We study the free energy of four-dimensional CFTs on deformed spheres. For generic nonsupersymmetric CFTs only the coefficient of the logarithmic divergence in the free energy is physical, which is an extremum for the round sphere. We then specialize to $\mathcal{N}=2$ SCFTs where one can preserve some supersymmetry on a compact manifold by turning on appropriate background fields. For deformations of the round sphere the $c$ anomaly receives corrections proportional to the supersymmetric completion of the (Weyl)$^2$ term, which we determine up to one constant by analyzing the scale dependence of various correlators in the stress-tensor multiplet. We further show that the double derivative of the free energy with respect to the marginal couplings is proportional to the two-point function of the bottom components of the marginal chiral multiplet placed at the two poles of the deformed sphere. We then use anomaly considerations and counter-terms to parametrize the finite part of the free energy which makes manifest its dependence on the Kähler potential. We demonstrate these results for a theory with a vector multiplet and a massless adjoint hypermultiplet using results from localization. Finally, by choosing a special value of the hypermultiplet mass where the free energy is independent of the deformation, we derive an infinite number of constraints between various integrated correlators in $\mathcal{N}=4$ super Yang-Mills with any gauge group and at all values of the coupling, extending previous results.
We study partial supersymmetry breaking from ${\cal N}=2$ to ${\cal N}=1$ by adding non-linear terms to the ${\cal N}=2$ supersymmetry transformations. By exploiting the necessary existence of a deformed supersymmetry algebra for partial breaking to occur, we systematically use ${\cal N}=2$ projective superspace with central charges to provide a streamlined setup. For deformed ${\cal O}(2)$ and ${\cal O}(4)$ hypermultiplets, besides reproducing known results, we describe new models exhibiting partial supersymmetry breaking with and without higher-derivative interactions.
It is shown that the deformed conifold solution with three-form flux, found by Klebanov and Strassler, is supersymmetric, and that it admits a simple F-theory description in terms of a direct product of the deformed conifold and a torus. Some general remarks on Ramond-Ramond backgrounds and warped compactifications are included.
We study N=2 supersymmetric U(1) gauge theory in non(anti)commutative N=2 harmonic superspace with the chirality preserving non-singlet deformation parameter. By solving the Wess-Zumino gauge preserving conditions for the analytic superfield, we construct the deformed N=(1,0) supersymmetry transformation for component fields up to the first order in the deformation parameter.
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-depende…
The field equations of the auxiliary fields are nonlinear and free of derivatives. Hence, it is argued, a Legendre transform to generate the 1PI Generating Functionals is not correct for the auxiliary fields. A corrected formulation of the BRS symmetry must be constructed by integrating the auxiliary fields. This necessarily destroys manifest supersymmetry. It also generates a new "Physical BRS-ZJ" cohomology problem. The resulting "Physical BRS-ZJ cohomology" is then described. The cohomology contains a rich spectrum of potential supersymmetry anomalies in certain composite operators that hav…
We solve the Wess-Zumino consistency conditions of $\mathcal{N}=1$ off-shell conformal supergravity in four dimensions and determine the general form of the superconformal anomalies for arbitrary $a$ and $c$ anomaly coefficients to leading non trivial order in the gravitino. Besides the well known Weyl and $R$-symmetry anomalies, we compute explicitly the fermionic $\mathcal{Q}$- and $\mathcal{S}$-supersymmetry anomalies. In particular, we show that $\mathcal{Q}$-supersymmetry is anomalous if and only if $R$-symmetry is anomalous. The $\mathcal{Q}$- and $\mathcal{S}$-supersymmetry anomalies gi…
We consider a deformation of N=1 four dimensional Minkowski superspace where odd coordinates $θ^α$ do not anticommute. We define supersymmetric and associative star product and show how the remaining (anti)commutation relations among the superspace coordinates are modified. In particular, the even coordinates do not commute as well. We also study chiral and vector superfields and their interactions. Suprisingly we find that ordinary undeformed N=1 supersymmetric field theories are compatible with the deformed supersymmetry considered.
