spin 1/2, like a quark or an electron. There are two aspects of this model which is studied extensively in this thesis. First, to investigate the symmetries of the spinning particle on an arbitrary Riemannian manifold. Second, attention is drawn to the application of supersymmetric quantum mechanical models (i.e. spinning particle models) defined on an arbitrary Riemannian manifold to the calculation of anomalies in quantum field theories defined on the same manifold. (author). 49 refs.; 7 figs
On supersymmetric Dirac delta interactions
Guilarte, J Mateos; Castaneda, J M Munoz
2014-01-01
In this paper we construct $\\mathcal{N}=2$ supersymmetric quantum mechanics over several configurations of Dirac delta potentials from one single delta to a Dirac "comb". We show in detail how the building of supersymmetry on potentials with delta interactions placed in two or more points on the real line requires the inclusion of quasi-square wells. We find an scenario of either unbroken supersymmetry with Witten index one or supersymmetry breaking when there is one "bosonic" and one "fermionic" ground state such that the Witten index is zero. We explain next the different structure of the scattering waves produced by three $\\delta/\\theta$ potentials with respect to the the eigenfunctions arising in the non-SUSY case. In particular, much more bound states paired by supersymmetry exist within the supersymmetric framework as compared with the non-SUSY problem. An infinite array of equally spaced $\\delta$-interactions of the same strength but alternatively attractive and repulsive are susceptible of being promo...
Supersymmetric unification at the millennium
Charanjit S Aulakh
2000-07-01
We argue that the discovery of neutrino mass effects at super-Kamiokande implies a clear logical chain leading from the Standard Model, through the MSSM and the recently developed minimal left right supersymmetric models with a renormalizable see-saw mechanism for neutrino mass, to left right symmetric SUSY GUTS: in particular, SO(10) and SU(2)× SU(2) × SU(4). The progress in constructing such GUTS explicitly is reviewed and their testability/falsiﬁability by lepton ﬂavour violation and proton decay measurements emphasized. SUSY violations of the survival principle and the interplay between third generation Yukawa coupling uniﬁcation and the structurally stable IR attractive features of the RG ﬂow in SUSY GUTS are also discussed.
Structure formation from supersymmetric inflation
Recently a supersymmetric inflationary potential was proposed by Ross and Sarkar, (OUTP-95-15p) which when normalised to COBE requires the inflationary scale to be about 3x1014 GeV, implying a reheating temperature of the order of 105 GeV. This is below the upper limit derived from considerations on the thermal generation of unstable gravitinos and their effects on primordial nucleosynthesis, but high enough to allow baryogenesis after inflation. In this project we investigate the consequences for structure formation given by the proposed potential. We calculate the form of the power spectrum normalized to COBE and obtain the theoretical predictions for observations of the distribution of galaxies and clusters of galaxies and the local streaming motion of galaxies. We find agreement with observations. (author)
Instability of supersymmetric microstate geometries
Eperon, Felicity C; Santos, Jorge E
2016-01-01
We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an "evanescent ergosurface": a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.
Supersymmetric Sneutrino-Higgs Inflation
Deen, Rehan; Purves, Austin
2016-01-01
It is shown that in the phenomenologically realistic supersymmetric $B-L$ MSSM theory, a linear combination of the neutral, up Higgs field with the third family left-and right-handed sneutrinos can play the role of the cosmological inflaton. Assuming that supersymmetry is softly broken at a mass scale of order $10^{13}~\\mathrm{GeV}$, the potential energy associated with this field allows for 60 e-foldings of inflation with the cosmological parameters being consistent with all Planck2015 data. The theory does not require any non-standard coupling to gravity and the physical fields are all sub-Planckian during the inflationary epoch. It will be shown that there is a "robust" set of initial conditions which, in addition to satisfying the Planck data, simultaneously are consistent with all present LHC phenomenological requirements.
Currents in supersymmetric field theories
Derendinger, Jean-Pierre
2016-01-01
A general formalism to construct and improve supercurrents and source or anomaly superfields in two-derivative N=1 supersymmetric theories is presented. It includes arbitrary gauge and chiral superfields and a linear superfield coupled to gauge fields. These families of supercurrent structures are characterized by their energy-momentum tensors and R currents and they display a specific relation to the dilatation current of the theory. The linear superfield is introduced in order to describe the gauge coupling as a background (or propagating) field. Supersymmetry does not constrain the dependence on this gauge coupling field of gauge kinetic terms and holomorphicity restrictions are absent. Applying these results to an effective (Wilson) description of super-Yang-Mills theory, matching or cancellation of anomalies leads to an algebraic derivation of the all-order NSVZ beta function.
Entropy current formalism for supersymmetric theories
L. Andrianopoli
2015-03-01
Full Text Available The recent developments in fluid/gravity correspondence give a new impulse to the study of fluid dynamics of supersymmetric theories. In that respect, the entropy current formalism requires some modifications in order to be adapted to supersymmetric theories and supergravities. We formulate a new entropy current in superspace with the properties: 1 it is conserved off-shell for non-dissipative fluids, 2 it is invariant under rigid supersymmetry transformations, 3 it is covariantly closed in local supersymmetric theories, 4 it reduces to its bosonic expression on space–time.
M. Daoud; Kibler, M.
2003-01-01
Paper accepted for publication in Physics Letters A. - Théorie A connection between fractionalsupersymmetric quantum mechanicsand ordinary supersymmetric quantum mechanics is established in this Letter.
Bubbles of Nothing and Supersymmetric Compactifications
Blanco-Pillado, Jose J; Sousa, Kepa; Urrestilla, Jon
2016-01-01
We investigate the non-perturbative stability of supersymmetric compactifications with respect to decay via a bubble of nothing. We show examples where this kind of instability is not prohibited by the spin structure, i.e., periodicity of fermions about the extra dimension. However, such "topologically unobstructed" cases do exhibit an extra-dimensional analog of the well-known Coleman-De Luccia suppression mechanism, which prohibits the decay of supersymmetric vacua. We demonstrate this explicitly in a four dimensional Abelian-Higgs toy model coupled to supergravity. The compactification of this model to $M_3 \\times S_1$ presents the possibility of vacua with different windings for the scalar field. Away from the supersymmetric limit, these states decay by the formation of a bubble of nothing, dressed with an Abelian-Higgs vortex. We show how, as one approaches the supersymmetric limit, the circumference of the topologically unobstructed bubble becomes infinite, thereby preventing the realization of this dec...
The character of the supersymmetric Casimir energy
Martelli, Dario
2015-01-01
We study the supersymmetric Casimir energy $E_\\mathrm{susy}$ of $\\mathcal{N}=1$ field theories with an R-symmetry, defined on rigid supersymmetric backgrounds $S^1\\times M_3$, using a Hamiltonian formalism. These backgrounds admit an ambi-Hermitian geometry, and we show that the net contributions to $E_\\mathrm{susy}$ arise from certain twisted holomorphic modes on $\\mathbb{R}\\times M_3$, with respect to both complex structures. The supersymmetric Casimir energy may then be identified as a limit of an index-character that counts these modes. In particular this explains a recent observation relating $E_\\mathrm{susy}$ on $S^1\\times S^3$ to the anomaly polynomial. As further applications we compute $E_\\mathrm{susy}$ for certain secondary Hopf surfaces, and discuss how the index-character may also be used to compute generalized supersymmetric indices.
Supersymmetric partners for the associated Lame potentials
Fernandez C, David J
2008-01-01
The general solution of the stationary Schrodinger equation for the associated Lame potentials with an arbitrary real energy is found. The supersymmetric partners are generated by employing seeds solutions for factorization energies inside the gaps.
Patterns of flavor signals in supersymmetric models
Quark and lepton flavor signals are studied in four supersymmetric models, namely the minimal supergravity model, the minimal supersymmetric standard model with right-handed neutrinos, SU(5) supersymmetric grand unified theory with right-handed neutrinos and the minimal supersymmetric standard model with U(2) flavor symmetry. We calculate b→s(d) transition observables in Bd and Bs decays, taking the constraint from the Bs- anti Bs mixing recently observed at Tevatron into account. We also calculate lepton flavor violating processes μ → eγ, τ → μγ and τ → eγ for the models with right-handed neutrinos. We investigate possibilities to distinguish the flavor structure of the supersymmetry breaking sector with use of patterns of various flavor signals which are expected to be measured in experiments such as MEG, LHCb and a future Super B Factory. (orig.)
The Minimal Supersymmetric Fat Higgs Model
Harnik, Roni; Kribs, Graham D.; Larson, Daniel T.; Murayama, Hitoshi
2003-11-26
We present a calculable supersymmetric theory of a composite"fat'" Higgs boson. Electroweak symmetry is broken dynamically through a new gauge interaction that becomes strong at an intermediate scale. The Higgs mass can easily be 200-450 GeV along with the superpartner masses, solving the supersymmetric little hierarchy problem. We explicitly verify that the model is consistent with precision electroweak data without fine-tuning. Gauge coupling unification can be maintained despite the inherently strong dynamics involved in electroweak symmetry breaking. Supersymmetrizing the Standard Model therefore does not imply a light Higgs mass, contrary to the lore in the literature. The Higgs sector of the minimal Fat Higgs model has a mass spectrum that is distinctly different from the Minimal Supersymmetric Standard Model.
Multi-instanton calculus in supersymmetric theories
In this talk I review some recent results concerning multi-instanton calculus in supersymmetric field theories. More in detail, I will show how these computations can be efficiently performed using the formalism of topological field theories. (author)
Supersymmetric Dilatations in the Presence of Dilaton
La, H S
1997-01-01
The supersymmetric generalization of dilatations in the presence of the dilaton is defined. This is done by defining the supersymmetric dilaton geometry which is motivated by the supersymmetric volume preserving diffeomorphisms. The resulting model is classical superconformal field theory with an additional dilaton-axion supermultiplet coupled to the supersymmetric gauge theory, where the dilaton-axion couplings are nonrenormalizable. The possibility of spontaneous scale symmetry breaking is investigated in this context. There are three different types of vacua with broken scale symmetry depending on the details of the dilaton sector: unbroken supersymmetry, spontaneously broken supersymmetry and softly broken supersymmetry. If the scale symmetry is broken in the bosonic vacuum, then the Poincaré supersymmetry must be broken at the same time. If the scale symmetry is broken in the fermionic vacuum but the bosonic vacuum remains invariant, then the Poincaré supersymmetry can be preserved as long as the R-sym...
Flow equation for supersymmetric quantum mechanics
We study supersymmetric quantum mechanics with the functional RG formulated in terms of an exact and manifestly off-shell supersymmetric flow equation for the effective action. We solve the flow equation nonperturbatively in a systematic super-covariant derivative expansion and concentrate on systems with unbroken supersymmetry. Already at next-to-leading order, the energy of the first excited state for convex potentials is accurately determined within a 1% error for a wide range of couplings including deeply nonperturbative regimes.
Flow Equation for Supersymmetric Quantum Mechanics
Synatschke, Franziska; Gies, Holger; Wipf, Andreas
2009-01-01
We study supersymmetric quantum mechanics with the functional RG formulated in terms of an exact and manifestly off-shell supersymmetric flow equation for the effective action. We solve the flow equation nonperturbatively in a systematic super-covariant derivative expansion and concentrate on systems with unbroken supersymmetry. Already at next-to-leading order, the energy of the first excited state for convex potentials is accurately determined within a 1% error for a wide range of couplings including deeply nonperturbative regimes.
Natural supersymmetric spectrum in mirage mediation
Asano, Masaki; Higaki, Tetsutaro
2012-01-01
Current results of LHC experiments exclude large area of light new particle region, namely natural parameter space, in supersymmetric extension models. One of the possibilities for achieving the correct electroweak symmetry breaking naturally is low scale messenger scenario. Actually, the next-to-minimal supersymmetric standard model with TeV scale mirage mediation realizes the natural electroweak symmetry breaking with various mass spectra. In this paper, we show the possible mass spectrum i...
Supersymmetric partners of the truncated harmonic oscillator
First and second order supersymmetric transformations are applied to the truncated harmonic oscillator to generate new Hamiltonians with known spectra. We also study the effect of these transformations on the eigenfunctions of the initial Hamiltonian. Finally the link between first and the second order supersymmetric partners of the truncated harmonic oscillator which possess third-order differential ladder operators with the Painlevé IV equation is used to obtain several solutions of this non-linear second-order differential equation.
