In this paper we perform, in the spirit of the holographic correspondence, a particular asymptotic limit of N=2, AdS_4 supergravity to N=2 supergravity on a locally AdS_3 boundary. Our boundary theory enjoys OSp(2|2) x SO(1,2) invariance and is shown to contain the D=3 super-Chern Simons OSp(2|2) theory considered in [Alvarez:2011gd] and featuring "unconventional local supersymmetry". The model constructed in that reference describes the dynamics of a spin-1/2 Dirac field in the absence of spin 3/2 gravitini and was shown to be relevant for the description of graphene, near the Dirac points, for specific spatial geometries. Our construction yields the model in [Alvarez:2011gd] with a specific prescription on the parameters. In this framework the Dirac spin-1/2 fermion originates from the radial components of the gravitini in D=4.
By applying generalized dimensional reduction on the type IIB supersymmetry variations, we derive the supersymmetry variations for the massive 9-dimensional supergravity. We use these variations and the ones for massive type IIA to derive the supersymmetry transformation of the gravitino for the proposed massive 11-dimensional supergravity.
We analyze maximal supersymmetry in eleven-dimensional supergravity from the point of view of the oriented matroid theory. The mathematical key tools in our discussion are the Englert solution and the chirotope concept. We argue that chirotopes may provide other solutions not only for eleven-dimensional supergravity but for any higher dimensional supergravity theory.
We construct the supergravity solution in 11 dimensions describing D6-branes wrapped around a Kahler four-cycle with a B-field along the flat directions of the brane. The configuration is dual to an N=2 noncommutative gauge theory in 2+1 dimensions. We also construct the four associated independent Killing spinors. The phenomenon of supersymmetry without supersymmetry appears naturally when compactifying to type IIA or 8d gauged supergravity. Therefore, this solution also provides an 11d background with four supercharges and four-form flux, which is not obtainable from 8d gauged supergravity.
We study the coupling of non-linear supersymmetry to supergravity. The goldstino nilpotent superfield of global supersymmetry coupled to supergravity is described by a geometric action of the chiral curvature superfield R subject to the constraint (R-λ)^2=0 with an appropriate constant λ. This constraint can be found as the decoupling limit of the scalar partner of the goldstino in a class of f(R) supergravity theories.
Some general aspects of supersymmetry and supergravity are briefly reviewed with emphasis on Noether supercurrents and their role in the discussion of supersymmetry breaking.
The supersymmetry invariance of flat supergravity (i.e., supergravity in the absence of any internal scale in the Lagrangian) in four dimensions on a manifold with non-trivial boundary is explored. Using a geometric approach we find that the supersymmetry invariance of the Lagrangian requires to add appropriate boundary terms. This is achieved by considering additional gauge fields to the boundary without modifying the bulk Lagrangian. We also construct an enlarged supergravity model from which, in the vanishing cosmological constant limit, flat supergravity with a non-trivial boundary emerges…
The complete supersymmetric action for eleven-dimensional supergravity is presented. The action is polynomial in the scalar fermionic pure spinor superfield, and contains only a minor modification to the recently proposed three-point coupling.
We derive a $2+1$ dimensional model with unconventional supersymmetry at the boundary of an ${\rm AdS}_4$ $\mathcal{N}$-extended supergravity, generalizing previous results. The (unconventional) extended supersymmetry of the boundary model is instrumental in describing, within a top-down approach, the electronic properties of graphene-like 2D materials at the two Dirac points, ${\bf K}$ and ${\bf K}'$. The two valleys correspond to the two independent sectors of the ${\rm OSp}(p|2)\times {\rm OSp}(q|2)$ boundary model in the $p=q$ case, which are related by a parity transformation. The Semenof…
We give an introduction to rigid supersymmetry, supergravity and superspace by considering a quantum mechanical model. We analyze the constraints in superspace in this simplified model, and compare the Hamiltonian and Lagrangian BRST formalism.