We describe an algorithmic method to calculate the $T\bar{T}$ deformed Lagrangian of a given seed theory by solving an algebraic system of equations. This method is derived from the topological gravity formulation of the deformation. This algorithm is far simpler than the direct partial differential equations needed in most earlier proposals. We present several examples, including the deformed Lagrangian of (1,1) supersymmetry. We show that this Lagrangian is off-shell invariant through order $λ^2$ in the deformation parameter and verify its SUSY algebra through order $λ$.
We study deformed supersymmetry in N=2 supersymmetric U(N) gauge theory in non(anti)commutative N=1 superspace. Using the component formalism, we construct deformed N=(1,1/2) supersymmetry explicitly. Based on the deformed supersymmetry, we discuss the C-dependence of the correlators. We also study the C-deformation of the instanton equation for the gauge group U(2).
We revisit quantum field theory anomalies, emphasizing the interplay with diffeomorphisms and supersymmetry. The Ward identities of the latter induce Noether currents of all continuous symmetries, and we point out how these consistent currents are replaced by their covariant form through the appearance of the Bardeen-Zumino currents, which play a central role in our study. For supersymmetry Ward identities, two systematic methods for solving the Wess-Zumino consistency conditions are discussed: anomaly inflow and anomaly descent. The simplest inflows are from supersymmetric Chern-Simons action…
A universal minimal spinor set of linear differential equations describing anyons and ordinary integer and half-integer spin fields is constructed with the help of deformed Heisenberg algebra with reflection. The construction is generalized to some d=2+1 supersymmetric field systems. Quadratic and linear forms of action functionals are found for the universal minimal as well as for supersymmetric spinor sets of equations. A possibility of constructing a universal classical mechanical model for d=2+1 spin systems is discussed.
We consider a deformed superspace in which the coordinates θdo not anticommute, but satisfy a Clifford algebra. We present results on the properties of N=1/2 supersymmetric theories of chiral superfields in deformed superspace, taking the Wess-Zumino model as the prototype. We prove new (non)renormalization theorems: the F-term is radiatively corrected and becomes indistinguishable from the D-term, while the Fbar-term is not renormalized. Supersymmetric vacua are critical points of the antiholomorphic superpotential. The vacuum energy is zero to all orders in perturbation theory. We illustrate…
We determine the general structure of quantum anomalies for the $R$-multiplet of four dimensional $\mathcal{N}=1$ supersymmetric quantum field theories in the presence of background fields for an arbitrary number of Abelian flavor multiplets. By solving the Wess-Zumino consistency conditions for off-shell new minimal supergravity in four dimensions with an arbitrary number of Abelian vector multiplets, we compute the anomaly in the conservation of the supercurrent to leading non trivial order in the gravitino and vector multiplet fermions. We find that both $R$-symmetry and flavor anomalies ne…
Non-anticommutative deformations have been studied in the context of supersymmetry (SUSY) in three and four space-time dimensions, and the general picture is that highly nontrivial to deform supersymmetry in a way that still preserves some of its important properties, both at the formal algebraic level (e.g., preserving the associativity of the deformed theory) as well as at the physical level (e.g., maintaining renormalizability). The Hopf algebra formalism allows the definition of algebraically consistent deformations of SUSY, but this algebraic consistency does not guarantee that physical m…
We summarize our recent work on supergravity backgrounds dual to part of the Coulomb branch of N=1 theories constructed as marginal deformations of N=4 Yang-Mills. In particular, we present a summary of the behaviour of the heavy quark-antiquark potential which shows confining behaviour in the IR as well as of the spectrum of the wave equation. The reduced supersymmetry is due to the implementation of T-duality in the construction of the deformed supergravity solutions. As a new result we analyze and explicitly solve the Killing spinor equations of the N=1 background in the superconformal limi…
The established results concerning the BRS cohomology of supersymmetric theories in four space-time dimensions are briefly reviewed. The current status of knowledge concerning supersymmetry anomalies and the possibility that supersymmetry breaks itself through anomalies in local composite operators is then discussed. It turns out that the simplest allowable supersymmetry anomalies occur only in conjunction with the spontaneous breaking of gauge symmetry. A simple example of such a possible supersymmetry anomaly is presented.