Neutral Supersymmetric Higgs Boson Searches
Robinson, Stephen Luke; /Imperial Coll., London
2009-09-01
In some Supersymmetric extensions of the Standard Model, including the Minimal Supersymmetric Standard Model (MSSM), the coupling of Higgs bosons to b-quarks is enhanced. This enhancement makes the associated production of the Higgs with b-quarks an interesting search channel for the Higgs and Supersymmetry at D0. The identification of b-quarks, both online and offline, is essential to this search effort. This thesis describes the author's involvement in the development of both types of b-tagging and in the application of these techniques to the MSSM Higgs search. Work was carried out on the Level-3 trigger b-tagging algorithms. The impact parameter (IP) b-tagger was retuned and the effects of increased instantaneous luminosity on the tagger were studied. An extension of the IP-tagger to use the z-tracking information was developed. A new b-tagger using secondary vertices was developed and commissioned. A tool was developed to allow the use of large multi-run samples for trigger studies involving b-quarks. Offline, a neural network (NN) b-tagger was trained combining the existing offline lifetime based b-tagging tools. The efficiency and fake rate of the NN b-tagger were measured in data and MC. This b-tagger was internally reviewed and certified by the Collaboration and now provides the official b-tagging for all analyses using the Run IIa dataset at D0. A search was performed for neutral MSSM Higgs bosons decaying to a b{bar b} pair and produced in association with one or more b-quarks. Limits are set on the cross-section times the branching ratio for such a process. The limits were interpreted in various MSSM scenarios. This analysis uses the NN b-tagger and was the first to use this tool. The analysis also relies on triggers using the Level-3 IP b-tagging tool described previously. A likelihood discriminant was used to improve the analysis and a neural network was developed to cross-check this technique. The result of the analysis has been submitted to PRL
Neutral Supersymmetric Higgs Boson Searches
Robinson, Stephen Luke [Imperial College, London (United Kingdom)
2008-07-01
In some Supersymmetric extensions of the Standard Model, including the Minimal Supersymmetric Standard Model (MSSM), the coupling of Higgs bosons to b-quarks is enhanced. This enhancement makes the associated production of the Higgs with b-quarks an interesting search channel for the Higgs and Supersymmetry at D0. The identification of b-quarks, both online and offline, is essential to this search effort. This thesis describes the author's involvement in the development of both types of b-tagging and in the application of these techniques to the MSSM Higgs search. Work was carried out on the Level-3 trigger b-tagging algorithms. The impact parameter (IP) b-tagger was retuned and the effects of increased instantaneous luminosity on the tagger were studied. An extension of the IP-tagger to use the z-tracking information was developed. A new b-tagger using secondary vertices was developed and commissioned. A tool was developed to allow the use of large multi-run samples for trigger studies involving b-quarks. Offline, a neural network (NN) b-tagger was trained combining the existing offline lifetime based b-tagging tools. The efficiency and fake rate of the NN b-tagger were measured in data and MC. This b-tagger was internally reviewed and certified by the Collaboration and now provides the official b-tagging for all analyses using the Run IIa dataset at D0. A search was performed for neutral MSSM Higgs bosons decaying to a b{bar b} pair and produced in association with one or more b-quarks. Limits are set on the cross-section times the branching ratio for such a process. The limits were interpreted in various MSSM scenarios. This analysis uses the NN b-tagger and was the first to use this tool. The analysis also relies on triggers using the Level-3 IP b-tagging tool described previously. A likelihood discriminant was used to improve the analysis and a neural network was developed to cross-check this technique. The result of the analysis has been submitted to PRL
The Supersymmetric origin of matter
Balazs, C.; /Argonne; Carena, M.; /Fermilab; Menon, A.; Morrissey, D.E.; Wagner, C.E.M.; /Argonne /Chicago U., EFI
2004-12-01
The Minimal Supersymmetric extension of the Standard Model (MSSM) can provide the correct neutralino relic abundance and baryon number asymmetry of the universe. Both may be efficiently generated in the presence of CP violating phases, light charginos and neutralinos, and a light top squark. Due to the coannihilation of the neutralino with the light stop, we find a large region of parameter space in which the neutralino relic density is consistent with WMAP and SDSS data. We perform a detailed study of the additional constraints induced when CP violating phases, consistent with the ones required for baryogenesis, are included. We explore the possible tests of this scenario from present and future electron Electric Dipole Moment (EDM) measurements, direct neutralino detection experiments, collider searches and the b {yields} s{gamma} decay rate. We find that the EDM constraints are quite severe and that electron EDM experiments, together with stop searches at the Tevatron and Higgs searches at the LHC, will provide a definite test of our scenario of electroweak baryogenesis in the next few years.
Quantum Supersymmetric Bianchi IX Cosmology
Damour, Thibault
2014-01-01
We study the quantum dynamics of a supersymmetric squashed three-sphere by dimensionally reducing to one timelike dimension the action of D=4 simple supergravity for a Bianchi IX cosmological model. After imposition of the diffeomorphism constraints, the wave function of the Universe becomes a spinor of Spin(8,4) depending on the three squashing parameters, which satisfies Dirac, and Klein-Gordon-like, wave equations describing the propagation of a quantum spinning particle reflecting off spin-dependent potential walls. The algebra of the susy constraints and of the Hamiltonian one is found to close. One finds that the quantum Hamiltonian is built from operators that generate a 64-dimensional representation of the maximally compact sub-algebra of the rank-3 hyperbolic Kac-Moody algebra AE3. The (quartic-in-fermions) squared-mass term entering the Klein-Gordon-like equation has several remarkable properties: 1)it commutes with all the other (Kac-Moody-related) building blocks of the Hamiltonian; 2)it is a quad...
Non-supersymmetric orientifolds of Gepner models
Gato-Rivera, B. [NIKHEF Theory Group, Kruislaan 409, 1098 SJ Amsterdam (Netherlands); Instituto de Fisica Fundamental, CSIC, Serrano 123, Madrid 28006 (Spain); Schellekens, A.N. [NIKHEF Theory Group, Kruislaan 409, 1098 SJ Amsterdam (Netherlands); Instituto de Fisica Fundamental, CSIC, Serrano 123, Madrid 28006 (Spain); IMAPP, Radboud Universiteit, Nijmegen (Netherlands)], E-mail: t58@nikhef.nl
2009-01-12
Starting from a previously collected set of tachyon-free closed strings, we search for N=2 minimal model orientifold spectra which contain the standard model and are free of tachyons and tadpoles at lowest order. For each class of tachyon-free closed strings - bulk supersymmetry, automorphism invariants or Klein bottle projection - we do indeed find non-supersymmetric and tachyon free chiral brane configurations that contain the standard model. However, a tadpole-cancelling hidden sector could only be found in the case of bulk supersymmetry. Although about half of the examples we have found make use of branes that break the bulk space-time supersymmetry, the resulting massless open string spectra are nevertheless supersymmetric in all cases. Dropping the requirement that the standard model be contained in the spectrum, we find chiral tachyon and tadpole-free solutions in all three cases, although in the case of bulk supersymmetry all massless spectra are supersymmetric. In the other two cases we find truly non-supersymmetric spectra, but a large fraction of them are nevertheless partly or fully supersymmetric at the massless level.
Spectral properties in supersymmetric matrix models
Boulton, Lyonell, E-mail: L.Boulton@hw.ac.uk [Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom); Garcia del Moral, Maria Pilar, E-mail: garciamormaria@uniovi.es [Departamento de Fisica, Universidad de Oviedo, Avda Calvo Sotelo 18, 33007 Oviedo (Spain); Restuccia, Alvaro, E-mail: arestu@usb.ve [Departamento de Fisica, Universidad Simon Bolivar, Apartado 89000, Caracas (Venezuela, Bolivarian Republic of); Departamento de Fisica, Universidad de Oviedo, Avda Calvo Sotelo 18, 33007 Oviedo (Spain)
2012-03-21
We formulate a general sufficiency criterion for discreteness of the spectrum of both supersymmmetric and non-supersymmetric theories with a fermionic contribution. This criterion allows an analysis of Hamiltonians in complete form rather than just their semiclassical limits. In such a framework we examine spectral properties of various (1+0) matrix models. We consider the BMN model of M-theory compactified on a maximally supersymmetric pp-wave background, different regularizations of the supermembrane with central charges and a non-supersymmetric model comprising a bound state of N D2 with m D0. While the first two examples have a purely discrete spectrum, the latter has a continuous spectrum with a lower end given in terms of the monopole charge.
New dualities of supersymmetric gauge theories
2016-01-01
This book reviews a number of spectacular advances that have been made in the study of supersymmetric quantum field theories in the last few years. Highlights include exact calculations of Wilson loop expectation values, and highly nontrivial quantitative checks of the long-standing electric-magnetic duality conjectures. The book starts with an introductory article presenting a survey of recent advances, aimed at a wide audience with a background and interest in theoretical physics. The following articles are written for advanced students and researchers in quantum field theory, string theory and mathematical physics, our goal being to familiarize these readers with the forefront of current research. The topics covered include recent advances in the classification and vacuum structure of large families of N=2 supersymmetric field theories, followed by an extensive discussion of the localisation method, one of the most powerful tools for exact studies of supersymmetric field theories. The quantities that have ...
The supersymmetric Dirac operator on noncommutative geometry
In order to incorporate supersymmetry, we extend naturally the spectral triple which defines noncommutative geometry and obtain a supersymmetric Dirac operator DM which acts on a Minkowskian manifold. Inversely, we can also construct a projection which reduces DM to the Dirac operator of the original spectral triple. We investigate properties of DM, some of which are inherited from the original Dirac operator. Z/2 grading and real structure are also supersymmetrically extended. We introduce a supersymmetric bilinear form and the form with DM provides the kinetic terms of chiral and antichiral supermultiplets which represent the wave functions of matter particles and their superpartners. Fluctuations of DM will be expected to produce vector supermultiplets with gauge degrees of freedom and will then lead to Super Yang–Mills theory
Maximally supersymmetric solutions of $R^2$ supergravity
Kuzenko, Sergei M
2016-01-01
There are five maximally supersymmetric backgrounds in four-dimensional off-shell N=1 supergravity, two of which are well known: Minkowski superspace M^{4|4} and anti-de Sitter superspace AdS^{4|4}. The three remaining supermanifolds support spacetimes of different topology, which are: R x S^3, AdS_3 x R, and a supersymmetric plane wave isometric to the Nappi-Witten group. As is well known, the Minkowski and anti-de Sitter superspaces are solutions of the Poincar\\'e and anti-de Sitter supergravity theories, respectively. Here we demonstrate that the other three superspaces are solutions of no-scale $R^2$ supergravity. We also present a new (probably the simplest) derivation of the maximally supersymmetric backgrounds of off-shell N=1 supergravity.
N=2 supersymmetric dynamics for pedestrians
Tachikawa, Yuji
2015-01-01
Understanding the dynamics of gauge theories is crucial, given the fact that all known interactions are based on the principle of local gauge symmetry. Beyond the perturbative regime, however, this is a notoriously difficult problem. Requiring invariance under supersymmetry turns out to be a suitable tool for analyzing supersymmetric gauge theories over a larger region of the space of parameters. Supersymmetric quantum field theories in four dimensions with extended N=2 supersymmetry are further constrained and have therefore been a fertile field of research in theoretical physics for quite some time. Moreover, there are far-reaching mathematical ramifications that have led to a successful dialogue with differential and algebraic geometry. These lecture notes aim to introduce students of modern theoretical physics to the fascinating developments in the understanding of N=2 supersymmetric gauge theories in a coherent fashion. Starting with a gentle introduction to electric-magnetic duality, the author guides r...
Supersymmetric relics from the big bang
We consider the cosmological constraints on supersymmetric theories with a new, stable particle. Circumstantial evidence points to a neutral gauge/Higgs fermion as the best candidate for this particle, and we derive bounds on the parameters in the lagrangian which govern its mass and couplings. One favored possibility is that the lightest neutral supersymmetric particle is predominantly a photino γtilde with mass above 1/2 GeV, while another is that the lightest neutral supersymmetric particle is a Higgs fermion with mass above 5 GeV or less than O(100) eV. We also point out that a gravitino mass of 10 to 100 GeV implies that the temperature after completion of an inflationary phase cannot be above 1014 GeV, and probably not above 3 x 1012 GeV. This imposes constraints on mechanisms for generating the baryon number of the universe. (orig.)
