Pure Supergravity Research Articles

N=1 supergravity and Maxwell superalgebras

We present the construction of the D = 4 supergravity action from the minimal Maxwell superalgebra sℳ4, which can be derived from the $$ \mathfrak{osp}\ \left(4\Big|1\right) $$ superalgebra by applying the abelian semigroup expansion procedure. We show that N = 1, D = 4 pure supergravity can be obtained alternatively as the MacDowell-Mansouri like action built from the curvatures of the Maxwell superalgebra sℳ4. We extend this result to all minimal Maxwell superalgebras type sℳ m + 2. The invariance under supersymmetry transformations is also analized.

N=1 and N=2 pure supergravities on a manifold with boundary

Working in the geometric approach, we construct the lagrangians of N = 1 and N = 2 pure supergravity in four dimensions with negative cosmological constant, in the presence of a non trivial boundary of space-time. We find that the supersymmetry invariance of the action requires the addition of topological terms which generalize at the supersymmetric level the Gauss-Bonnet term. Supersymmetry invariance is achieved without requiring Dirichlet boundary conditions on the fields at the boundary, rather we find that the boundary values of the fieldstrengths are dynamically fixed to constant values in terms of the cosmological constant Λ. From a group-theoretical point of view this means in particular the vanishing of the OSp(N|4)-supercurvatures at the boundary.

Minimal [formula omitted] supergravity from the superMaxwell algebra

We show that the first-order D=4, N=1 pure supergravity lagrangian four-form can be obtained geometrically as a quadratic expression in the curvatures of the Maxwell superalgebra. This is achieved by noticing that the relative coefficient between the two terms of the lagrangian that makes the action locally supersymmetric also determines trivial field equations for the gauge fields associated with the extra generators of the Maxwell superalgebra. Along the way, a convenient geometric procedure to check the local supersymmetry of a class of lagrangians is developed.

One-loop four-graviton amplitudes inN=4supergravity models

We evaluate in great detail one-loop four-graviton field theory amplitudes in pure N=4 D=4 supergravity. The expressions are obtained by taking the field theory limits of (4,0) and (2,2) space-time supersymmetric string theory models. For each model we extract the contributions of the spin-1 and spin-2 N=4 supermultiplets running in the loop. We show that all of those constructions lead to the same four-dimensional result for the four-graviton amplitudes in pure supergravity even though they come from different string theory models.

An R4 non-renormalization theorem in super-gravity

We consider the four-graviton amplitudes in CHL constructions providing four-dimensional models with various numbers of vector multiplets. We show that in these models the two-loop amplitude has a prefactor of ∂2R4. This implies a non-renormalization theorem for the R4 term, which forbids the appearance of a three-loop ultraviolet divergence in four dimensions in the four-graviton amplitude. We connect the special nature of the R4 term to the U(1) anomaly of pure super-gravity.

A dual formulation of supergravity–matter theories

Generating supersymmetric AdS solutions in non-minimal supergravity in four dimensions is notoriously difficult. Indeed, it is a longstanding lore that such solutions exist only for old minimal supergravity. In this paper, we construct a dual formulation for general N = 1 supergravity–matter systems that avoids the problem. In the case of pure supergravity without a cosmological constant, it coincides with the usual non-minimal ( n = − 1 ) supergravity, but in the presence of matter (or a cosmological constant) our formulation differs considerably. We also elaborate upon the framework of conformal superspace and the compensator method as applied to our theory. In particular, we show that one can encode the details of the Kähler potential and superpotential entirely within the geometry of superspace so that the general sigma-model action is encoded in a single compact term: the supervolume. Finally, we discuss the issue of supercurrents and propose a general form for the supercurrent in AdS.

Generalized mirror symmetry and trace anomalies

We consider the compactification of M-theory on X7 with Betti numbers (b0, b1, b2, b3, b3, b2, b1, b0) and define a generalized mirror symmetry (b0, b1, b2, b3) → (b0, b1, b2 − ρ/2, b3 + ρ/2) under which ρ ≡ 7b0 − 5b1 + 3b2 − b3 changes sign. Generalized self-mirror theories with ρ = 0 have massless sectors with vanishing trace anomaly (before dualization). Examples include pure supergravity with and supergravity plus matter with .

Superconformal symmetry, NMSSM, and inflation

We identify a particularly simple class of supergravity models describing superconformal coupling of matter to supergravity. In these models, which we call the canonical superconformal supergravity models, the kinetic terms in the Jordan frame are canonical, and the scalar potential is the same as in the global theory. The pure supergravity part of the total action has a local Poincar\'e supersymmetry, whereas the chiral and vector multiplets coupled to supergravity have a larger local superconformal symmetry. The scale-free globally supersymmetric theories, such as the NMSSM with a scale-invariant superpotential, can be naturally embedded into this class of theories. After the supergravity embedding, the Jordan frame scalar potential of such theories remains scale free; it is quartic, it contains no mass terms, no nonrenormalizable terms, no cosmological constant. The local superconformal symmetry can be broken by additional terms, which, in the small field limit, are suppressed by the gravitational coupling. This can be achieved by introducing the nonminimal scalar-curvature coupling, and by taking into account interactions with a hidden sector. In this approach, the smallness of the mass parameters in the NMSSM may be traced back to the original superconformal invariance. This allows one to address the $\ensuremath{\mu}$ problem and the cosmological domain wall problem in this model, and to implement chaotic inflation in the NMSSM. We discuss the gravitino problem in the NMSSM inflation, as well as the possibility to obtain a broad class of new versions of chaotic inflation in supergravity.