New models of the SU(2|1) supersymmetric mechanics based on gauging the systems with dynamical (1,4,3) and semi-dynamical (4,4,0) supermultiplets are presented. We propose a new version of SU(2|1) harmonic superspace approach which makes it possible to construct the Wess-Zumino term for interacting (4,4,0) multiplets. A new N=4 extension of d=1 Calogero-Moser multiparticle system is obtained by gauging the U(n) isometry of matrix SU(2|1) harmonic superfield model.
We consider models of dynamical supersymmetry breaking in which the extremization of a tree-level superpotential conflicts with a quantum constraint. We show that in such models the low-energy effective theory near the origin of moduli space is an O'Raifeartaigh model, and the sign of the mass-squared for the pseudo-flat direction at the origin is calculable. We analyze vector-like models with gauge groups SU(N) and Sp(2N) with and without global symmetries. In all cases there is a stable minimum at the origin with an unbroken U(1)_R symmetry.
The relation between the trace and R-current anomalies in 4D supersymmetric theories implies that the U(1)$_R$F$^2$, U(1)$_R$ and U(1)$^3_R$ anomalies which matched in studies of N=1 Seiberg duality satisfy positivity constraints. These constraints are tested in a large number of N=1 supersymmetric gauge theories in the non-Abelian Coulomb phase, and they are satisfied in all renormalizable models with unique anomaly-free R-current, including those with accidental symmetry. Most striking is the fact that the flow of the Euler anomaly coefficient, $a_{UV}-a_{IR}$, is always positive, as conject…
The $γ_i$-deformed $\mathcal{N}=4$ super-Yang-Mills theory is a non-supersymmetric deformation of the maximally-supersymmetric gauge theory in four dimensions which is conformally-invariant at the planar level. At the non-planar level non-trivial renormalization of marginal double-trace operators appears to break conformal invariance. At non-planar level, however, the behavior of this theory is less well understood. We study the one loop renormalization of the theory and the resulting flow of Yukawa and scalar coupling at the order ${\cal O}(\fracλ{N^2})$, and find $γ_i$ parameters receive non…
We study the dimensional reduction of ten-dimensional super Yang-Mills theory in curved backgrounds with torsion. We examine the parallel spinor conditions and the constraints for the torsion parameters which preserve supersymmetry and gauge symmetry in four dimensions. In particular we examine the ten-dimensional Omega-background with the torsion which is identified with the R-symmetry Wilson line gauge fields. After the dimensional reduction, we obtain the Omega-deformed N=4 super Yang-Mills theory. Solving the parallel spinor conditions and the torsion constraints, we classify the deformed …
It was recently noted that the dispersion relation for the magnons of planar N=4 SYM can be identified with the Casimir of a certain deformation of the Poincare algebra, in which the energy and momentum operators are supplemented by a boost generator J. By considering the relationship between J and su(2|2) x R^2, we derive a q-deformed super-Poincare symmetry algebra of the kinematics. Using this, we show that the dynamic magnon representations may be obtained by boosting from a fixed rest-frame representation. We comment on aspects of the coalgebra structure and some implications for the ques…
We study the consequences of unbroken rigid supersymmetry of four-dimensional field theories placed on curved manifolds. We show that in Lorentzian signature the background vector field coupling to the R-current is determined by the Weyl tensor of the background metric. In Euclidean signature, the same holds if two supercharges of opposite R-charge are preserved, otherwise the (anti-)self-dual part of the vector field-strength is fixed by the Weyl tensor. As a result of this relation, the trace and R-current anomalies of superconformal field theories simplify, with the trace anomaly becoming p…
We study supersymmetry of N=4 super Yang-Mills theory in four dimensions deformed in the Omega-background. We take the Nekrasov-Shatashvili limit of the background so that two-dimensional super Poincare symmetry is recovered. We compute the deformed central charge of the superalgebra and study the 1/2 and 1/4 BPS states. We obtain the Omega-deformed 1/2 and 1/4 BPS dyon equations from the deformed supersymmetry transformation and the Bogomol'nyi completion of the energy.