Supersymmetric relics from the big bang
The authors discuss cosmological constraints on supersymmetric theories with a new stable particle. Circumstantial evidence points to a neutral gauge/Higgs fermion as the best candidate for this particle, and they give bounds on the parameters in the Lagrangian which govern its mass and couplings. One favored possibility is that the lightest supersymmetric particle (LSP) is predominantly a photino γ/sup --/ with mass above 1/2 GeV, while another is that the lightest neutral supersymmetric particle is a Higgs fermion H/sup --/ with mass above 5 GeV or less than 0(100) eV. It is also conceivable that the LSP is a scalar neutrino upsilon/sup --/, which could have interesting phenomenological implications
Supersymmetric leptogenesis with a light hidden sector
Supersymmetric scenarios incorporating thermal leptogenesis as the origin of the observed matter-antimatter asymmetry generically predict abundances of the primordial elements which are in conflict with observations. In this paper we propose a simple way to circumvent this tension and accommodate naturally thermal leptogenesis and primordial nucleosynthesis. We postulate the existence of a light hidden sector, coupled very weakly to the Minimal Supersymmetric Standard Model, which opens up new decay channels for the next-to-lightest supersymmetric particle, thus diluting its abundance during nucleosynthesis. We present a general model-independent analysis of this mechanism as well as two concrete realizations, and describe the relevant cosmological and astrophysical bounds and implications for this dark matter scenario. Possible experimental signatures at colliders and in cosmic-ray observations are also discussed
Supersymmetric Higgs production in gluon fusion
Harlander, Robert V; Mantler, Hendrik
2010-01-01
The cross section through gluon fusion is calculated for the production of the light neutral Higgs boson through next-to-leading order QCD within the Minimal Supersymmetric Standard Model. The quark-mediated contributions are taken into account exactly, while for the genuinely supersymmetric terms we use expressions obtained in the limit of large squark, gluino and top quark masses. We present numerical results for the total inclusive cross section as well as for kinematical distributions of the Higgs boson. We also consider the effect of an MSSM-like fourth generation on the total Higgs production cross section.
Natural supersymmetric spectrum in mirage mediation
Asano, Masaki; Higaki, Tetsutaro
2012-08-01
The current results of LHC experiments exclude a large area of the light new particle region, namely, natural parameter space, in supersymmetric extension models. One of the possibilities for achieving the correct electroweak symmetry breaking naturally is the low-scale messenger scenario. Actually, the next-to-minimal supersymmetric standard model with TeV scale mirage mediation realizes the natural electroweak symmetry breaking with various mass spectra. In this paper, we show the possible mass spectrum in the scenario, e.g., the degenerate and/or hierarchical mass spectrum, and discuss these features.
Natural supersymmetric spectrum in mirage mediation
Asano, Masaki
2012-01-01
Current results of LHC experiments exclude large area of light new particle region, namely natural parameter space, in supersymmetric extension models. One of the possibilities for achieving the correct electroweak symmetry breaking naturally is low scale messenger scenario. Actually, the next-to-minimal supersymmetric standard model with TeV scale mirage mediation realizes the natural electroweak symmetry breaking with various mass spectra. In this paper, we show the possible mass spectrum in the scenario, e.g. degenerate and/or hierarchical mass spectrum, and discuss these features.
Supersymmetric asymptotic safety is not guaranteed
Intriligator, Kenneth; Sannino, Francesco
It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety in...... supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those of...
Indirect detection of heavy supersymmetric dark matter
If neutralinos reside in the galactic halo they will be captured in the Sun and annihilate therein producing high-energy neutrinos. Present limits on the flux of such neutrinos from underground detectors such as IMB and Kamiokande 2 may be used to rule out certain supersymmetric dark-matter candidates, while in many other supersymmetric models the rates are large enough that if neutralinos do reside in the galactic halo, observation of a neutrino signal may be possible in the near future. 10 refs., 2 figs
Superconformal models and the supersymmetric coulomb gas
The obtention of the supersymmetric 19-vertex model from an inhomogeneous 6-vertex model, is discussed. The 19-vertex model is considered the underlying theory and applied to calculate the partition function of the torus. A similar scheme to that for the critical models obtention, concerning the restriction procedure at special points of the gaussian line (of the 6-vertex model) is used. The critical line, in the supersymmetric model, is described by a free superfield and related to the XY model. The ''fused'' lattice models are outlined. It is shown that the results can be generalized to the models obtained by SU(2) coset construction
N=2 minimal model from 4d supersymmetric theory
Honda, Masazumi
2015-01-01
Previous studies have shown that supersymmetric partition function on $T^2 \\times S^2$ is related to elliptic genus of two dimensional supersymmetric theory. In this short note we find a four dimensional supersymmetric theory, whose partition function on $T^2 \\times S^2$ is the same as elliptic genera of $\\mathcal{N}=2$ minimal models in two dimensions.
Supersymmetric Dirac particles in external fields
A classical Lagrangian is proposed for a relativistic particle with spin. It is supersymmetric under transformations between position and spin variables. The theory can be quantized and becomes identical with conventional Dirac theory. This correspondence continues to be valid when the particle interacts with external electromagnetic or gravitational fields as long as its coupling to these fields conserves the supersymmetry. (Auth.)
Supersymmetric Model Builing (and Sweet Spot Supersymmetry)
Ibe, Masahiro; /SLAC /Stanford U., Phys. Dept.; Kitano, Ryuichiro; /Los Alamos
2008-01-08
It has been more than twenty years since theorists started discussing supersymmetric model building/phenomenology. We review mechanisms of supersymmetry breaking/mediation and problems in each scenario. We propose a simple model to address those problems and discuss its phenomenology.
The spinorial method of classifying supersymmetric backgrounds
Gran, U.; Gutowski, J.; Papadopoulos, G.; Roest, D.
2006-01-01
We review how the classification of all supersymmetric backgrounds of IIB supergravity can be reduced to the evaluation of the Killing spinor equations and their integrability conditions, which contain the field equations, on five types of spinors. This is an extension of the work [hep-th/0503046] t
Supersymplectic geometry of supersymmetric quantum field theories
We develop a conceptually new, geometric approach to supersymmetry. In particular, we argue that the construction of a generic supersymmetric theory entails only symplectic geometry either in a loop space parameterized by the bosonic degrees of freedom or in a superloop space parameterized by both bosonic and fermionic degrees of freedom. In the bosonic loop space a generic supersymmetric theory can be constructed using a model dependent loop space symplectic two-form, the corresponding symplectic one-form and a model independent vector field that determines circle action in the loop space. In the superloop space the construction of a generic supersymmetric theory employs a model independent symplectic two-form, the pertinent symplectic one-form, a model independent vector field that determines circle action in the superloop space, and the interaction is obtained by introducing a canonical transformation in the superloop space. A Poincare supersymmetric quantum field theory is a realization of our formalism in terms of space-time variables that admit a natural Lorentz-invariant interpretation. We expect that our geometric approach to supersymmetry opens a novel point of view to a large class of problems, including the mechanism of supersymmetry breaking, structure of topological field theories and even aspects of quantum integrability. (orig.)
Effective action for supersymmetrical chiral anomaly
It is proved that the consistency conditions of the type of Wess-Zumino conditions are necessary and sufficient for local integrability of supersymmetrical chiral anomaly. The global integrability condition implies discreteness of the coefficient in anomalous action. Explicit formulas for consistent anomalies and corresponding functional depending on superfields of various types are obtained
Spectral properties of supersymmetric shape invariant potentials
Barnali Chakrabarti
2008-01-01
We present the spectral properties of supersymmetric shape invariant potentials (SIPs). Although the folded spectrum is completely random, unfolded spectrum shows that energy levels are highly correlated and absolutely rigid. All the SIPs exhibit harmonic oscillator-type spectral statistics in the unfolded spectrum. We conjecture that this is the reflection of shape invariant symmetry.
Supersymmetric black lenses in five dimensions
Tomizawa, Shinya
2016-01-01
We present an asymptotically flat supersymmetric black lens solution with the horizon topology L(n,1)=S^3/Z_n in the five-dimensional minimal ungauged supergravity. We show that the black lens carries a mass, two independent angular momenta, electric charge and (n-1) magnetic fluxes, among which only the (n+1) quantities are independent.
We show that the only supersymmetric vacuum invariant under the standard gauge group has a larger symmetry given by SO(10), if one takes the Higgs in the 78 + 27 + 27 representations and the superpotential contains a term linear in the three representation. (orig.)
Buccella, F.; Miele, G.
1987-04-01
We show that the only supersymmetric vacuum invariant under the standard gauge group has a larger symmetry given by SO(10), if one takes the Higgs in the 78⊺27⊺27 representations and the superpotential contains a term linear in the three representation.
N=2 supersymmetric dynamics for dummies
Tachikawa, Yuji
2013-01-01
We give a pedagogical introduction to the dynamics of N=2 supersymmetric systems in four dimensions. The topic ranges from the Lagrangian and the Seiberg-Witten solutions of SU(2) gauge theories to Argyres-Douglas CFTs and Gaiotto dualities, while discussions on instanton integrals are intentionally left out.
Light fermion mass hierarchies in supersymmetric models
We discuss radiative fermion mass hierarchies in grand unified supersymmetric models. There are arguments in the literature that these cannot arise. It is shown that these arguments only apply to a certain type of radiative hierarchy. Another type of radiative hierarchy can arise in simple SUSY-GUTs. We discuss examples. 15 references, 5 figures
Supersymmetric particles from light meson decay
The decays π0, K0 → (invisible) are examined to determine whether they can put useful constraints on supersymmetric theories. Sneutrino and Higgsino final states are considered, and we find that the present experimental limit for π0 → (invisible) is close to the production of Higgsino of mass in the tens of MeV
Functional integral in supersymmetric quantum mechanics
The solution of the square root of the Schroedinger equation for the supersymmetric quantum mechanics is expressed in the form of series. The formula may be considered as a functional integral of the chronological exponent of the super-pseudodifferential operator symbol over the superspace. 10 refs
Exact Adler Function in Supersymmetric QCD
Shifman, M
2014-01-01
The Adler function D is found {\\em exactly} in supersymmetric QCD. Our exact formula relates D(Q^2) to the anomalous dimension of the matter superfields \\gamma (\\alpha_s(Q^2)). En rout we prove another theorem: the absence of the so-called singlet contribution to D. While such singlet contributions are present in individual supergraphs, they cancel in the sum.
Neutrino masses and mixing in supersymmetric theories
Sudhir K Vempati
2000-07-01
It has been known for sometime that supersymmetric theories with -parity violation provide a natural framework where small neutrino masses can be generated. We discuss neutrino masses and mixing in these theories in the presence of trilinear lepton number violating couplings. It will be shown that simultaneous solutions to solar and atmospheric neutrino problems can be realized in these models.
Supersymmetric Decays of the Z' Boson
Chang, Chun-Fu; Yuan, Tzu-Chiang
2011-01-01
The decay of the Z' boson into supersymmetric particles is studied. We investigate how these supersymmetric modes affect the current limits from the Tevatron and project the expected sensitivities at the LHC. Employing three representative supersymmetric Z' models, namely, E_6, U(1)_{B-L}, and the sequential model, we show that the current limits of the Z' mass from the Tevatron could be reduced substantially due to the weakening of the branching ratio into leptonic pairs. The mass reach for the E_6 Z' bosons is about 1.3-1.5 TeV at the LHC-7 (1 fb^{-1}), about 2.5 - 2.6 TeV at the LHC-10 (10 fb^{-1}), and about 4.2 - 4.3 TeV at the LHC-14 (100 fb^{-1}). A similar mass reach for the U(1)_{B-L} Z' is also obtained. We also examine the potential of identifying various supersymmetric decay modes of the Z' boson because it may play a crucial role in the detailed dynamics of supersymmetry breaking.
Lattice formulations of supersymmetric gauge theories with matter fields
Joseph, Anosh [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2014-12-15
Certain classes of supersymmetric gauge theories, including the well known N=4 supersymmetric Yang-Mills theory, that takes part in the AdS/CFT correspondence, can be formulated on a Euclidean spacetime lattice using the techniques of exact lattice supersymmetry. Great ideas such as topological field theories, Dirac-Kaehler fermions, geometric discretization all come together to create supersymmetric lattice theories that are gauge-invariant, doubler free, local and exact supersymmetric. We discuss the recent lattice constructions of supersymmetric Yang-Mills theories in two and three dimensions coupled to matter fields in various representations of the color group.
