Chiral Supergravity Research Articles

Super Cartan Geometry and the Super Ashtekar Connection

This work is devoted to the geometric approach to supergravity. More precisely, we interpret mathcal {N}=1, D=4 supergravity as a super Cartan geometry which provides a link between supergravity and Yang–Mills theory. To this end, we first review important aspects of the theory of supermanifolds and we establish a link between various different approaches. We then introduce super Cartan geometries using the concept of so-called enriched categories. This, among other things, will enable us to implement anticommutative fermionic fields. We will then also show that non-extended D=4 supergravity naturally arises in this framework. Finally, using this gauge-theoretic interpretation as well as the chiral structure of the underlying supersymmetry algebra, we will derive graded analoga of Ashtekar’s self-dual variables and interpret them in terms of generalized super Cartan connections. This gives canonical chiral supergravity the structure of a Yang–Mills theory with gauge supergroup similar to the self-dual variables in ordinary first-order Einstein gravity. We then construct the parallel transport map corresponding to the super connection in mathematical rigorous way using again enriched categories. This provides the possibility of quantizing gravity and matter degrees of freedom in loop quantum gravity in a unified way.Kindly check and confirm inserted city and country name are correctly identified.City and country name are correct.

Super Virasoro Algebras From Chiral Supergravity

In this note, we construct Noether charges for the chiral supergravity, which contains the Lorentz Chern–Simons term, by applying Wald’s prescription to the vielbein formalism. We investigate the AdS3/CFT2 correspondence by using the vielbein formalism. The asymptotic symmetry group is carefully examined by taking into account the local Lorentz transformation, and we construct super Virasoro algebras with central extensions from the chiral supergravity.

Kac-Moody and Borcherds symmetries of six-dimensional chiral supergravity

We investigate the conjectured infinite-dimensional hidden symmetries of six-dimensional chiral supergravity coupled to two vector multiplets and two tensor multiplets, which is known to possess the $F_{4,4}$ symmetry upon dimensional reduction to three spacetime dimensions. Two things are done. (i) First, we analyze the geodesic equations on the coset space $F_{4,4}^{++}/K(F_{4,4}^{++})$ using the level decomposition associated with the subalgebra $\mathfrak{gl}(5)\oplus \mathfrak{sl}(2)$ of $F_{4,4}^{++}$ and show their equivalence with the bosonic equations of motion of six-dimensional chiral supergravity up to the level where the dual graviton appears. In particular, the self-duality condition on the chiral $2$-form is automatically implemented in the sense that no dual potential appears for that $2$-form, in contradistinction with what occurs for the non chiral $p$-forms. (ii) Second, we describe the $p$-form hierarchy of the model in terms of its $V$-duality Borcherds superalgebra, of which we compute the Cartan matrix.

Gravitational forces on a codimension-2 brane

We compute the gravitational response of six dimensional gauged, chiral supergravity to localized stress energy on one of two space-filling branes, including the effects of compactifying the extra dimensions and brane back-reaction. We find a broad class of exact solutions, including various black-brane solutions. Several approximate solutions are also described, such as the near-horizon geometry of a small black hole which is argued to be approximately described by a 6D Schwarzschild (or Kerr) black hole, with event horizon appropriately modified to encode the brane back-reaction. The general linearized far-field solutions are found in the 4D regime very far from the source, and all integration constants are related to physical quantities describing the branes and the localized energy source. The localized source determines two of these, corresponding to the source mass and the size of the strength of a coupling to a 4D scalar mode whose mass is parametrically smaller than the KK scale. At large distances the solutions agree with those of 4D general relativity, but for an intermediate range of distances (larger than the KK scale) the solutions better fit a Brans-Dicke theory. For a realistic choice of parameters the KK scale could lie at a micron, while the crossover to Brans-Dicke behaviour could occur at around 10 microns. While allowed by present data this points to potentially measurable changes to Newton's Law arising at distances larger than the KK scale.