We give a self-contained discussion of recent progress in computing the non-perturbative effects of small non-holomorphic soft supersymmetry breaking, including a simple new derivation of these results based on an anomaly-free gauged U(1)_R background. We apply these results to N = 1 theories with deformed moduli spaces and conformal fixed points. In an SU(2) theory with a deformed moduli space, we completely determine the vacuum expectation values and induced soft masses. We then consider the most general soft breaking of supersymmetry in N = 2 SU(2) super-Yang-Mills theory. An N = 2 superfie…
We write explicit Lagrangian and supersymmetry transformation rules using the component fields in the ${\cal N}=2,3$ GT theories. In the component field expansion, the manifestation of an additional ${\cal N}=1$ supersymmetry is verified in the ${\cal N}=3$ GT theory. We find maximal supersymmetry preserving mass-deformation of the GT theories and their classical supersymmetric discrete vacua. Some interesting aspects of the set of discrete vacua are discussed in comparison with the ABJM case.
In this paper, we will study the deformation of a three dimensional $\mathcal{N} = 2$ supersymmetry gauge theory. We will deform this theory by imposing non-anticommutativity. This will break the supersymmetry of the theory from $\mathcal{N} = 2$ supersymmetry to $\mathcal{N} = 1$ supersymmetry. We will address the problem that occurs in the Landau gauge due to the existence of multiple solutions to the gauge fixing condition. This will be done by generalizing the Faddeev-Popov method. This formalism is motivated from the Nicolai map in topological field theories. Finally, we will study the ex…
We investigate higher-dimensional analogues of the $bc$ systems of 2D RCFT. When coupled to gauge fields and Beltrami differentials defining integrable holomorphic structures the $bc$ partition functions can be explicitly evaluated using anomalies and holomorphy. The resulting induced actions generalize the chiral algebras of 2D RCFT to $2n$ dimensions. Moreover, $bc$ systems in four and six dimensions are closely related to supersymmetric matter. In particular, we show that $d=4, \mathcal{N}=2$ hypermultiplets induce a theory of self-dual Yang-Mills fields coupled to self-dual gravity. In thi…
We present a BRST analysis of supersymmetry anomalies of $\mathcal{N} = 1$ supersymmetric quantum field theories with anomalous R symmetry. To this end, we consider the coupling of the matter theory to classical $\mathcal{N} = 1$ new minimal supergravity. We point out that a supersymmetry anomaly cocycle associated to the $\mathrm{U}(1){}_\mathrm{R}$ field does exist for this theory. It is non-trivial in the space of supergravity fields (and ghosts), but it becomes BRST-exact in the functional space that includes antifields. Equivalently, the $\mathrm{U}(1){}_\mathrm{R}$ supersymmetry anomaly …
Within a group-theoretical approach to the description of (2+1)-dimensional anyons, the minimal covariant set of linear differential equations is constructed for the fractional spin fields with the help of the deformed Heisenberg algebra (DHA), $[a^{-},a^{+}]=1+νK$, involving the Klein operator $K$, $\{K,a^{\pm}\}=0$, $K^{2}=1$. The connection of the minimal set of equations with the earlier proposed `universal' vector set of anyon equations is established. On the basis of this algebra, a bosonization of supersymmetric quantum mechanics is carried out. The construction comprises the cases of e…
We develop an efficient technique to compute anomalies in supersymmetric theories by combining the so-called nonlocal regularization method and superspace techniques. To illustrate the method we apply it to a four dimensional toy model with potentially anomalous N=1 supersymmetry and prove explicitly that in this model all the candidate supersymmetry anomalies have vanishing coefficients at the one-loop level.