(Non-)decoupled supersymmetric field theories
We study some consequences of coupling supersymmetric theories to (super)gravity. To linear order, the couplings are determined by the energy-momentum supermultiplet. At higher orders, the couplings are determined by contact terms in correlation functions of the energy-momentum supermultiplet. We focus on the couplings of one particular field in the supergravity multiplet, the auxiliary field M. We discuss its linear and quadratic (seagull) couplings in various supersymmetric theories. In analogy to the local renormalization group formalism (http://dx.doi.org/10.1016/0370-2693(89)90729-6; http://dx.doi.org/10.1016/0550-3213(90)90584-Z; http://dx.doi.org/10.1016/0550-3213(91)80030-P), we provide a prescription for how to fix the quadratic couplings. They generally arise at two-loops in perturbation theory. We check our prescription by explicitly computing these couplings in several examples such as mass-deformed N=4 and in the Coulomb phase of some theories. These couplings affect the Lagrangians of rigid supersymmetric theories in curved space. In addition, our analysis leads to a transparent derivation of the phenomenon known as Anomaly Mediation. In contrast to previous approaches, we obtain both the gaugino and scalar masses of Anomaly Mediation by relying just on classical, minimal supergravity and a manifestly local and supersymmetric Wilsonian point of view. Our discussion naturally incorporates the connection between Anomaly Mediation and supersymmetric AdS4 Lagrangians. This note can be read without prior familiarity with Anomaly Mediated Supersymmetry Breaking (AMSB)
(Non-)decoupled supersymmetric field theories
Pietro, Lorenzo Di [Department of Particle Physics and Astrophysics,Weizmann Institute of Science, Rehovot 76100 (Israel); Dine, Michael [Santa Cruz Institute for Particle Physics and Department of Physics,Santa Cruz CA 95064 (United States); Komargodski, Zohar [Department of Particle Physics and Astrophysics,Weizmann Institute of Science, Rehovot 76100 (Israel)
2014-04-10
We study some consequences of coupling supersymmetric theories to (super)gravity. To linear order, the couplings are determined by the energy-momentum supermultiplet. At higher orders, the couplings are determined by contact terms in correlation functions of the energy-momentum supermultiplet. We focus on the couplings of one particular field in the supergravity multiplet, the auxiliary field M. We discuss its linear and quadratic (seagull) couplings in various supersymmetric theories. In analogy to the local renormalization group formalism (http://dx.doi.org/10.1016/0370-2693(89)90729-6; http://dx.doi.org/10.1016/0550-3213(90)90584-Z; http://dx.doi.org/10.1016/0550-3213(91)80030-P), we provide a prescription for how to fix the quadratic couplings. They generally arise at two-loops in perturbation theory. We check our prescription by explicitly computing these couplings in several examples such as mass-deformed N=4 and in the Coulomb phase of some theories. These couplings affect the Lagrangians of rigid supersymmetric theories in curved space. In addition, our analysis leads to a transparent derivation of the phenomenon known as Anomaly Mediation. In contrast to previous approaches, we obtain both the gaugino and scalar masses of Anomaly Mediation by relying just on classical, minimal supergravity and a manifestly local and supersymmetric Wilsonian point of view. Our discussion naturally incorporates the connection between Anomaly Mediation and supersymmetric AdS{sub 4} Lagrangians. This note can be read without prior familiarity with Anomaly Mediated Supersymmetry Breaking (AMSB)
Supersymmetric solutions to Euclidean Romans supergravity
Alday, Luis F.; Fluder, Martin; Gregory, Carolina Matte; Richmond, Paul; Sparks, James
2016-02-01
We study Euclidean Romans supergravity in six dimensions with a non-trivial Abelian R-symmetry gauge field. We show that supersymmetric solutions are in one-to-one correspondence with solutions to a set of differential constraints on an SU(2) structure. As an application of our results we (i) show that this structure reduces at a conformal boundary to the five-dimensional rigid supersymmetric geometry previously studied by the authors, (ii) find a general expression for the holographic dual of the VEV of a BPS Wilson loop, matching an exact field theory computation, (iii) construct holographic duals to squashed Sasaki-Einstein backgrounds, again matching to a field theory computation, and (iv) find new analytic solutions.
The gravitino problem in supersymmetric warm inflation
The warm inflation paradigm considers the continuous production of radiation during inflation due to dissipative effects. In its strong dissipation limit, warm inflation gives way to a radiation dominated Universe. High scale inflation then yields a high reheating temperature, which then poses a severe gravitino overproduction problem for the supersymmetric realisations of warm inflation. In this paper we show that, in a certain class of supersymmetric models, the dissipative dynamics of the inflaton is such that the field can avoid its complete decay after inflation. In some cases, the residual energy density stored in the inflaton field oscillations may come to dominate over the radiation bath at a later epoch. If the inflaton field finally decays much later than the onset of this matter dominated phase, the entropy produced from its decay may be sufficient to counteract the excess of gravitinos produced during the last stages of warm inflation
Mapping Anomalous Currents in Supersymmetric Dualities
Abel, Steven; Komargodski, Zohar
2011-01-01
In many strongly-coupled systems, the infrared dynamics is described by different degrees of freedom from the ultraviolet. It is then natural to ask how operators written in terms of the microscopic variables are mapped to operators composed of the macroscopic ones. Certain types of operators, like conserved currents, are simple to map, and in supersymmetric theories one can also follow the chiral ring. In this note, we consider supersymmetric theories and extend the mapping to anomalous currents (and gaugino bilinears). Our technique is completely independent of subtleties associated with the renormalization group, thereby shedding new light on previous approaches to the problem. We demonstrate the UV/IR mapping in several examples with different types of dynamics, emphasizing the uniformity and simplicity of the approach. Natural applications of these ideas include the effects of soft breaking on the dynamics of various theories and new models of electroweak symmetry breaking.
The semiclassical approximation to supersymmetric quantum gravity
Kiefer, C; Moniz, P; Kiefer, Claus; Lueck, Tobias; Moniz, Paulo
2005-01-01
We develop a semiclassical approximation scheme for the constraint equations of supersymmetric canonical quantum gravity. This is achieved by a Born-Oppenheimer type of expansion, in analogy to the case of the usual Wheeler-DeWitt equation. The formalism is only consistent if the states at each order depend on the gravitino field. We recover at consecutive orders the Hamilton-Jacobi equation, the functional Schrodinger equation, and quantum gravitational correction terms to this Schrodinger equation. In particular, the following consequences are found: (i) the Hamilton-Jacobi equation and therefore the background spacetime must involve the gravitino, (ii) a (many fingered) local time parameter has to be present on $SuperRiem \\Sigma$ (the space of all possible tetrad and gravitino fields), (iii) quantum supersymmetric gravitational corrections affect the evolution of the very early universe. The physical meaning of these equations and results, in particular the similarities to and differences from the pure bos...
Flavor Mixing Phenomenology in Supersymmetric Models
Rehman, Muhammad
2016-01-01
This dissertation investigates the flavor mixing effects in supersymmetric models on electroweak precision observables, Higgs boson mass predictions, B-physics observables, quark flavor violating Higgs decays, lepton flavor violating charged lepton decays and lepton flavor violating Higgs decays. The flavor mixing effects are studied in model independent way i.e. by putting off-diagonal entries in the sfermion mass matrix by hand as well as in the minimal flavor violating constrained MSSM, where mixing can originate from CKM matrix in the case of squarks and from PMNS matrix in the case of sleptons. We found that flavor mixing can have large impact to some observables, enabling us to put new constraints on parameter space in supersymmetric models.
Phenomenology of the utilitarian supersymmetric standard model
Fraser, Sean; Kownacki, Corey; Ma, Ernest; Pollard, Nicholas; Popov, Oleg; Zakeri, Mohammadreza
2016-08-01
We study the 2010 specific version of the 2002 proposed U(1)X extension of the supersymmetric standard model, which has no μ term and conserves baryon number and lepton number separately and automatically. We consider in detail the scalar sector as well as the extra ZX gauge boson, and their interactions with the necessary extra color-triplet particles of this model, which behave as leptoquarks. We show how the diphoton excess at 750 GeV, recently observed at the LHC, may be explained within this context. We identify a new fermion dark-matter candidate and discuss its properties. An important byproduct of this study is the discovery of relaxed supersymmetric constraints on the Higgs boson's mass of 125 GeV.
Nontrivial fermion states in supersymmetric minisuperspace
Csordás, A; Csordas, Andras; Graham, Robert
1995-01-01
In this lecture supersymmetric minisuperspace models of any Bianchi type within class A of the classification of Ellis and McCallum are considered. The algebra of the supersymmetry generators, the Lorentz generators, the diffeomorphism generators and the Hamiltonian generator is determined explicitely and found to close. Different from earlier work it is established that physical states, which are annihilated by all these generators, exist in {\\it all } sectors of these models with fixed even fermion number. A state in the 4-fermion sector of the Bianchi type IX model is considered as a specific example, which satisfies the `no-boundary' condition of Hartle and Hawking. The conclusion is that supersymmetric minisuperspace models have a much richer manifold of physical states than had been recognized before.
Heterotic supersymmetric backgrounds with compact holonomy revisited
We simplify the classification of supersymmetric solutions with compact holonomy of the Killing spinor equations of heterotic supergravity using the field equations and the additional assumption that the 3-form flux is closed. We determine all the fractions of supersymmetry that the solutions preserve and find that there is a restriction on the number of supersymmetries which depends on the isometry group of the background. We examine the geometry of spacetime in all cases. We find that the supersymmetric solutions of heterotic supergravity are associated with a large number of geometric structures which include seven-dimensional manifolds with G2 structure, six-dimensional complex and almost complex manifolds, and four-dimensional hyper-Kaehler, Kaehler and anti-self-dual Weyl manifolds.
Isomonodromic deformations and supersymmetric gauge theories
Takasaki, K; Takasaki, Kanehisa; Nakatsu, Toshio
1996-01-01
Seiberg-Witten solutions of four-dimensional supersymmetric gauge theories possess rich but involved integrable structures. The goal of this paper is to show that an isomonodromy problem provides a unified framework for understanding those various features of integrability. The Seiberg-Witten solution itself can be interpreted as a WKB limit of this isomonodromy problem. The origin of underlying Whitham dynamics (adiabatic deformation of an isomonodromy problem), too, can be similarly explained by a more refined asymptotic method (multiscale analysis). The case of N=2 SU(s) supersymmetric Yang-Mills theory without matter is considered in detail for illustration. The isomonodromy problem in this case is closely related to the third Painlev\\'e equation and its multicomponent analogues. An implicit relation to t\\tbar fusion of topological sigma models is thereby expected.
Supersymmetric QCD: Exact Results and Strong Coupling
Dine, Michael; Pack, Lawrence; Park, Chang-Soon; Ubaldi, Lorenzo; Wu, Weitao
2011-01-01
We revisit two longstanding puzzles in supersymmetric gauge theories. The first concerns the question of the holomorphy of the coupling, and related to this the possible definition of an exact (NSVZ) beta function. The second concerns instantons in pure gluodynamics, which appear to give sensible, exact results for certain correlation functions, which nonetheless differ from those obtained using systematic weak coupling expansions. For the first question, we extend an earlier proposal of Arkani-Hamed and Murayama, showing that if their regulated action is written suitably, the holomorphy of the couplings is manifest, and it is easy to determine the renormalization scheme for which the NSVZ formula holds. This scheme, however, is seen to be one of an infinite class of schemes, each leading to an exact beta function; the NSVZ scheme, while simple, is not selected by any compelling physical consideration. For the second question, we explain why the instanton computation in the pure supersymmetric gauge theory is...
Topological solitons in the supersymmetric Skyrme model
Gudnason, Sven Bjarke; Sasaki, Shin
2016-01-01
A supersymmetric extension of the Skyrme model was obtained recently, which consists of only the Skyrme term in the Nambu-Goldstone (pion) sector complemented by the same number of quasi-Nambu-Goldstone bosons. Scherk-Schwarz dimensional reduction yields a kinetic term in three or lower dimensions and a potential term in two dimensions, preserving supersymmetry. Euclidean solitons (instantons) are constructed in the supersymmetric Skyrme model. In four dimensions, the soliton is an instanton first found by Speight. Scherk-Schwarz dimensional reduction is then performed once to get a 3-dimensional theory in which a 3d Skyrmion-instanton is found and then once more to get a 2d theory in which a 2d vortex-instanton is obtained. Although the last one is a global vortex it has finite action in contrast to conventional theory. All of them are non-BPS states breaking all supersymmetries.
Measuring And Explaining The Supersymmetric Lagrangian
Wang, L
2002-01-01
The issues of measuring the supersymmetric Lagrangian once data is available, and making the connections between the low energy effective Lagrangian and fundamental theory, are considered. After a brief introduction to the fundamentals of supersymmetry and overview of Minimal Supersymmetric Standard Model (MSSM), case studies in ways of measuring different parameters in the low energy MSSM Lagrangian are presented. They include: measuring CP violation phases and LSP masses in gluino decay; Higgs production and detection; flavor and CP violation in b → sγ processes; signature of cold dark matter in the cosmic rays. Potential ambiguities in the process of recovering the high energy effective Lagrangian from low energy data are discussed. A new basis, which is explicitly independent of unphysical parameters, is proposed to write the renormalization group equations. After a brief survey of some basic issues of string theory phenomenology, a string theory motivated Pati-Salam like model is const...