We study the coupling of supergravity with a purely bosonic brane source (bosonic p-brane). The interaction, described by the sum of their respective actions, is self-consistent if the bosonic p-brane is the pure bosonic limit of a super-p-brane. In that case the dynamical system preserves 1/2 of the local supersymmetry characteristic of the `free' supergravity.
By applying Noether method to N=1 local supersymmetry in eleven dimensions, we obtained two candidates of R^4 corrections to the supergravity. The bosonic parts of these two completely match with the results obtained by type IIA string perturbative calculations. We also obtained 13 parameters which relate only fermionic terms.
We consider the minimal three-form ${\cal N}=1$ supergravity coupled to nilpotent three-form chiral superfields. The supersymmetry breaking is sourced by the three-forms of the chiral multiplets, while the value of the gravitino mass is controlled by the three-form of the supergravity multiplet. The three-forms can nucleate membranes which scan both the supersymmetry breaking scale and the gravitino mass. The peculiar supergravity feature that the cosmological constant is the sum of a positive contribution from the supersymmetry breaking scale and a negative contribution from the gravitino mas…
We consider the interplay of duality symmetries and gauged isometries of supergravity models giving N-extended, spontaneously broken supergravity with a no-scale structure. Some examples, motivated by superstring and M-theory compactifications are described.
Supersymmetry is used to derive conditions on higher derivative terms in the effective action of type IIB supergravity. Using these conditions, we are able to prove earlier conjectures that certain modular invariant interactions of order alpha' **3 relative to the Einstein-Hilbert term are proportional to eigenfunctions of the Laplace operator on the fundamental domain of SL(2,Z). We also discuss how these arguments generalize to terms of higher order in alpha', as well as to compactifications of supergravity.
Induced supersymmetry representations on composite operators are studied. In superspace the ensuing transformation rules (trivially) lead to an effective superfield. On the other hand, an induced representation must exist for non-linear (``on-shell'') supersymmetry as well. As this choice of the representation is physically irrelevant, any formulation of an effective action starting from the superspace representation must equally well be possible in a non-linear representation. We show that this leads to very relevant constraints on the formulation of effective actions in terms of composite op…
We consider the stability of non-supersymmetric critical points of general N=4 supergravities. A powerful method to analyse this issue based on the sGoldstino direction has been developed for minimal supergravity. We adapt this to the present case, and address the conceptually new features arising for extended supersymmetry. As an application, we investigate the stability when supersymmetry breaking proceeds via either the gravity or the matter sector. Finally, we outline the N=8 case.
We introduce and completely describe the analogues of the Riemann curvature tensor for the curved supergrassmannian of the passing through the origin (0|2)-dimensional subsupermanifolds in the (0|4)-dimensional supermanifold with the preserved volume form. The underlying manifold of this supergrassmannian is the conventional Penrose's complexified and compactified version of the Minkowski space, i.e., the Grassmannian of 2-dimensional subspaces in the 4-dimensional space. The result provides with yet another counterexample to Coleman-Mandula's theorem.
We investigate the occurrence of divergences in maximal supergravity in various dimensions from the point of view of supersymmetry constraints on the U-duality invariant threshold functions defining the higher derivative couplings in the effective action. Our method makes use of tensorial differential equations that constrain these couplings. We study in detail the Fourier modes and wave-front sets of the associated automorphic functions and find that they are always associated to special nilpotent orbits.
We report on the gauged supergravity interpretation of certain compactifications of superstring theories with p-form fluxes turned on. We discuss in particular the interplay of duality symmetries in type IIB orientifolds and gauged isometries in the corresponding supergravity models. Turning on fluxes is generally described by the gauging of some nilpotent Lie group whose generators correspond to axion symmetries of R-R and N-S scalars.