In this paper we construct N=(1,0) and N=(1,1/2) non-singlet Q-deformed supersymmetric U(1) actions in components. We obtain an exact expression for the enhanced supersymmetry action by turning off particular degrees of freedom of the deformation tensor. We analyze the behavior of the action upon restoring weekly some of the deformation parameters, obtaining a non trivial interaction term between a scalar and the gauge field, breaking the supersymmetry down to N=(1,0). Additionally, we present the corresponding set of unbroken supersymmetry transformations. We work in harmonic superspace in fo…
We study the solutions of the (2+1)-dimensional kappa-deformed Dirac oscillator in the presence of a constant transverse magnetic field. We demonstrate how the deformation parameter affects the energy eigenvalues of the system and the corresponding eigenfunctions. Our findings suggest that this system could be used to detect experimentally the effect of the deformation. We also show that the hidden supersymmetry of the non-deformed system reduces to a hidden pseudo-supersymmetry having the same algebraic structure as a result of the k-deformation.
A search for supersymmetry anomalies requires an examination of the BRS cohomology of supersymmetric Yang-Mills coupled to chiral matter, and the physically interesting (on-shell) anomalies are those which cannot be eliminated using the equations of motion. An analysis of this cohomology problem shows that the simplest situation where a physically interesting supersymmetry anomaly can arise is when: 1. the anomaly occurs in the renormalization of a composite antichiral spinor superfield operator constructed from the chiral matter in the theory, 2. the anomalous diagrams are one-loop triangle d…
We study phase structure of mass-deformed ABJM theory which is a three dimensional $\mathcal{N}=6$ superconformal theory deformed by mass parameters and has the gauge group $\text{U}(N)\times \text{U}(N)$ with Chern-Simons levels $(k,-k)$ which may have a gravity dual. We discuss that the mass deformed ABJM theory on $S^3$ breaks supersymmetry in a large-$N$ limit if the mass is larger than a critical value. To see some evidence for this conjecture, we compute the partition function exactly, and numerically by using the Monte Carlo Simulation for small $N$. We discover that the partition funct…
We study a marginal deformation of N=4 Yang-Mills, with a real deformation parameter beta. This beta-deformed model has only N=1 supersymmetry and a U(1)xU(1) flavor symmetry. The introduction of a new superspace star-product allows us to formulate the theory in N=4 light-cone superspace, despite the fact that it has only N=1 supersymmetry. We show that this deformed theory is conformally invariant, in the planar approximation, by proving that its Green functions are ultra-violet finite to all orders in perturbation theory.
We consider quantum models corresponding to superymmetrizations of the two-dimensional harmonic oscillator based on worldline $d=1$ realizations of the supergroup SU$(\,{\cal N}/2\,|1)$, where the number of supersymmetries ${\cal N}$ is arbitrary even number. Constructed models possess the hidden supersymmetry SU$(\,{\cal N}/2\,|2)$. Degeneracies of energy levels are spanned by representations of the hidden supersymmetry group.