Higgcision in the Minimal Supersymmetric Standard Model
Cheung, Kingman; Tseng, Po-Yan
2015-01-01
We perform global fits to the most recent data (after summer 2014) on Higgs boson signal strengths in the framework of the minimal supersymmetric standard model (MSSM). The heavy supersymmetric (SUSY) particles such as squarks enter into the loop factors of the $Hgg$ and $H\\gamma\\gamma$ vertices while other SUSY particles such as sleptons and charginos also enter into that of the $H\\gamma\\gamma$ vertex. We also take into account the possibility of other light particles such as other Higgs bosons and neutralinos, such that the 125.5 GeV Higgs boson can decay into. We use the data from the ATLAS, CMS, and the Tevatron, with existing limits on SUSY particles, to constrain on the relevant SUSY parameters. We obtain allowed regions in the SUSY parameter space of squark, slepton and chargino masses, and the $\\mu$ parameter.
Supersymmetric composite gauge fields with compensators
Nishino, Hitoshi; Rajpoot, Subhash
2016-06-01
We study supersymmetric composite gauge theory, supplemented with compensator mechanism. As our first example, we give the formulation of N = 1 supersymmetric non-Abelian composite gauge theory without the kinetic term of a non-Abelian gauge field. The important ingredient is the Proca-Stueckelberg-type compensator scalar field that makes the gauge-boson field equation non-singular, i.e., the field equation can be solved for the gauge field algebraically as a perturbative expansion. As our second example, we perform the gauging of chiral-symmetry for N = 1 supersymmetry in four dimensions by a composite gauge field. These results provide supporting evidence for the consistency of the mechanism that combines the composite gauge field formulations and compensator formulations, all unified under supersymmetry.
Phenomenology of the Utilitarian Supersymmetric Standard Model
Fraser, Sean; Ma, Ernest; Pollard, Nicholas; Popov, Oleg; Zakeri, Mohammadreza
2016-01-01
We study the 2010 specific version of the 2002 proposed $U(1)_X$ extension of the supersymmetric standard model, which has no $\\mu$ term and conserves baryon number and lepton number separately and automatically. We consider in detail the scalar sector as well as the extra $Z_X$ gauge boson, and their interactions with the necessary extra color-triplet particles of this model, which behave as leptoquarks. We show how the diphoton excess at 750 GeV, recently observed at the LHC, may be explained within this context. We identify a new fermion dark-matter candidate and discuss its properties. An important byproduct of this study is the discovery of relaxed supersymmetric constraints on the Higgs boson's mass of 125 GeV.
Supersymmetric Goedel Universes in string theory
Supersymmetric backgrounds in string and M-theory of the Goedel Universe type are studied. We find several new Goedel Universes that preserve up to 20 supersymmetries. In particular, we obtain an interesting Goedel Universe in M-theory with 18 supersymmetries which does not seem to be dual to a pp-wave. We show that not only T-duality but also the type-IIA/M-theory S-duality can give supersymmetric Goedel Universes from pp-waves. We find solutions that can interpolate between Goedel Universes and pp-waves. We also compute the string spectrum on two type IIA Goedel Universes. Furthermore, we obtain the spectrum of D-branes on a Goedel Universe and find the supergravity solution for a D4-brane on a Goedel Universe
Proton stability in supersymmetric SU(5)
Within supersymmetric SU(5) grand unified theory (GUT) we suggest mechanisms for suppression of baryon number violating dimension five and six operators. The mechanism is based on the idea of split multiplets (i.e. quarks and leptons are not coming from a single GUT state) which is realized by an extension with additional vectorlike matter. The construction naturally avoids wrong asymptotic relation M-circumflexD=M-circumflexE. Thus, the long-standing problems of the minimal supersymmetric SU(5) GUT can be resolved. In a particular example of flavor structure and with additional U(1)xZ3N symmetry we demonstrate how the split multiplet mechanism works out. Namely, the considered model is compatible with successful gauge coupling unification and realistic fermion mass pattern. The nucleon decay rates are relatively suppressed and can be well compatible with current experimental bounds
Supersymmetric gauge theories, vortices and equivariant cohomology
Machin, W; Papadopoulos, G [Department of Mathematics, King' s College London, Strand, London WC2R 2LS (United Kingdom)
2003-04-07
We construct actions for (p, 0)- and (p, 1)-supersymmetric, 1 {<=} p {<=} 4, two-dimensional gauge theories coupled to nonlinear sigma model matter with a Wess-Zumino term. We derive the scalar potential for a large class of these models. We then show that the Euclidean actions of the (2, 0)- and (4, 0)-supersymmetric models without Wess-Zumino terms are bounded by topological charges which involve the equivariant extensions of the Kaehler forms of the sigma model target spaces evaluated on the two-dimensional spacetime. We give similar bounds for Euclidean actions of appropriate gauge theories coupled to nonlinear sigma model matter in higher spacetime dimensions which now involve the equivariant extensions of the Kaehler forms of the sigma model target spaces and the second Chern character of gauge fields. The BPS configurations are generalizations of Abelian and non-Abelian vortices.
Spinorial cohomology and maximally supersymmetric theories
Fields in supersymmetric gauge theories may be seen as elements in a spinorial cohomology. We elaborate on this subject, specialising to maximally supersymmetric theories, where the superspace Bianchi identities, after suitable conventional constraints are imposed, put the theories on shell. In these cases, the spinorial cohomologies describe in a unified manner gauge transformations, fields and possible deformations of the models, e.g. string-related corrections in an α' expansion. Explicit cohomologies are calculated for super-Yang-Mills theory in D=10, for the N=(2,0) tensor multiplet in D=6 and for supergravity in D=11, in the latter case from the point of view of both the super-vielbein and the super-3-form potential. The techniques may shed light on some questions concerning the α'-corrected effective theories, and result in better understanding of the role of the 3-form in D=11 supergravity. (author)
CP violation versus flavour in supersymmetric theories
Abel, S.; Branco, G. C.; Khalil, S.
2003-09-01
We show that the quark flavour structure and CP violating phenomena are strongly correlated in supersymmetric theories. For a generic pattern of supersymmetry breaking the two broad categories of Yukawa couplings, democratic and hierarchical textures, have entirely different phenomenological implications. With hierarchical Yukawas, the rephasing invariant phase, arg(VusVcbVcb∗Vcs∗), in the CKM mixing matrix has to be of order unity, while the SUSY CP violating phases are severely constrained by electric dipole moments, giving rise to the so-called SUSY CP problem. With democratic Yukawas, all experimental CP results can be accommodated with small values for the CKM and SUSY CP violating phases (i.e., CP can be considered as an approximate symmetry at the high energy scale). We also show that within this scenario, an entirely real CKM matrix in supersymmetric models is still allowed by the present experimental results.
CP violation versus flavour in supersymmetric theories
Abel, S A; Khalil, S
2003-01-01
We show that the quark flavour structure and CP violating phenomena are strongly correlated in supersymmetric theories. For a generic pattern of supersymmetry breaking the two broad categories of Yukawa couplings, democratic and hierarchical textures, have entirely different phenomenological implications. With hierarchical Yukawas, the rephasing invariant phase, arg(V_us V_cb V_cb^* V_cs^*), in the CKM mixing matrix has to be of order unity, while the SUSY CP violating phases are severely constrained by electric dipole moments, giving rise to the so-called SUSY CP problem. With democratic Yukawas, all experimental CP results can be accommodated with small values for the CKM and SUSY CP violating phases (i.e., CP can be considered as an approximate symmetry at the high energy scale). We also show that within this scenario, an entirely real CKM matrix in supersymmetric models is still allowed by the present experimental results.
On supersymmetric effective theories of axion
Higaki, Tetsutaro [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Kitano, Ryuichiro [Tohoku Univ., Sendai (Japan). Dept. of Physics
2011-04-15
We study effective theories of an axion in spontaneously broken supersymmetric theories. We consider a system where the axion supermultiplet is directly coupled to a supersymmetry breaking sector whereas the standard model sector is communicated with those sectors through loops of messenger fields. The gaugino masses and the axion-gluon coupling necessary for solving the strong CP problem are both obtained by the same effective interaction. We discuss cosmological constraints on this framework. (orig.)
Thermal leptogenesis in extended supersymmetric seesaw
Hirsch, M; Romão, J C; Sarkar, U; Valle, J W F
2007-01-01
We consider an extended supersymmetric SO(10) seesaw model with only doublet Higgs scalars, in which neutrino masses are suppressed by the scale of D-parity violation. Leptogenesis can occur at the TeV scale through the decay of a singlet Sigma, thereby avoiding the gravitino crisis. Washout of the asymmetry can be effectively suppressed by the absence of direct couplings of Sigma to leptons.
Symmetries of N = 4 supersymmetric CPn mechanics
We explicitly constructed the generators of the SU(n + 1) group that commute with the supercharges of N = 4 supersymmetric CPn mechanics in the background U(n) gauge fields. The corresponding classical Hamiltonian can be represented as a direct sum of two Casimir operators: one Casimir operator on the SU(n + 1) group contains our bosonic and fermionic coordinates and momenta, while the second one, on the SU(1, n) group, is constructed from isospin degrees of freedom only. (paper)
Equivariant Localization for Supersymmetric Quantum Mechanics
Akant, Levent
2005-01-01
We apply equivariant localization to supersymmetric quantum mechanics and show that the partition function localizes on the instantons of the theory. Our construction of equivariant cohomology for SUSY quantum mechanics is different than the ones that already exist in the literature. A hidden bosonic symmetry is made explicit and the supersymmetry is extended. New bosonic symmetry is the square of the new fermionic symmetry. The D term is now the parameter of the bosonic symmetry. This constr...
Additional symmetries of supersymmetric KP hierarchies
We investigate the additional symmetries of several supersymmetric KP hierarchies: the SKP hierarchy of Manin and Radul, the SKP2 hierarchy, and the Jacobian SKP hierarchy. In all three cases we find that the algebra of symmetries is isomorphic to the algebra of superdifferential operators, or equivalently SW1+∞. These results seem to suggest that despite their realization depending on the dynamics, the additional symmetries are kinematical in nature. (orig.)
On supersymmetric effective theories of axion
We study effective theories of an axion in spontaneously broken supersymmetric theories. We consider a system where the axion supermultiplet is directly coupled to a supersymmetry breaking sector whereas the standard model sector is communicated with those sectors through loops of messenger fields. The gaugino masses and the axion-gluon coupling necessary for solving the strong CP problem are both obtained by the same effective interaction. We discuss cosmological constraints on this framework. (orig.)
The goldstone and goldstino of supersymmetric inflation
Kahn, Yonatan; Roberts, Daniel; Thaler, Jesse
2015-01-01
We construct the minimal effective field theory (EFT) of supersymmetric inflation, whose field content is a real scalar, the goldstone for time-translation breaking, and a Weyl fermion, the goldstino for supersymmetry (SUSY) breaking. The inflating background can be viewed as a single SUSY-breaking sector, and the degrees of freedom can be efficiently parameterized using constrained superfields. Our EFT is comprised of a chiral superfield X [subscript NL] containing the goldstino and satisfyi...
Supersymmetric black holes in string theory
Mohaupt, T.
2007-01-01
We review recent developments concerning supersymmetric black holes in string theory. After a general introduction to the laws of black hole mechanics and to black hole entropy in string theory, we discuss black hole solutions in N=2 supergravity, special geometry, the black hole attractor equations and the underlying variational principle. Special attention is payed to the crucial role of higher derivative corrections. Finally we discuss black hole partition functions and their relation to t...
Domain Walls Zoo in Supersymmetric QCD
Smilga, A V
1998-01-01
Solving numerically the equations of motion for the effective lagrangian describing supersymmetric QCD with the SU(2) gauge group, we find a menagerie of complex domain wall solutions connecting different chirally asymmetric vacua. Some of these solutions are BPS saturated walls; they exist when the mass of the matter fields does not exceed some critical value m m*, the complex walls disappear altogether and only the walls connecting a chirally asymmetric vacuum with the chirally symmetric one survive.
Domain Walls Zoo in Supersymmetric QCD
Smilga, A. V.; Veselov, A. I.
1997-01-01
Solving numerically the equations of motion for the effective lagrangian describing supersymmetric QCD with the SU(2) gauge group, we find a menagerie of complex domain wall solutions connecting different chirally asymmetric vacua. Some of these solutions are BPS saturated walls; they exist when the mass of the matter fields does not exceed some critical value m < m* < 4.67059... There are also sphaleron branches (saddle points of the ebergy functional). In the range m* < m < m** \\approx 4.83...