We review the general gauged N=2 supergravity coupled to an arbitrary number of vector multiplets and hypermultiplets. We consider two different models where N=2 supersymmetry is broken to N=1 spontaneously, one has a U(1) vector multiplet and the other has a U(N) vector multiplet. In both cases, partial breaking of N=2 supersymmetry is accomplished by the Higgs and the super-Higgs mechanisms. The mass spectrum can be evaluated and we conclude that the resulting models have N=1 supersymmetry. This is based on master thesis submitted to Graduate School of Science, Osaka City University, in Marc…
In this paper we consider the problem of spontaneous supersymmetry breaking in $N=4$ supergravity interacting with vector multiplets. We start with the ordinary version of such model with the scalar field geometry $SU(1,1)/U(1)\otimes SO(6,m)/SO(6)\otimes SO(m)$. Then we construct a dual version of this theory with the same scalar field geometry, which corresponds to the interaction of arbitrary number of vector multiplets with the hidden sector, admitting spontaneous supersymmetry breaking without a cosmological term. We show that supersymmetry breaking is still possible in the presence of ma…
We consider superconformal field theories in three and six dimensions with eight supercharges which can be realized on the world-volume of M-theory branes sitting at orbifold singularities. We find that they should admit a N=4 and N=2 supergravity dual in AdS_4 and AdS_7, respectively. We discuss the characteristics of the corresponding gauged supergravities.
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 discuss an $\cal{N}=2$ supergravity model that interpolates the full and the partial supersymmetry breakings. In particular, we find the conditions for an $\cal{N}=0$ Minkowski vacuum, which is continuously connected to the partial-breaking ($\cal{N}=1$ preserving) one. The model contains multiple (Abelian) vector multiplets and a single hypermultiplet, and is constructed by employing the embedding tensor technique. We compute the mass spectrum on the Minkowski vacuum, and find some non-trivial mass relations among the massive fields. Our model allows us to choose the two supersymmetry-brea…
We study the rigid limit of 5d conformal supergravity with minimal supersymmetry on Riemannian manifolds. The necessary and sufficient condition for the existence of a solution is the existence of a conformal Killing vector. Whenever a certain $SU(2)$ curvature becomes abelian the backgrounds define a transversally holomorphic foliation. Subsequently we turn to the question under which circumstances these backgrounds admit a kinetic Yang-Mills term in the action of a vector multiplet. Here we find that the conformal Killing vector has to be Killing. We supplement the discussion with various ap…
From a gauge $SU(2,2|2)$ model with broken supersymmetry, we construct an action for $SU(2)\times U(1)$ Yang-Mills theory coupled to gravity and matter. The connection components for AdS boosts and special conformal translations are auxiliary fields and their fixing reduces the theory to two distintive sectors: a vector-like gauge theory with general relativity and a chiral gauge theory where gravity drops out. We discuss some of the main classical features of the model such as the predicted tree level gauge couplings, cosmological constant value, mass-like terms and the Einstein equations.
We study a minimal model of U(N) gauged N=2 supergravity with one hypermultiplet parametrizing SO(4,1)/SO(4) quaternionic manifold. Local N=2 supersymmetry is known to be spontaneously broken to N=1 in the Higgs phase of U(1)_{graviphoton} \times U(1). Several properties are obtained of this model in the vacuum of unbroken SU(N) gauge group. In particular, we derive mass spectrum analogous to the rigid counterpart and put the entire effective potential on this vacuum in the standard superpotential form of N=1 supergravity.
We begin with the simplest possible introduction to supergravity. Then we discuss its spin 3/2 stress tensor; these results are new. Next, we discuss boundary conditions on fields and boundary actions for N=1 supergravity. Finally, we discuss new boundary contributions to the mass and central charge of monopoles in N=4 super Yang-Mills theory. All models are in 3+1 dimensions.
Chiral/self-dual restrictions of various super Yang-Mills and supergravity theories in (2,2) dimensions are described. These include the N=1 supergravity with a cosmological term and the N=1 new minimal supergravity theory. In the latter case, a self-duality condition on a torsionful Riemann curvature is possible, and it implies the equations of motion that follow from an $R^2$ type supergravity action.