Old-minimal supergravity models of inflation

We study three types of the old-minimal higher-derivative supergravity theories extending the $f(R)$ gravity, towards their use for the inflationary model building in supergravity, by using both superfields and their field components. In the curved superspace all those theories are described in terms of a single chiral scalar curvature superfeld $\mathcal{R}$. Each of those theories can be dualized into a matter-coupled supergravity without higher derivatives. The first type is parametrized by a single non-holomorphic potential $N(\mathcal{R},\bar{\mathcal{R}})$, and gives rise to the dual matter-coupled supergravities with two dynamical chiral matter superfields having a no-scale K\"ahler potential. We find that a generic potential $N(\mathcal{R},\bar{\mathcal{R}})$ generates both the $(R+R^2)$ gravity and the non-minimal coupling of the propagating complex scalar field to the $R$, needed for the Starobinsky and Higgs inflation, respectively. We find the general conditions for the Starobinsky inflation and compute the inflaton mass. The second type is given by the chiral supergravity actions whose superfield Lagrangian $F(\mathcal{R},\Sigma({\bar{\mathcal R}}))$ also depends upon the chiral projection $\Sigma$ of the anti-chiral superfield ${\bar{\mathcal R}}$. We find that the actions of the second type always give rise to ghosts. We also revisit the $F(\mathcal{R})$ supergravity actions of the third type (without the $\Sigma$-dependence) with the reduced number of the extra physical degrees of freedom, comprising a single chiral matter superfeld with a no-scale K\"ahler potential. We confirm that the pure $F(\mathcal{R})$ supergravity is insufficient for realization of the Starobinsky inflation, though by the reason different from those proposed in the recent literature.

Dirac-Born-Infeld-Volkov-Akulov and deformation of supersymmetry

We deform the action and the supersymmetry transformations of the d = 10 and d = 4 Maxwell supermultiplets so that at each order of the deformation the theory has 16 Maxwell multiplet deformed supersymmetries as well as 16 Volkov-Akulov type non-linear supersymmetries. The result agrees with the expansion in the string tension of the explicit action of the Dirac-Born-Infeld model and its supersymmetries, extracted from D9 and D3 superbranes, respectively. The half-maximal Dirac-Born-Infeld models with 8 Maxwell supermultiplet deformed supersymmetries and 8 Volkov-Akulov type supersymmetries are described by a new class of d = 6 vector branes related to chiral (2,0) supergravity, which we denote as ‘Vp-branes’. We use a space-filling V5 superbrane for the d = 6 model and a V3 superbrane for the d = 4 half-maximal Dirac-Born-Infeld (DBI) models. In this way we present a completion to all orders of the deformation of the Maxwell supermultiplets with maximal 16+16 supersymmetries in d = 10 and 4, and half-maximal 8+8 supersymmetries in d = 6 and 4.

Bulk renormalization and particle spectrum in codimension-two brane worlds

We study the Casimir energy due to bulk loops of matter fields in codimension-two brane worlds and discuss how effective field theory methods allow us to use this result to renormalize the bulk and brane operators. In the calculation we explicitly sum over the Kaluza-Klein (KK) states with a new convenient method, which is based on a combined use of zeta function and dimensional regularization. Among the general class of models we consider we include a supersymmetric example, 6D gauged chiral supergravity. Although much of our discussion is more general, we treat in some detail a class of compactifications, where the extra dimensions parametrize a rugby ball shaped space with size stabilized by a bulk magnetic flux. The rugby ball geometry requires two branes, which can host the Standard Model fields and carry both tension and magnetic flux (of the bulk gauge field), the leading terms in a derivative expansion. The brane properties have an impact on the KK spectrum and therefore on the Casimir energy as well as on the renormalization of the brane operators. A very interesting feature is that when the two branes carry exactly the same amount of flux, one half of the bulk supersymmetries survives after the compactification, even if the brane tensions are large. We also discuss the implications of these calculations for the natural value of the cosmological constant when the bulk has two large extra dimensions and the bulk supersymmetry is partially preserved (or completely broken).

Accidental SUSY: enhanced bulk supersymmetry from brane back-reaction

We compute how bulk loops renormalize both bulk and brane effective interactions for codimension-two branes in 6D gauged chiral supergravity, as functions of the brane tension and brane-localized flux. We do so by explicitly integrating out hyper- and gauge-multiplets in 6D gauged chiral supergravity compactified to 4D on a flux-stabilized 2D rugby-ball geometry, specializing the results of a companion paper, arXiv:1210.3753, to the supersymmetric case. While the brane back-reaction generically breaks supersymmetry, we show that the bulk supersymmetry can be preserved if the amount of brane-localized flux is related in a specific BPS-like way to the brane tension, and verify that the loop corrections to the brane curvature vanish in this special case. In these systems it is the brane-bulk couplings that fix the size of the extra dimensions, and we show that in some circumstances the bulk geometry dynamically adjusts to ensure the supersymmetric BPS-like condition is automatically satisfied. We investigate the robustness of this residual supersymmetry to loops of non-supersymmetric matter on the branes, and show that supersymmetry-breaking effects can enter only through effective brane-bulk interactions involving at least two derivatives. We comment on the relevance of this calculation to proposed applications of codimension-two 6D models to solutions of the hierarchy and cosmological constant problems.