The geometry of supersymmetric partition functions
Cyril Closset; Dumitrescu, Thomas T.; Guido Festuccia; Zohar Komargodski
2014-01-01
We consider supersymmetric field theories on compact manifolds $ \\mathcal{M} $ and obtain constraints on the parameter dependence of their partition functions $ {Z_{\\mathcal{M}}} $ . Our primary focus is the dependence of $ {Z_{\\mathcal{M}}} $ on the geometry of $ \\mathcal{M} $ , as well as background gauge fields that couple to continuous flavor symmetries. For $ \\mathcal{N} $ = 1 theories with a U(1) R symmetry in four dimensions, $ \\mathcal{M} $ must be a complex manifold with a Hermitian ...
A realistic renormalizable supersymmetric E6 model
Bajc, Borut
2013-01-01
A complete realistic model based on the supersymmetric version of $E_6$ is presented. It consists of three copies of matter 27, and a Higgs sector made of $2\\times(27+\\bar{27})+351'+\\bar{351'}$ representations. An analytic solution to the equations of motion is found which spontaneously breaks the gauge group into the Standard Model. The light fermion mass matrices are written down explicitly as non-linear functions of three Yukawa matrices. This contribution is based on Ref. [1].
Hyperconfluent third-order supersymmetric quantum mechanics
C, David J Fernandez
2011-01-01
The hyperconfluent third-order supersymmetric quantum mechanics, in which all the factorization energies tend to a common value, is analyzed. It will be shown that the final potential as well can be achieved by applying consecutively a confluent second-order and a first-order SUSY transformations, both with the same factorization energy. The technique will be applied to the free particle and the Coulomb potential.
Non-supersymmetric Orientifolds of Gepner Models
Gato-Rivera, B
2008-01-01
Starting from a previously collected set of tachyon-free closed strings, we search for N=2 minimal model orientifold spectra which contain the standard model and are free of tachyons and tadpoles at lowest order. For each class of tachyon-free closed strings -- bulk supersymmetry, automorphism invariants or Klein bottle projection -- we do indeed find non-supersymmetric and tachyon free chiral brane configurations that contain the standard model. However, a tadpole-cancelling hidden sector could only be found in the case of bulk supersymmetry. Although about half of the examples we have found make use of branes that break the bulk space-time supersymmetry, the resulting massless open string spectra are nevertheless supersymmetric in all cases. Dropping the requirement that the standard model be contained in the spectrum, we find chiral tachyon and tadpole-free solutions in all three cases, although in the case of bulk supersymmetry all massless spectra are supersymmetric. In the other two cases we find truly ...
Cosmological consequences of supersymmetric flat directions
Riva, Francesco; Sarkar, Subir; Giudice, Gian
In this work we analyze various implications of the presence of large field vacum expectation values (VEVs) along supersymmetric flat direct ions during the early universe. First, we discuss supersymmetric leptogenesis and the grav itino bound. Supersym- metric thermal leptogenesis with a hierarchical right-han ded neutrino mass spectrum normally requires the mass of the lightest right-handed neu trino to be heavier than about 10 9 GeV. This is in conflict with the upper bound on the reheating t empera- ture which is found by imposing that the gravitinos generate d during the reheating stage after inflation do not jeopardize successful nucleosy nthesis. We show that a solution to this tension is actually already incorporated i n the framework, because of the presence of flat directions in the supersymmetric scalar potential. Massive right- handed neutrinos are efficiently produced non-thermally and the observed baryon asymmetry can be explained even for a reheating temperature respecting the grav- itino bound...
Non-supersymmetric Black Holes and Topological Strings
Saraikin, Kirill; Vafa, C.
2007-01-01
We study non-supersymmetric, extremal 4 dimensional black holes which arise upon compactification of type II superstrings on Calabi-Yau threefolds. We propose a generalization of the OSV conjecture for higher derivative corrections to the non-supersymmetric black hole entropy, in terms of the one parameter refinement of topological string introduced by Nekrasov. We also study the attractor mechanism for non-supersymmetric black holes and show how the inverse problem of fixing charges in terms...
Anti-Periodic Boundary Conditions in Supersymmetric DLCQ
Pinsky, S.; Trittmann, U.
2000-01-01
It is of considerable importance to have a numerical method for solving supersymmetric theories that can support a non-zero central charge. The central charge in supersymmetric theories is in general a boundary integral and therefore vanishes when one uses periodic boundary conditions. One is therefore prevented from studying BPS states in the standard supersymmetric formulation of DLCQ (SDLCQ). We present a novel formulation of SDLCQ where the fields satisfy anti-periodic boundary conditions...
On supersymmetric Chern-Simons-type theories in five dimensions
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.
Vertex Operators for Irregular Conformal Blocks: Supersymmetric Case
Polyakov, Dimitri
2016-01-01
We construct supersymmetric irregular vertex operators of arbitrary rank, appearing in the colliding limit of primary fields. We find that the structure of the supersymmetric irregular vertices differs significantly from the bosonic case: upon supersymmetrization, the irregular operators are no longer the eigenstates of positive Virasoro and $W_N$ generators but block-diagonalize them. We relate the block-diagonal structure of the irregular vertices to contributions of the Ramond sector to the colliding limit.
Supersymmetric Contributions to the Decay of an Extra Z Boson
Gherghetta, Tony; Kaeding, Thomas A.; Kane, Gordon L.
1997-01-01
We analyse in detail the supersymmetric contributions to the decay of an extra Z boson in effective rank 5 models, including the important effect of D-terms on sfermion masses. The inclusion of supersymmetric decay channels will reduce the Z' branching ratio to standard model particles resulting in lower Z' mass limits than those often quoted. In particular, the supersymmetric parameter space motivated by the recent Fermilab $ee\\gamma\\gamma$ event and other suggestive evidence results in a br...
Deviations From Newton's Law in Supersymmetric Large Extra Dimensions
Callin, P.; Burgess, C. P.
2005-01-01
Deviations from Newton's Inverse-Squared Law at the micron length scale are smoking-gun signals for models containing Supersymmetric Large Extra Dimensions (SLEDs), which have been proposed as approaches for resolving the Cosmological Constant Problem. Just like their non-supersymmetric counterparts, SLED models predict gravity to deviate from the inverse-square law because of the advent of new dimensions at sub-millimeter scales. However SLED models differ from their non-supersymmetric count...
Non-renormalization theorems andN=2 supersymmetric backgrounds
The conditions for fully supersymmetric backgrounds of general N = 2 locally supersymmetric theories are derived based on the off-shell superconformal multiplet calculus. This enables the derivation of a non-renormalization theorem for a large class of supersymmetric invariants with higher-derivative couplings. The theorem implies that the invariant and its first order variation must vanish in a fully supersymmetric background. The conjectured relation of one particular higher-derivative invariant with a specific five-dimensional invariant containing the mixed gauge-gravitational Chern-Simons term is confirmed
Supersymmetric Quantum Hall Liquid with a Deformed Supersymmetry
Hasebe, Kazuki
2009-01-01
We construct a supersymmetric quantum Hall liquid with a deformed supersymmetry. One parameter is introduced in the supersymmetric Laughlin wavefunction to realize the original Laughlin wavefunction and the Moore-Read wavefunction in two extremal limits of the parameter. The introduced parameter corresponds to the coherence factor in the BCS theory. It is pointed out that the parameter-dependent supersymmetric Laughlin wavefunction enjoys a deformed supersymmetry. Based on the deformed supersymmetry, we construct a pseudo-potential Hamiltonian whose groundstate is exactly the parameter-dependent supersymmetric Laughlin wavefunction. Though the SUSY pseudo-potential Hamiltonian is parameter-dependent and non-Hermitian, its eigenvalues are parameter-independent and real.
Equivariant Localization for Supersymmetric Quantum Mechanics
Akant, L
2005-01-01
We apply equivariant localization to supersymmetric quantum mechanics and show that the partition function localizes on the instantons of the theory. Our construction of equivariant cohomology for SUSY quantum mechanics is different than the ones that already exist in the literature. A hidden bosonic symmetry is made explicit and the supersymmetry is extended. New bosonic symmetry is the square of the new fermionic symmetry. The D term is now the parameter of the bosonic symmetry. This construction provides us with an equivariant complex together with a Cartan differential and makes the use of localization principle possible.
On Geometric Engineering of Supersymmetric Gauge Theories
Belhaj, Adil
2000-01-01
We present the basic ideas of geometric engineering of the supersymmetric quantum field theories viewed as a low energy limit of type II strings and F-theory on singular Calabi Yau manifolds. We first give the main lines of toric geometry as it is a powerful technique to deal compact complex manifolds. Then we introduce mirror symmetry which plays a crucial role in the study of superstring dualities and finally we give elements on Calabi Yau singularities. After that we study the geometric en...
Supersymmetric Gauge Theories from String Theory
Metzger, Steffen
2005-01-01
The subject of this thesis are various ways to construct four-dimensional quantum field theories from string theory. In a first part we study the generation of a supersymmetric Yang-Mills theory, coupled to an adjoint chiral superfield, from type IIB string theory on non-compact Calabi-Yau manifolds, with D-branes wrapping certain subcycles. Properties of the gauge theory are then mapped to the geometric structure of the Calabi-Yau space. In particular, the low energy effective superpotential...
Masses of Higgs bosons in supersymmetric theories
A simple method for Higgs boson mass calculation in the MSSM and in its minimal extension, the so-called next-to-minimal supersymmetric standard model (NMSSM), is suggested. The approach is based on the hierarchic structure of the mass matrix. Such matrices are obtained within the framework of MSSM and NMSSM. The simple analytical expression for Higgs boson spectrum in both these models are obtained. It was shown that the mass of the lightest Higgs boson in the NMSSM can be essentially lighter than its upper bound
Covariant Hamiltonian evolution in supersymmetric quantum systems
Schreiber, U
2003-01-01
We develop a general formalism for covariant Hamiltonian evolution of supersymmetric (field) theories by making use of the fact that these can be represented on the exterior bundle over their bosonic configuration space as generalized Dirac-Kaehler systems of the form $(d \\pm d^\\dag)\\ket{\\psi} = 0$. By using suitable deformations of the supersymmetry generators we find covariant Hamiltonians for target spaces with general gravitational and Kalb-Ramond field backgrounds and discuss their perturbation theory. Our results will be applied in another paper to the study of curvature corrections to superstring spectra in nontrivial backgrounds, such as ${\\rm AdS}$ close to its pp-wave limit.
Supersymmetric Z' decays at the LHC
Corcella, Gennaro
2015-01-01
Searching for Z' bosons, predicted in GUT-inspired U(1)' gauge models and in the Sequential Standard Model, is one of the main challenges of the experiments carried out at the Large Hadron Collider. Such searches have so far focused on high-mass dilepton pairs, assuming that the Z' has only Standard Model decay modes, and have set mass exclusion limits around 2.5-3 TeV. In this talk, I investigate supersymmetric Z' decays at 14 TeV LHC, extending the MSSM in such a way to accommodate extra he...
Beta function in supersymmetric gauge theoris
Within the background field formalism vacuum loops in supersymmetric gauge theories are discussed. A direct connection is revealed between the absence (or presence) of high order contributions and infrared regularization. A simple explanation is given why the instanton amplitude is exhausted by one loop whilst in the standard supergraph technique the effective action contains terms of all orders in the coupling constant. Exact relation between the Gell-Mann-Low function and anomalous dimensions of matter superfields stemming from the instanton calculus are presented
Minimal fine tuning in supersymmetric Higgs inflation
We investigate characteristic features of a realistic parameter choice for primordial inflation with the supersymmetric Higgs inflaton as an example of a particle physics inflation model. We discuss constraints from observational results and analyze the degree of fine tuning needed to induce slow-roll inflation for a wide range of soft supersymmetry-breaking scales. The observed amplitude of density fluctuations implies that the minimal fine tuning for the combined electroweak scale and inflaton flatness predicts a spectral index of ns=0.950−0.965, which includes the central value from observational data
Supersymmetric extension of a coupled Korteweg-de Vries system
We introduce a supersymmetric extension for a parametric coupled Korteweg- de Vries system. The supersymmetric system has two real hamiltonian functionals and two associated basic Poisson structures. The basic Poisson structures allows the construction of a pencil of Poisson brackets and associated to them a hamiltonian functional depending on the parameter of the pencil. The two basic Poisson brackets are compatible
Resolution of axial anomaly problem in supersymmetric gauge theories
The explicit form of transformation is found which converters the operators, involved in axial anomaly, from the renormalization scheme obeying the Adler-BaAdeen theorem to a supersymmetric one. It is shown that there is no contradiction between axial current and superconformal anomalies. In supersymmetric scheme the axial current and its anomaly belong to the corresponding supermultiplets
Superconformal indices and partition functions for supersymmetric field theories
Gahramanov, I.B. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Vartanov, G.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-12-15
Recently there was a substantial progress in understanding of supersymmetric theories (in particular, their BPS spectrum) in space-times of different dimensions due to the exact computation of superconformal indices and partition functions using localization method. Here we discuss a connection of 4d superconformal indices and 3d partition functions using a particular example of supersymmetric theories with matter in antisymmetric representation.