Universal BPS structure of stationary supergravity solutions

We study asymptotically flat stationary solutions of four-dimensional supergravity theories via the associated G/H ∗ pseudo-Riemannian non-linear sigma models in three spatial dimensions. The Noether charge C associated to G is shown to satisfy a characteristic equation that determines it as a function of the four-dimensional conserved charges. The matrix C is nilpotent for non-rotating extremal solutions. The nilpotency degree of C is directly related to the BPS degree of the corresponding solution when they are BPS. Equivalently, the charges can be described in terms of a Weyl spinor |C i of Spin ∗ (2N), and then the characteristic equation becomes equivalent to a generalisation of the Cartan pure spinor constraint on |C i . The invariance of a given solution with respect to supersymmetry is determined by an algebraic ‘Dirac equation’ on the Weyl spinor |C i . We explicitly solve this equation for all pure supergravity theories and we characterise the stratified structure of the moduli space of asymptotically Taub–NUT black holes with respect to their BPS degree. The analysis is valid for any asymptotically flat stationary solutions for which the singularities are protected by horizons. The H ∗ -orbits of extremal solutions are identified as Lagrangian submanifolds of nilpotent orbits of G, and so the moduli space of extremal spherically symmetric black holes is identified as a Lagrangian subvariety of the variety of nilpotent elements of g. We also generalise the notion of active duality transformations to an ‘almost action’ of the three-dimensional duality group G on asymptotically flat stationary solutions.

Noncommutative supergravity inD= 3 andD= 4

We present a noncommutative D=3, N=1 supergravity, invariant under diffeomorphisms, local U(1,1) noncommutative \star-gauge transformations and local \star-supersymmetry. Its commutative limit is the usual D=3 pure supergravity, without extra fields. A noncommutative deformation of D=4, N=1 supergravity is also obtained, reducing to the usual simple supergravity in the commutative limit. Its action is invariant under diffeomorphisms and local GL(2,C) \star-gauge symmetry. The supersymmetry of the commutative action is broken by noncommutativity. Local \star-supersymmetry invariance can be implemented in a noncommutative D=4, N=1 supergravity with chiral gravitino and complex vierbein.

D=4attractors, effective horizon radius, and fake supergravity

We consider extremal black hole attractors [both Bogomol'nyi-Prasad-Sommerfield (BPS) and non-BPS] for $\mathcal{N}=3$ and $\mathcal{N}=5$ supergravity in $d=4$ space-time dimensions. Attractors for matter-coupled $\mathcal{N}=3$ theory are similar to attractors in $\mathcal{N}=2$ supergravity minimally coupled to Abelian vector multiplets. On the other hand, $\mathcal{N}=5$ attractors are similar to attractors in $\mathcal{N}=4$ pure supergravity, and in such theories only $\frac{1}{\mathcal{N}}$-BPS nondegenerate solutions exist. All the above-mentioned theories have a simple interpretation in the first order (fake supergravity) formalism. Furthermore, such theories do not have a $d=5$ uplift. Finally we comment on the duality relations among the attractor solutions of $\mathcal{N}\ensuremath{\ge}2$ supergravities sharing the same full bosonic sector.

Supersymmetry breaking and the radion inAdS4brane worlds

We compute the one-loop correction to the radion potential in the Randall-Sundrum model with detuned brane tensions, with supersymmetry broken by boundary conditions. We concentrate on the small warping limit, where the one-loop correction is significant. With pure supergravity, the correction is negative, but with bulk hypermultiplets, the correction can be positive, so that the 4d curvature can be lowered, with the radion stable. We use both the KK theory, and the 4d radion effective theory for this study.

Five-dimensional supergravity and the hyperbolic Kac–Moody algebra GH2

Motivated by the recent analysis of the E10 sigma model for the study of M-theory, we study a one-dimensional sigma model associated with the hyperbolic Kac–Moody algebra GH2 and its link to pure supergravity, which closely resembles in many ways D = 11 supergravity. The bosonic equations of motion and the Bianchi identity for D = 5 pure supergravity match the equations of the level ℓ ⩽ 3 truncation of the GH2 sigma model up to higher level terms, just as they do for the D = 11 case. We also compute low level root and outer multiplicities in the A3 decomposition, and indeed find singlets at ℓ = 4k, k = 2, 3, … corresponding to the scaling of ERk+1 terms, although the missing singlet at ℓ = 4 remains a puzzle.