In this paper, using a model of N=2 supergravity - vector multiplets interaction with the scalar field geometry $SU(1,m)/SU(m)\otimes U(1)$ as an example, we show that even when the geometry is fixed one can have a whole family of the Lagrangians that differ by the vector field duality transformations. As a byproduct, for this geometry we have constructed a model of (m-1) vector multiplets interacting with the hidden sector admitting spontaneous supersymmetry breaking with two arbitrary scales and without a cosmological term.
We study the large $N$ limit of a little string theory that reduces in the IR to U(N) ${\cal N} =1$ supersymmetric Yang-Mills with Chern Simons coupling $k$. Witten has shown that this field theory preserves supersymmetry if $k\geq N/2$ and he conjectured that it breaks supersymmetry if $k< N/2$. We find a non-singular solution that describes the $k=N/2$ case, which is confining. We argue that increasing $k$ corresponds to adding branes to this solution, in a way that preserves supersymmetry, while decreasing $k$ corresponds to adding anti-branes, and therefore breaking supersymmetry.
We review on a recent construction of the on-shell supersymmetric brane action for the codimension-two branes with nonzero tension in the flux compactification of a 6D chiral gauged supergravity. On dimesionally reducing on 4D gauged supergravity for a new supersymmetric unwarped background with conical branes, we consider the modulus stabilization for determining the soft masses of the scalars localized on the branes and show that the bulk U(1)_R provides a new mechanism for mediating the SUSY breaking.
In the framework of N=2 conformal supergravity in four dimensions, we introduce a nilpotent chiral superfield suitable for the description of partial supersymmetry breaking in maximally supersymmetric spacetimes. As an application, we construct Maxwell-Goldstone multiplet actions for partial N=2 --> N=1 supersymmetry breaking on R x S^3, AdS_3 x S^1 (or its covering AdS_3 x R), and a pp-wave spacetime. In each of these cases, the action coincides with a unique curved-superspace extension of the N=1 supersymmetric Born-Infeld action, which is singled out by the requirement of U(1) duality invar…
We study the one-loop corrections to the effective on-shell action of N=2 supergravity in the background of the Reissner-Nordstrom black hole. In the extreme case the contributions from graviton, gravitino and photon to the one-loop corrections to the entropy are shown to cancel. This gives the first explicit example of the supersymmetric non-renormalization theorem for the on-shell action (entropy) for BPS configurations which admit Killing spinors. We display the residual supersymmetry of the perturbations of a general supersymmetric theory in a bosonic BPS background.
In this paper we derive higher derivative corrections to the eleven dimensional supergravity by applying the Noether method with respect to the N=1 local supersymmetry. An ansatz for the higher derivative effective action, which includes quartic terms of the Riemann tensor, is parametrized by 132 parameters. Then we show that by the requirement of the local supersymmetry, the higher derivative effective action is essentially described by two parameters. The bosonic parts of these two superinvariants completely match with the known results obtained by the perturbative calculations in the type I…
An action for the higher-derivative corrections to minimal gauged supergravity in four dimensions has been recently proposed. We demonstrate that the supersymmetric solutions of this model are those of the two-derivative action, and investigate some of their properties. In particular, we prove a formula for the renormalised on-shell action in terms of contributions from fixed points of a $U(1)$ action, and confirm that it is invariant under deformations which preserve the boundary almost contact structure.