N=2 supersymmetric quantum mechanics and the inverse scattering problem
Connection between the N=2 supersymmetrical quantum mechanics and the inverse scattering problem is established. In contrast to the N=1 supersymmetrical quantum mechanics, in the approach under consideration, the rearrangement of spectra is possible in the construction of isospectral Hamiltonians which concern both ground and excited states
N = 2 supersymmetric quantum mechanics and the inverse scattering problem
A connection between N = 2 supersymmetric quantum mechanics and the inverse scattering problem is established. In contrast to N = 1 supersymmetric quantum mechanics, construction of the isospectral Hamiltonians in the considered approach reveals the possibility of rearrangement of the spectrum, this affecting not only the ground state but also the excited states
Origin of Structure in a Supersymmetric Quantum Universe
Moniz, P V
1998-01-01
In this report we advance the current repertoire of quantum cosmological models to incorporate inhomogenous field modes in a supersymmetric manner. In particular, we introduce perturbations about a supersymmetric FRW model. A quantum state of our model has properties typical of the no-boundary (Hartle--Hawking) proposal. This solution may then lead to a scale--free spectrum of density perturbations.
Supersymmetrized Schroedinger equation for Fermion-Dyon system
Supersymmetrized Schroedinger equation for Fermion-Dyon system has been obtained by dimensional reduction of supersymmetrized four-dimensional harmonic oscillator and it has been interpreted as an ensemble of two Schroedinger and one Pauli's equation each describing the motion of an electrically charged particle in the field of a Dyon with different magnetic charges. (author)
Implications for supersymmetric dark matter detection from radiative b decays
We point out that combinations of parameters that predict large counting rates in experiments searching for supersymmetric dark matter often tend to predict a very large branching ratio for the inclusive decay b→sγ. The recent experimental upper bound on this branching ratio, therefore, indicates that searches for supersymmetric dark matter might be even more difficult than previously anticipated. (orig.)
M-theory on Less Supersymmetric PP-Waves
Lee, K M
2002-01-01
There are fractionally supersymmetric pp-waves in 11 dimensional supergravity. We study the corresponding supersymmetric Yang-Mills matrix dynamics for M-theory and find its superalgebra and vacuum equations. We show that the ground state energy of the Hamiltonian with nontrivial dynamical superysmmetry can be zero, positive or negative depending on parameters.
Higher dimensional supersymmetric quantum mechanics and Dirac equation
L P Singh; B Ram
2002-04-01
We exhibit the supersymmetric quantum mechanical structure of the full 3+1 dimensional Dirac equation considering `mass' as a function of coordinates. Its usefulness in solving potential problems is discussed with speciﬁc examples. We also discuss the `physical' signiﬁcance of the supersymmetric states in this formalism.
Do supersymmetric anti-de Sitter black rings exist?
We determine the most general near-horizon geometry of a supersymmetric, asymptotically anti-de Sitter, black hole solution of five-dimensional minimal gauged supergravity that admits two rotational symmetries. The near-horizon geometry is that of the supersymmetric, topologically spherical, black hole solution of Chong et al. This proves that regular supersymmetric anti-de Sitter black rings with two rotational symmetries do not exist in minimal supergravity. However, we do find a solution corresponding to the near-horizon geometry of a supersymmetric black ring held in equilibrium by a conical singularity, which suggests that nonsupersymmetric anti-de Sitter black rings may exist but cannot be 'balanced' in the supersymmetric limit
Ultraviolet divergences in non-renormalizable supersymmetric theories
Smilga, A V
2016-01-01
We present a pedagogical review of our current understanding of the ultraviolet structure of N = (1,1) 6D supersymmetric Yang-Mills theory and of N = 8 4D supergravity. These theories are not renormalizable, they involve power ultraviolet divergences and, in all probability, an infinite set of higher-dimensional counterterms that contribute to on-mass-shell scattering amplitudes. A specific feature of supersymmetric theories (especially, of extended supersymmetric theories) is that these counterterms may not be invariant off shell under the full set of supersymmetry transformations. The lowest-dimensional nontrivial counterterm is supersymmetric on shell. Still higher counterterms may lose even the on-shell invariance. On the other hand, the full effective Lagrangian, generating the amplitudes and representing an infinite sum of counterterms, still enjoys the complete symmetry of original theory. We also discuss simple supersymmetric quantum-mechanical models that exhibit the same behaviour.
Aspects of extra dimensional supersymmetric unified theories
The purpose of this work is to investigate Grand Unified Theories (GUTs) and to make the link with passed and upcoming experiments. The structure of this thesis is as follows. In the first chapter, we will briefly review the sequence of arguments leading to the Higgs mechanism, then to the different concepts underlying physics beyond the Standard Model, and to the paradigm of extra dimensional supersymmetric grand unified theories. At each level of the argumentation, we will mention the different solutions available. The second chapter introduces more formally supersymmetry and extra dimensions, focusing in particular on the aspects of symmetry breaking. Then, in the third chapter, we present in details the two frameworks of extra dimensional theories in which we worked, called supersymmetric gauge-Higgs unification (GHU) and holographic grand unification (HGU) as well as the developments and modifications we brought to them. The fourth chapter is devoted to the low energy viability of the GHU framework, as well as its phenomenological implications. The fifth chapter presents a more generic study of the property of GUT-scale degenerate Higgs mass matrix, common to both frameworks. Finally, the sixth chapter is devoted to the viability and phenomenological implications of the HGU framework, with special emphasis on lepton flavour violation. This quantitative study takes properly into account effects of matrix anarchy, as well as exact flavour observables. The results obtained should generalize, at least qualitatively, to any other model with similar localization and supersymmetry breaking features
Toward precision holography with supersymmetric Wilson loops
Faraggi, Alberto; Pando Zayas, Leopoldo A.; Silva, Guillermo A.; Trancanelli, Diego
2016-04-01
We consider certain 1/4 BPS Wilson loop operators in SU( N) N=4 supersymmetric Yang-Mills theory, whose expectation value can be computed exactly via supersymmetric localization. Holographically, these operators are mapped to fundamental strings in AdS 5 × S 5. The string on-shell action reproduces the large N and large coupling limit of the gauge theory expectation value and, according to the AdS/CFT correspondence, there should also be a precise match between subleading corrections to these limits. We perform a test of such match at next-to-leading order in string theory, by deriving the spectrum of quantum fluctuations around the classical string solution and by computing the corresponding 1-loop effective action. We discuss in detail the supermultiplet structure of the fluctuations. To remove a possible source of ambiguity in the ghost zero mode measure, we compare the 1/4 BPS configuration with the 1/2 BPS one, dual to a circular Wilson loop. We find a discrepancy between the string theory result and the gauge theory prediction, confirming a previous result in the literature. We are able to track the modes from which this discrepancy originates, as well as the modes that by themselves would give the expected result.
Towards gauge unified, supersymmetric hidden strong dynamics
Chiang, Cheng-Wei; Ye, Fang
2016-01-01
We consider a class of models with extra complex scalars that are charged under both the Standard Model and a hidden strongly coupled $SU(N)_H$ gauge sector, and discuss the scenarios where the new scalars are identified as the messenger fields that mediate the spontaneously broken supersymmetries from the hidden sector to the visible sector. The new scalars are embedded into 5-plets and 10-plets of an $SU(5)_V$ gauge group that potentially unifies the Standard Model gauge groups. They also form a tower of bound states via hidden strong dynamics around the TeV scale. The Higgs bosons remain as elementary particles. Quadratically divergent contributions to the Higgs mass from the Standard Model fermions are canceled by the new scalar contributions to alleviate the fine-tuning problem. We also discuss a supersymmetrized version of this class of models, consisting of the minimal supersymmetric Standard Model plus extra chiral multiplets where the new scalars reside. Due to the hidden strong force, the new low-en...
Supersymmetric Standard Model Spectra from RCFT orientifolds
Dijkstra, T P T; Schellekens, Adrian Norbert
2007-01-01
We present supersymmetric, tadpole-free d=4,N=1 orientifold vacua with a three family chiral fermion spectrum that is identical to that of the Standard Model. Starting with all simple current orientifolds of all Gepner models we perform a systematic search for such spectra. We consider several variations of the standard four-stack intersection brane realization of the standard model, with all quarks and leptons realized as bifundamentals and perturbatively exact baryon and lepton number symmetries, and with a U(1)_Y vector boson that does not acquire a mass from Green-Schwarz terms. The number of supersymmetric Higgs pairs H_1 + H_2 is left free. In order to cancel all tadpoles, we allow a "hidden" gauge group, which must bechirally decoupled from the standard model. We also allow for non-chiral mirror-pairs of quarks and leptons, non-chiral exotics and (possibly chiral) hidden, standard model singlet matter, as well as a massless B-L vector boson. All of these less desirable features are absent in some cases...
Supersymmetric quantum mechanics of the flux tube
Belitsky, A V
2016-01-01
The Operator Product Expansion approach to scattering amplitudes in maximally supersymmetric gauge theory operates in terms of pentagon transitions for excitations propagating on a color flux tube. These obey a set of axioms which allow to determine them to all orders in 't Hooft coupling and confront against explicit calculations. One of the simplifying features of the formalism is the factorizability of multiparticle transitions in terms of single-particle ones. In this paper we extend an earlier consideration of a sector populated by one kind of excitations to the case of a system with fermionic as well as bosonic degrees of freedom to address the origin of the factorization. While the purely bosonic case was analyzed within an integrable noncompact open-spin chain model, the current case is solved in the framework of a supersymmetric sl(2|1) magnet. We find the eigenfunctions for the multiparticle system making use of the R-matrix approach. Constructing resulting pentagon transitions, we prove their facto...
Semiclassical approximation to supersymmetric quantum gravity
Kiefer, Claus; Lück, Tobias; Moniz, Paulo
2005-08-01
We develop a semiclassical approximation scheme for the constraint equations of supersymmetric canonical quantum gravity. This is achieved by a Born-Oppenheimer type of expansion, in analogy to the case of the usual Wheeler-DeWitt equation. The formalism is only consistent if the states at each order depend on the gravitino field. We recover at consecutive orders the Hamilton-Jacobi equation, the functional Schrödinger equation, and quantum gravitational correction terms to this Schrödinger equation. In particular, the following consequences are found: (i) the Hamilton-Jacobi equation and therefore the background spacetime must involve the gravitino, (ii) a (many-fingered) local time parameter has to be present on super Riem Σ (the space of all possible tetrad and gravitino fields), (iii) quantum supersymmetric gravitational corrections affect the evolution of the very early Universe. The physical meaning of these equations and results, in particular, the similarities to and differences from the pure bosonic case, are discussed.
Higgs boson masses in supersymmetric models
Imposing supersymmetry on a Higgs potential constrains the parameters that define the potential. In supersymmetric extensions to the stranded model containing only Higgs SU(2)L doublets there exist Higgs boson mass sum rules and bounds on the Higgs masses at tree level. The prescription for renormalizing these sum rules is derived. An explicit calculation is performed in the minimal supersymmetric extension to the standard model (MSSM). In this model at tree level the mass sum rule is MH2 + Mh2 = MA2 + MZ2. The results indicate that large corrections to the sum rules may arise from heavy matter fields, e.g. a heavy top quark. Squarks significantly heavier than their fermionic partners contribute large contributions when mixing occurs in the squark sector. These large corrections result from squark-Higgs couplings that become large in this limit. Contributions to individual Higgs boson masses that are quadratic in the squark masses cancel in the sum rule. Thus the naturalness constraint on Higgs boson masses is hidden in the combination of Higgs boson masses that comprise the sum rule. 39 refs., 13 figs
Minimal E_6 Supersymmetric Standard Model
Howl, R
2008-01-01
We propose a Minimal E_6 Supersymmetric Standard Model (ME$_6$SSM) which allows Planck scale unification, provides a solution to the $\\mu$ problem and predicts a new Z'. Above the conventional GUT scale $M_{GUT}\\sim 10^{16}$ GeV the gauge group corresponds to a left-right symmetric Supersymmetric Pati-Salam model, together with an additional $U(1)_{\\psi}$ gauge group arising from an E_6 gauge group broken near the Planck scale. Below $M_{GUT}$ the ME$_6$SSM contains three reducible $\\mathbf{27}$ representations of the Standard Model gauge group together with an additional U(1)_X gauge group, consisting of a novel and non-trivial linear combination of $U(1)_{\\psi}$ and two Pati-Salam generators, which is broken at the TeV scale by the same singlet which also generates the effective $\\mu$ term, resulting in a new low energy Z' gauge boson. We discuss the phenomenology of the new Z' gauge boson in some detail.