Charged rotating black holes in five dimensionalU(1)3gaugedN=2supergravity

We obtain the general solution for non-extremal 3-charge dilatonic rotating black holes in the U(1)^3 gauged five-dimensional N=2 supergravity coupled to two vector multiplets, in the case where the two rotation parameters are set equal. These solutions encompass all the previously-known extremal solutions, and, by setting the three charges equal, the recently-obtained non-extremal solutions of N=2 gauged five-dimensional pure supergravity.

Scalar-field amplitudes in black-hole evaporation

We consider the quantum-mechanical decay of a Schwarzschild-like black hole into almost-flat space and weak radiation at a very late time. That is, we are concerned with evaluating quantum amplitudes (not just probabilities) for transitions from initial to final states. In this quantum description, no information is lost because of the black hole. The Lagrangian is taken, in the first instance, to consist of the simplest locally supersymmetric generalization of Einstein gravity and a massless scalar field. The quantum amplitude to go from given initial to final bosonic data in a slightly complexified time-interval T=τexp(−iθ) at infinity may be approximated by the form const×exp(−I), where I is the (complex) Euclidean action of the classical solution filling in between the boundary data. Additionally, in a pure supergravity theory, the amplitude const×exp(−I) is exact. Suppose that Dirichlet boundary data for gravity and the scalar field are posed on an initial spacelike hypersurface extending to spatial infinity, just prior to collapse, and on a corresponding final spacelike surface, sufficiently far to the future of the initial surface to catch all the Hawking radiation. Only in an averaged sense will this radiation have an approximately spherically-symmetric distribution. If the time-interval T had been taken to be exactly real, then the resulting ‘hyperbolic Dirichlet boundary-value problem’ would, as is well known, not be well posed. Provided instead (‘Euclidean strategy’) that one takes T complex, as above (0<θ⩽π/2), one expects that the field equations become strongly elliptic, and that there exists a unique solution to the classical boundary-value problem. Within this context, by expanding the bosonic part of the action to quadratic order in perturbations about the classical solution, one obtains the quantum amplitude for weak-field final configurations, up to normalization. Such amplitudes are here calculated for weak final scalar fields.

Unitary and Complex Matrix Models as 1-d Type 0 Strings

We propose that the double scaling behavior of the unitary matrix models, and that of the complex matrix models, is related to type 0B and 0A fermionic string theories. The particular backgrounds involved correspond to $\hat c<1 $ matter coupled to super-Liouville theory. We examine in detail the $\hat c=0$ or pure supergravity case, which is related to the double scaling limit around the Gross-Witten transition, and find that reversing the sign of the Liouville superpotential interchanges the 0A and 0B theories. We also find smooth transitions between weakly coupled string backgrounds with D-branes, and backgrounds with Ramond-Ramond fluxes only. Finally, we discuss matrix models with multicritical potentials that are conjectured to correspond to 0A/0B string theories based on $(2, 4k)$ super-minimal models.

Killing spinor equations from nonlinear realisations

Starting from a nonlinear realisation of eleven-dimensional supergravity based on the group G 11 , whose generators appear as low level generators of E 11 , we present a super extended algebra, which leads to a covariant derivative of spinors identical to the Killing spinor equation of this theory. A similar construction leads to the Killing spinor equation of N = 1 pure supergravity in ten dimensions.

AN APPROACH TO SOLVE SLAVNOV–TAYLOR IDENTITY IN D4 ${\mathcal N}=1$ SUPERGRAVITY

We consider a particular solution to Slavnov–Taylor identity in four-dimensional supergravity. The consideration is performed for pure supergravity, no matter superfields are included. The solution is obtained by inserting dressing functions into ghost part of the classical action for supergravity. As a consequence, physical part of the effective action is local invariant with respect to diffeomorphism and structure groups of transformation for dressed effective superfields of vielbein and spin connection.

New D=6, [formula omitted] gauged supergravity with supersymmetric (Minkowski)4×S2 vacuum

We obtain a new gauged D=6, N=(1,1) pure supergravity by a generalised consistent Kaluza–Klein reduction of M-theory on K3×R. The reduction requires a conspiratory gauging of both the Cremmer–Julia type global (rigid) symmetry and the homogeneous rescaling symmetry of the supergravity equations of motion. The gauged supergravity is different from the Romans D=6 gauged supergravity in that the four vector fields in our new theory are all abelian. We show that it admits a supersymmetric (Minkowski)4×S2 vacuum, which can be lifted to D=11 where it becomes the near-horizon geometry of two intersecting M5-branes wrapping on a supersymmetric two-cycle of K3.

Gauged locally supersymmetric D=3 nonlinear sigma models

We construct supersymmetric deformations of general, locally supersymmetric, nonlinear sigma models in three spacetime dimensions, by extending the pure supergravity theory with a Chern–Simons term and gauging a subgroup of the sigma model isometries, possibly augmented with R-symmetry transformations. This class of models is shown to include theories with standard Yang–Mills Lagrangians, with optional moment interactions and topological mass terms. The results constitute a general classification of three-dimensional gauged supergravities.