A manifestly supersymmetric nonperturbative matrix regularization for a twisted version of N=(8,8) theory on a curved background (a two-sphere) is constructed. Both continuum and the matrix regularization respect four exact scalar supersymmetries under a twisted version of the supersymmetry algebra. We then discuss a succinct Q=1 deformed matrix model regularization of N=4 SYM in d=4, which is equivalent to a non-commutative $A_4^*$ orbifold lattice formulation. Motivated by recent progress in supersymmetric lattices, we also propose a N=1/4 supersymmetry preserving deformation of N=4 SYM theo…
Testing $(q)$-Deformed Dunkl-Fokker-Planck Equation Algebra with Supersymmetry (SUSY) and Foldy-Wouthuysen (FW) Measurement
Laboratory of Theoretical and Applied Physics, Echahid Cheikh Larbi Tebessi University（应用物理与理论物理实验室，Echahid Cheikh Larbi Tebessi大学）；Research Center of Astrophysics and Cosmology, Khazar University（天体物理学与宇宙学研究中心，Khazar大学）
We consider recent claims that supersymmetry is anomalous in the presence of a R-symmetry anomaly. We revisit arguments that such an anomaly in supersymmetry can be removed and write down an explicit counterterm that accomplishes it. Removal of the supersymmetry anomaly requires enlarging the corresponding current multiplet. As a consequence the Ward identities for other symmetries that are already anomalous acquire extra terms. This procedure can only be impeded when the choice of current multiplet is forced. We show how Wess-Zumino consistency conditions are modified when the anomaly is remo…
The supersymmetric standard model (SSM) contains a wealth of potential supersymmetry anomalies, all of which occur in the renormalization of composite operators of the theory. The coefficients of the weak-E.M. superanomalies should be related to the Witten indices of the neutrino and photon superfields, and the coefficients of the strong superanomalies should be related to the Witten indices of the gluon and photon superfields. Assuming the coefficients are non-zero, the superanomalies break supersymmetry in observable states. However the neutral Higgs particles should remain in a supermultipl…
The computation of $κ$-anomalies in the Green-Schwarz heterotic superstring sigma-model and the corresponding Wess-Zumino consistency condition constitute a powerful alternative approach for the derivation of manifestly supersymmetric string effective actions. With respect to the beta-function approach this technique presents the advantage that a result which is obtained with the computation of beta-functions at $n$ loops can be obtained through the calculation of $κ$-anomalies at \hbox{$n-1$} loops. In this paper we derive by a direct one-loop perturbative computation the $κ$-anomaly associat…
Deformed Heisenberg algebra with reflection appeared in the context of Wigner's generalized quantization schemes underlying the concept of parafields and parastatistics of Green, Volkov, Greenberg and Messiah. We review the application of this algebra for the universal description of ordinary spin-$j$ and anyon fields in 2+1 dimensions, and discuss the intimate relation between parastatistics and supersymmetry.
We show that the anomaly-mediated supersymmetry breaking via the Kahler and sigma-model anomalies is suppressed by conformal dynamics in the supersymmetry breaking sector.
Power-counting arguments based on extended superfields have been used to argue that two-dimensional supersymmetric sigma models with (4,0) supersymmetry are finite. This result is confirmed up to three loop order in pertubation theory by an explicit calculation using (1,0) superfields. In particular, it is shown that the finite counterterms which must be introduced into the theory in order to maintain (4,0) supersymmetry are precisely the terms that are required to establish ultra-violet finiteness.
Non(anti)commutative gauge theories are supersymmetric Yang-Mills and matter system defined on a deformed superspace whose coordinates obey non(anti)commutative algebra. We prove that these theories in four dimensions with N=1/2 supersymmetry are renormalizable to all orders in perturbation theory. Our proof is based on operator analysis and symmetry arguments. In a case when the Grassman-even coordinates are commutative, deformation induced by non(anti)commutativity of the Grassman-odd coordinates contains operators of dimension-four or higher. Nevertheless, they do not lead to power divergen…
The gauging of axionic, Stueckelberg-type, shift symmetries with generalized Chern-Simons terms and the Green-Schwarz mechanism of anomaly cancellation has recently been studied in the context of certain string compactifications and with regard to the phenomenology of unusual variants of Z'-bosons. In this talk, following recent work with De Rydt, Rosseel, Schmidt and Van Proeyen, I summarize how such theories can be reconciled with global and local N=1 supersymmetry. Two simple consistency conditions are shown to encode strong constraints on the allowed anomalies for different types of gauge …
We consider mass-deformed theories with ${\cal N}\geq2$ supersymmetry on round and squashed three-spheres. By embedding the supersymmetric backgrounds in extended supergravity we show that at special values of mass deformations the supersymmetry is enhanced on the squashed spheres. When the $3d$ partition function can be obtained by a limit of a $4d$ index we also show that for these special mass deformations only the states annihilated by extra supercharges contribute to the index. By using an equivalence between partition functions on squashed spheres and ellipsoids, we explain the recently …
We discuss the interplay between IR and UV divergences in vacuum configurations with open and unoriented strings. We establish a general one-to-one correspondence between anomalies and R-R tadpoles associated to sectors with non-trivial Witten index. The result does not require any supersymmetry to be preserved by the configuration. Under very mild conditions of supersymmetry, a similar correspondence is found between NS-NS tadpoles and RG-flows in gauge theories on D-branes and O-planes. We briefly comment on the AdS/CFT counterpart of the results.