Supersymmetric Electroweak Baryogenesis Via Resonant Sfermion Sources
Kozaczuk, Jonathan; Ramsey-Musolf, Michael J; Wainwright, Carroll L
2012-01-01
We calculate the baryon asymmetry produced at the electroweak phase transition by quasi-degenerate third generation sfermions in the minimal supersymmetric extension of the Standard Model. We evaluate constraints from Higgs searches, from collider searches for supersymmetric particles, and from null searches for the permanent electric dipole moment (EDM) of the electron, of the neutron and of atoms. We find that resonant sfermion sources can in principle provide a large enough baryon asymmetry in various corners of the sfermion parameter space, and we focus, in particular, on the case of large $\\tan\\beta$, where third-generation down-type (s)fermions become relevant. We show that in the case of stop and sbottom sources, the viable parameter space is ruled out by constraints from the non-observation of the Mercury EDM. We introduce a new class of CP violating sources, quasi-degenerate staus, that escapes current EDM constraints while providing large enough net chiral currents to achieve successful "slepton-med...
Anomaly-Free Supergravities in Six Dimensions
Avramis, S D
2006-01-01
This thesis reviews minimal N=2 chiral supergravities coupled to matter in six dimensions with emphasis on anomaly cancellation. In general, six-dimensional chiral supergravities suffer from gravitational, gauge and mixed anomalies which render the theories inconsistent at the quantum level. Consistency is restored if the anomalies of the theory cancel via the Green-Schwarz mechanism or generalizations thereof. The anomaly cancellation conditions translate into a certain set of constraints for the gauge group of the theory as well as on its matter content. For the case of ungauged theories these constraints admit numerous solutions but, in the case of gauged theories, the allowed solutions are remarkably few. In this thesis, we examine these anomaly cancellation conditions in detail and we present all solutions to these conditions under certain restrictions on the allowed gauge groups and representations, imposed for practical reasons. We also briefly examine anomaly cancellation in the context of Horava-Witt...
We investigate a minimal U(1)′ extension of the Standard Model with one extra complex scalar and generic gauge charge assignments. We use a type-I seesaw mechanism with three heavy right handed neutrinos to illustrate the constraints on the charges, on their mass and on the mixing angle of the two scalars, derived by requiring the vacuum stability of the scalar potential. We focus our study on a scenario which could be accessible at the LHC, by selecting a vacuum expectation value of the extra Higgs in the TeV range and determining the constraints that emerge in the parameter space. To illustrate the generality of the approach, specific gauge choices corresponding to U(1)B−L, U(1)R and U(1)χ are separately analyzed. Our results are based on a modified expression of one of the β functions of the quartic couplings of the scalar potential compared to the previous literature. This is due to a change in the coefficient of the Yukawa term of the right handed neutrinos. Differently from previous analysis, we show that this coupling may destabilize the vacuum
Vacuum stability in U(1-prime extensions of the Standard Model with TeV scale right handed neutrinos
Claudio Corianò
2014-11-01
Full Text Available We investigate a minimal U(1′ extension of the Standard Model with one extra complex scalar and generic gauge charge assignments. We use a type-I seesaw mechanism with three heavy right handed neutrinos to illustrate the constraints on the charges, on their mass and on the mixing angle of the two scalars, derived by requiring the vacuum stability of the scalar potential. We focus our study on a scenario which could be accessible at the LHC, by selecting a vacuum expectation value of the extra Higgs in the TeV range and determining the constraints that emerge in the parameter space. To illustrate the generality of the approach, specific gauge choices corresponding to U(1B−L, U(1R and U(1χ are separately analyzed. Our results are based on a modified expression of one of the β functions of the quartic couplings of the scalar potential compared to the previous literature. This is due to a change in the coefficient of the Yukawa term of the right handed neutrinos. Differently from previous analysis, we show that this coupling may destabilize the vacuum.
Perturbative stability along the supersymmetric directions of the landscape
We consider the perturbative stability of non-supersymmetric configurations in N=1 supergravity models with a spectator sector not involved in supersymmetry breaking. Motivated by the supergravity description of complex structure moduli in Large Volume Compactifications of type IIB-superstrings, we concentrate on models where the interactions are consistent with the supersymmetric truncation of the spectator fields, and we describe their couplings by a random ensemble of generic supergravity theories. We characterise the mass spectrum of the spectator fields in terms of the statistical parameters of the ensemble and the geometry of the scalar manifold. Our results show that the non-generic couplings between the spectator and the supersymmetry breaking sectors can stabilise all the tachyons which typically appear in the spectator sector before including the supersymmetry breaking effects, and we find large regions of the parameter space where the supersymmetric sector remains stable with probability close to one. We discuss these results about the stability of the supersymmetric sector in two physically relevant situations: non-supersymmetric Minkowski vacua, and slow-roll inflation driven by the supersymmetry breaking sector. For the class of models we consider, we have reproduced the regimes in which the KKLT and Large Volume Scenarios stabilise all supersymmetric moduli. We have also identified a new regime in which the supersymmetric sector is stabilised at a very robust type of dS minimum without invoking a large mass hierarchy
Perturbative stability along the supersymmetric directions of the landscape
Sousa, Kepa [Department of Theoretical Physics and History of Science, University of the Basque Country UPV/EHU, 48080 Bilbao (Spain); Ortiz, Pablo, E-mail: kepa.sousa@ehu.es, E-mail: ortiz@lorentz.leidenuniv.nl [Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, Niels Bohrweg 2, 2333 CA Leiden (Netherlands)
2015-02-01
We consider the perturbative stability of non-supersymmetric configurations in N=1 supergravity models with a spectator sector not involved in supersymmetry breaking. Motivated by the supergravity description of complex structure moduli in Large Volume Compactifications of type IIB-superstrings, we concentrate on models where the interactions are consistent with the supersymmetric truncation of the spectator fields, and we describe their couplings by a random ensemble of generic supergravity theories. We characterise the mass spectrum of the spectator fields in terms of the statistical parameters of the ensemble and the geometry of the scalar manifold. Our results show that the non-generic couplings between the spectator and the supersymmetry breaking sectors can stabilise all the tachyons which typically appear in the spectator sector before including the supersymmetry breaking effects, and we find large regions of the parameter space where the supersymmetric sector remains stable with probability close to one. We discuss these results about the stability of the supersymmetric sector in two physically relevant situations: non-supersymmetric Minkowski vacua, and slow-roll inflation driven by the supersymmetry breaking sector. For the class of models we consider, we have reproduced the regimes in which the KKLT and Large Volume Scenarios stabilise all supersymmetric moduli. We have also identified a new regime in which the supersymmetric sector is stabilised at a very robust type of dS minimum without invoking a large mass hierarchy.
Phases of supersymmetric O(N) theories
Heilmann, Marianne; Synatschke-Czerwonka, Franziska; Wipf, Andreas
2012-01-01
We perform a global renormalization group study of O(N) symmetric Wess-Zumino theories and their phases in three euclidean dimensions. At infinite N the theory is solved exactly. The phases and phase transitions are worked out for finite and infinite short-distance cutoffs. A distinctive new feature arises at strong coupling, where the effective superfield potential becomes multi-valued, signalled by divergences in the fermion-boson interaction. Our findings resolve the long-standing puzzle about the occurrence of degenerate O(N) symmetric phases. At finite N, we find a strongly-coupled fixed point in the local potential approximation and explain its impact on the phase transition. We also examine the possibility for a supersymmetric Bardeen-Moshe-Bander phenomenon, and relate our findings with the spontaneous breaking of supersymmetry in other models.
Supersymmetric quantum mechanics for string-bits
The authors develop possible versions of supersymmetric single particle quantum mechanics, with application to superstring-bit models in view. The authors focus principally on space dimensions d = 1,2,4,8, the transverse dimensionalities of superstring in 3, 4, 7, 10 space-time dimensions. These are the cases for which classical superstring makes sense, and also the values of d for which Hooke's force law is compatible with the simplest superparticle dynamics. The basic question they address is: when is it possible to replace such harmonic force laws with more general ones, including forces which vanish at large distances? This is an important question because forces between string-bits that do not fall off with distance will almost certainly destroy cluster decomposition. They show that the answer is affirmative for d = 1,2, negative for d = 8, and so far inconclusive for d = 4
Supersymmetric partition functions on Riemann surfaces
Benini, Francesco
2016-01-01
We present a compact formula for the supersymmetric partition function of 2d N=(2,2), 3d N=2 and 4d N=1 gauge theories on $\\Sigma_g \\times T^n$ with partial topological twist on $\\Sigma_g$, where $\\Sigma_g$ is a Riemann surface of arbitrary genus and $T^n$ is a torus with n=0,1,2, respectively. In 2d we also include certain local operator insertions, and in 3d we include Wilson line operator insertions along $S^1$. For genus g=1, the formula computes the Witten index. We present a few simple Abelian and non-Abelian examples, including new tests of non-perturbative dualities. We also show that the large N partition function of ABJM theory on $\\Sigma_g \\times S^1$ reproduces the Bekenstein-Hawking entropy of BPS black holes in AdS4 whose horizon has $\\Sigma_g$ topology.
The supersymmetric Ward identities on the lattice
Supersymmetric (SUSY) Ward identities are considered for the N=1 SU(2) SUSY Yang Mills theory discretized on the lattice with Wilson fermions (gluinos). They are used in order to compute non-perturbatively a subtracted gluino mass and the mixing coefficient of the SUSY current. The computations were performed at gauge coupling β=2.3 and hopping parameter κ=0.1925, 0.194, 0.1955 using the two-step multi-bosonic dynamical-fermion algorithm. Our results are consistent with a scenario where the Ward identities are satisfied up to O(a) effects. The vanishing of the gluino mass occurs at a value of the hopping parameter which is not fully consistent with the estimate based on the chiral phase transition. This suggests that, although SUSY restoration appears to occur close to the continuum limit of the lattice theory, the results are still affected by significant systematic effects. (orig.)
SUSYCAL - symbolic computations in supersymmetric theories
The calculation of supergraphs within the superfield-formalism entails complex expressions and numerous divergent integrals. This is even more so for non-covariant supergauges. SUSYCAL is a package of PASCAL procedures which is able to manipulate formulae and perform these calculations. The algebra of the non-covariant operators of the FD-gauge and the covariant derivatives is included in SUSYCAL as a fixed set of rules. This first version of SUSYCAL to be presented comprises also the (symbolic) evaluation of several divergent non-corvariant self-energies. The method of dimensional regularization is used for all computations by SUSYCAL. Because of the universal applicability of the non-covariant operators, SUSYCAL is a tool for calculations in all N=1 supersymmetric theories. (orig.)
Effective action of softly broken supersymmetric theories
We study the renormalization of (softly) broken supersymmetric theories at the one loop level in detail. We perform this analysis in a superspace approach in which the supersymmetry breaking interactions are parameterized using spurion insertions. We comment on the uniqueness of this parameterization. We compute the one loop renormalization of such theories by calculating superspace vacuum graphs with multiple spurion insertions. To preform this computation efficiently we develop algebraic properties of spurion operators, that naturally arise because the spurions are often surrounded by superspace projection operators. Our results are general apart from the restrictions that higher super covariant derivative terms and some finite effects due to non-commutativity of superfield dependent mass matrices are ignored. One of the soft potentials induces renormalization of the Kaehler potential. (author)
Supersymmetric backgrounds and generalised special holonomy
Coimbra, André; Strickland-Constable, Charles; Waldram, Daniel
2016-06-01
We define intrinsic torsion in generalised geometry and use it to introduce a new notion of generalised special holonomy. We then consider generic warped supersymmetric flux compactifications of M theory and Type II of the form {{{R}}}D-{1,1}× M. Using the language of {E}d(d)× {{{R}}}+ generalised geometry, we show that, for D≥slant 4, preserving minimal supersymmetry is equivalent to the manifold M having generalised special holonomy and list the relevant holonomy groups. We conjecture that this result extends to backgrounds preserving any number of supersymmetries. As a prime example, we consider { N }=1 in D = 4. The corresponding generalised special holonomy group is {SU}(7), giving the natural M theory extension to the notion of a G 2 manifold, and, for Type II backgrounds, reformulating the pure spinor {SU}(3)× {SU}(3) conditions as an integrable structure.