We obtain a four-dimensional supergravity with spontaneously broken supersymmetry allowing for de Sitter vacua by coupling a superspace action of minimal N=1, D=4 supergravity to a locally supersymmetric generalization of the Volkov-Akulov goldstino action describing the dynamics of a space-filling non-BPS 3-brane in N=1, D=4 superspace. To the quadratic order in the goldstino field the obtained action coincides with earlier constructions of supergravities with nilpotent superfields, while matching the higher-order contributions will require a non-linear redefinition of fields. In the unitary …
The status of the gaugino condensation as the source of supersymmetry breaking is reexamined. It is argued that one cannot have stable minima with broken supersymmetry in models where the dilaton is coupled only linearly to the gaugino condensate. We show that the problems of the gaugino condensate mechanism can be solved by considering nonstandard gauge kinetic functions, created by nonperturbative effects. As an example we use the principle of S-duality to modify the coupling of the gaugino condensate to effective supergravity (superstring) Lagrangians. We show that such an approach can solv…
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 …
In this paper we investigate the problem of spontaneous supersymmetry breaking without a cosmological term in $N=3$ supergravity with matter vector multiplets, scalar fields geometry being $SU(3,m)/SU(3)\otimes SU(m)\otimes U(1)$. At first, we consider the case of minimal coupling with different possible gaugings (compact as well as non-compact). Then we show that there exist dual version of such a theory (with the same scalar field geometry), which turns out to be the generalization of the $N=3$ hidden sector, constructed some time ago by one of us, to the case of arbitrary number of vector m…
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…
We propose a scenario where the effects of dislocations, in bidimensional Dirac materials at low energies, can be described within a Dirac field theory by a vertex proportional to the totally antisymmetric component of the torsion generated by such dislocations. The well-known geometrical obstruction to have a nonzero torsion term of that kind in this two-dimensional settings is overcome through exotic time-loops, obtained from ingeniously manipulated particle-hole dynamics. If such torsion/dislocation is indeed present, a net flow of particles-antiparticles (holes) can be inferred and possibl…
The coupling of matter to supergravity with $N=1$ supersymmetry in $d=4$ dimensions is described in a geometric manner by Kähler superspace. A straightforward way to implement Kähler superspace is via $\mathrm{U}(1)$ superspace by identifying the $\mathrm{U}(1)$ pre-potential with the Kähler potential, which is a function of the matter (chiral) superfields. In this framework, the components of the supergravity multiplet are contained in the supervielbein and torsion tensor of superspace. Furthermore, interactions with the Yang-Mills (vector) multiplet are formulated by introducing a connection…
We obtain a bosonization prescription that allows to represent the energy-momentum tensor and supersymmetry generators of non-critical superstring theories with minimal matter as those of topological supergravity. Superstrings with $N=1$ and $N=2$ world-sheet supersymmetry are considered. The topological symmetry associated with the topological supergravity representation is studied. It is shown, in particular, that the compatibility of this topological structure with the supersymmetry enhances the superconformal symmetry of the models concerned.
We show that CP-violating Weyl anomaly induces a supersymmetry anomaly in the formulation of superconformal supergravity as is observed in CP-preserving cases. This supersymmetry anomaly can be removed in the old minimal supergravity by adding suitable local counterterms, and it becomes a consistent theory.
We use a new mechanism for generating a Fayet-Iliopoulos term in supergravity, which is not associated to an R symmetry, to construct a semi-realistic theory of slow-roll inflation for a theory with the same Kähler potential and superpotential as the KKLT string background (without anti-D3 branes). In our model, supersymmetry must be broken at a high scale in a hidden sector to ensure that the cutoff of the effective field theory is above the Hubble scale of inflation. The gravitino has a super-EeV mass and supersymmetry breaking is communicated to the observable sector through gravity mediati…
We present a description for amplitude diagrams in maximal supergravities obtained by dimensional reduction from D=11, derived from a field theory point of view using the pure spinor formalism. The advantages of this approach are the manifest supersymmetry present in the formalism, and the limited number of interaction terms in the action. Furthermore, we investigate the conditions set by this description in order for amplitudes in maximal supergravity to be finite in the ultraviolet limit. Typically, there is an upper limit to the dimension, set by the loop order, which for an arbitrary numbe…
We discuss various aspects of rigid supersymmetry within minimal N=1 off-shell supergravity using the old and new minimal formulations both in Lorentzian and Euclidean signatures. In particular, we construct all rigid supersymmetry backgrounds with a hypersurface orthogonal Killing vector. In the Lorentzian signature we show that AdS_4 provides a rigid supersymmetric background in both formulations albeit with different amounts of preserved supersymmetry. In the Euclidean signature we find new backgrounds of the old-minimal supergravity, including squashed four-spheres and a half-BPS version o…
For extended $\mathcal{N}\leq 8$ supersymmetry we classify all possible gauge groups for a scalar multiplet allowed by the algebras of global and local supersymmetry in three dimensions. A detailed discussion of supersymmetry enhancement is included. For the corresponding topologically massive gravity with negative cosmological constant the mass of the graviton is determined algebraically as a function of $\mathcal{N}$ and the possible gauge couplings.