Supersymmetric theories in four dimensions with chiral superfields have very rich BRS cohomology, which gives rise to potential anomalies in theories that contain composite antichiral spinor superfields. Assuming the coefficients are non-zero, absence of the anomalies would generate new constraints on theories. In addition, the anomalies give rise to a new kind of supersymmetry breaking which is quite different from the known kinds, and also naturally yields a zero cosmological constant after supersymmetry breaking.
We present a comprehensive analysis of supersymmetry anomalies in the free and massless Wess-Zumino (WZ) model in perturbation theory. At the classical level the model possesses ${\mathcal N}=1$ superconformal symmetry, which is partially broken by quantum anomalies. The form of the anomalies and the part of the symmetry they break depend on the multiplet of conserved currents used. It was previously shown that the R-symmetry anomaly of the conformal current multiplet induces an anomaly in Q-supersymmetry, which appears first in 4-point functions. Here we confirm this result by an explicit 1-l…
We give a concise geometric recipe for constructing D-brane gauge theories that exhibit metastable SUSY breaking. We present two simple examples in terms of branes at deformed CY singularities.
Local terms in the Operator Product Expansion in Superconformal Theories with extended supersymmetry are identified. Assuming a factorized structure for these terms their contributions are discussed.
Maximally supersymmetric mass deformation of the Bagger-Lambert-Gustavsson (BLG) theory corresponds to a {non-central} extension of the d=3 N=8 Poincare superalgebra (allowed in three dimensions). We obtain its light-cone superspace formulation which has a novel feature of the dynamical supersymmetry generators being {cubic} in the kinematical ones. The mass deformation picks a quaternionic direction, which breaks the SO(8) R-symmetry down to SO(4)xSO(4). The Hamiltonian of the theory is shown to be a quadratic form of the dynamical supersymmetry transformations, to all orders in the mass para…
We construct a solvable deformation of two-dimensional theories with $(2,2)$ supersymmetry using an irrelevant operator which is a bilinear in the supercurrents. This supercurrent-squared operator is manifestly supersymmetric, and equivalent to $T\bar{T}$ after using conservation laws. As illustrative examples, we deform theories involving a single $(2,2)$ chiral superfield. We show that the deformed free theory is on-shell equivalent to the $(2,2)$ Nambu-Goto action. At the classical level, models with a superpotential exhibit more surprising behavior: the deformed theory exhibits poles in th…
We present a derivation of the chiral ring relations, arising in ${\cal N}=1$ gauge theories in the presence of (anti-)self-dual background gravitational field $G_{αβγ}$ and graviphoton field strength $F_{αβ}$. These were previously considered in the literature in order to prove the relation between gravitational F-terms in the gauge theory and coefficients of the topological expansion of the related matrix integral. We consider the spontaneous breaking of ${\cal N} =2$ to ${\cal N} =1$ supergravity coupled to vector- and hyper-multiplets, and take a rigid limit which keeps a non-trivial $G_{α…
We study the realization of anomalous Ward identities in deconstructed (latticized) supersymmetric theories. In a deconstructed four-dimensional theory with N=2 supersymmetry, we show that the chiral symmetries only appear in the infrared and that the anomaly is reproduced in the usual framework of lattice perturbation theory with Wilson fermions. We then realize the theory on the world-volume of fractional D-branes on an orbifold. In this brane realization, we show how deconstructed theory anomalies can be computed via classical supergravity. Our methods and observations are more generally ap…