We comment on the ubiquity of the so-called warped anti-de Sitter spacetimes in three-dimensional (2,0) supergravity theory. By using isometry-invariant tensors and simple counting, we prove their existence for arbitrary $(2,0)$ supergravity models suitably defined close to a minimal model. We also analyze their offshell supersymmetry and the supersymmetry of two geometric orbifolds.
We discuss the supersymmetry and fermionic sector of the recently obtained consistent truncations of IIB supergravity containing massive modes. In particular, we present the general form of the five-dimensional N = 4 supersymmetry transformations and equations of motion for the fermions arising in the reduction of IIB theory on T^{1,1} which contains all modes invariant under the SU(2) x SU(2) isometry group. The N = 4 reduction can be further truncated to two different N = 2 sub-sectors. For each of these, we present the N = 2 fermionic supersymmetry transformations and corresponding superpot…
Candidate counterterms break E7 type U-duality symmetry of $N \geq 5$ supergravity theories in four dimensions \cite{Kallosh:2011dp}. A proposal was made in \cite{Bossard:2011ij} to restore it, starting with a double set of vector fields and argued that a supersymmetric extension of their proposal should exist. We show that the extra vectors, needed for the deformation, can not be auxiliary fields in an eventual off-shell formulation $N \geq 5$ supergravity, assuming that such a formulation exists. Furthermore we show that these extra vector fields can not be dynamical either since that change…
We study the effect of T-duality on supersymmetry in the context of type II supergravity. For both U(1) Abelian and SU(2) non-Abelian T-duality, we demonstrate that the supersymmetry variations after T-duality are related to the variations before T-duality through the Kosmann spinorial Lie derivative, which vanishes when the Killing spinors are independent of the T-duality directions. As a byproduct of our analysis, we present closed expressions for SU(2) T-duality in a class of spacetimes with diagonal Bianchi IX symmetry and comment on specific examples of T-dual geometries, including a nove…
We construct a new harmonic family: dielectric flow solutions with maximal supersymmetry in eleven-dimensional supergravity. These solutions are asymptotically AdS_4 x S^7, while in the infra-red the M2 branes are dielectrically polarized into M5 branes. These solutions are holographically dual to vacua of the mass deformed theory on M2 branes. They also provide an interesting insight on the supergravity solutions sourced by giant gravitons, allowing one to see how supergravity solves the giant graviton puzzle.
We introduce thermal superspace and show how it can be used to reconcile the superfield formulation of supersymmetry with finite temperature environments
We study the conditions under which a generic supergravity model involving chiral and vector multiplets can admit vacua with spontaneously broken supersymmetry and realistic cosmological constant. We find that the existence of such viable vacua implies some constraints involving the curvature tensor of the scalar geometry and the charge and mass matrices of the vector fields, and also that the vector of F and D auxiliary fields defining the Goldstino direction is constrained to lie within a certain domain. We illustrate the relevance of these results through some examples and also discuss the …
We examine domain wall solutions of N=1, D=4 supergravity which preserve half of the supersymmetry and arise from Euclidean M2-brane instantons on M5-branes wrapping associative 3-cycles of G_2 holonomy manifolds. We also investigate composite solutions which break an additional half of the supersymmetry.