Spectrum of higher derivative 6D chiral supergravity on Minkowski ×S 2

Gauged off-shell Maxwell-Einstein supergravity in six dimensions with N = (1, 0) supersymmetry has a higher derivative extension afforded by a supersymmetrized Riemann squared term. This theory admits a supersymmetric Minkowski ×S 2 compactification with a U(1) monopole of unit charge on S 2. We determine the full spectrum of the theory on this background. We also determine the spectrum on a non-supersymmetric version of this compactification in which the monopole charge is different from unity, and we find the peculiar feature that there are massless gravitini in a representation of the S 2 isometry group determined by the monopole charge.

Higgsing M2 to D2 with gravity: $ \mathcal{N} = 6 $ chiral supergravity from topologically gauged ABJM theory

We present the higgsing of three-dimensional N=6 superconformal ABJM type theories coupled to conformal supergravity, so called topologically gauged ABJM theory, thus providing a gravitational extension of previous work on the relation between N M2 and N D2-branes. The resulting N=6 supergravity theory appears at a chiral point similar to that of three-dimensional chiral gravity introduced recently by Li, Song and Strominger, but with the opposite sign for the Ricci scalar term in the lagrangian. We identify the supersymmetry in the broken phase as a particular linear combination of the supersymmetry and special conformal supersymmetry in the original topologically gauged ABJM theory. We also discuss the higgsing procedure in detail paying special attention to the role played by the U(1) factors in the original ABJM model and the U(1) introduced in the topological gauging.

Mapping 6D $ \mathcal{N} = 1 $ supergravities to F-theory

We develop a systematic framework for realizing general anomaly-free chiral 6D supergravity theories in F-theory. We focus on 6D (1, 0) models with one tensor multiplet whose gauge group is a product of simple factors (modulo a finite abelian group) with matter in arbitrary representations. Such theories can be decomposed into blocks associated with the simple factors in the gauge group; each block depends only on the group factor and the matter charged under it. All 6D chiral supergravity models can be constructed by gluing such blocks together in accordance with constraints from anomalies. Associating a geometric structure to each block gives a dictionary for translating a supergravity model into a set of topological data for an F-theory construction. We construct the dictionary of F-theory divisors explicitly for some simple gauge group factors and associated matter representations. Using these building blocks we analyze a variety of models. We identify some 6D supergravity models which do not map to integral F-theory divisors, possibly indicating quantum inconsistency of these 6D theories.

A bound on 6D 𝒩 = 1 supergravities

We prove that there are only finitely many distinct semi-simple gauge groups and matter representations possible in consistent 6D chiral (1,0) supergravity theories with one tensor multiplet. The proof relies only on features of the low-energy theory; the consistency conditions we impose are that anomalies should be cancelled by the Green-Schwarz mechanism, and that the kinetic terms for all fields should be positive in some region of moduli space. This result does not apply to the case of the non-chiral (1,1) supergravities, which are not constrained by anomaly cancellation.

Chiral supergravity actions and superforms

The superform construction of supergravity actions, christened the ``ectoplasm method,'' is based on the use of a closed super $d$-form in the case of $d$ space-time dimensions. In known examples, such superforms are obtained by iteratively solving nontrivial cohomological problems. The latter usually makes this scheme no less laborious than the normal coordinate method for deriving component actions for matter-coupled supergravity. In this paper we present an alternative procedure to generate required superforms in four space-time dimensions, which makes use of self-dual vector multiplets. It provides the shortest derivation of chiral actions in two different theories: (i) $\mathcal{N}=1$ old minimal supergravity; and (ii) $\mathcal{N}=2$ conformal supergravity. The $\mathcal{N}=2$ superform construction is developed here for the first time. Although our consideration is restricted to the case of four dimensions, a generalization to higher dimensions is plausible.

Chiral supergravity

We study the linearized approximation of N=1 topologically massive supergravity around AdS3. Linearized gravitino fields are explicitly constructed. For appropriate boundary conditions, the conserved charges demonstrate chiral behavior, so that chiral gravity can be consistently extended to chiral supergravity.

FLUX COMPACTIFICATIONS AND SUPERSYMMETRY BREAKING IN 6D GAUGED SUPERGRAVITY

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 dimensionally 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.

Exact wave solutions to 6D gauged chiral supergravity

We describe a broad class of time-dependent exact wave solutions to 6D gauged chiral supergravity with two compact dimensions. These 6D solutions are nontrivial warped generalizations of 4D pp-waves and Kundt class solutions and describe how a broad class of previously-static compactifications from 6D to 4D (sourced by two 3-branes) respond to waves moving along one of the uncompactified directions. Because our methods are generally applicable to any higher dimensional supergravity they are likely to be of use for finding the supergravity limit of time-dependent solutions in string theory. The 6D solutions are interesting in their own right, describing 6D shock waves induced by high energy particles on the branes, and as descriptions of the near-brane limit of the transient wavefront arising from a local bubble-nucleation event on one of the branes, such as might occur if a tension-changing phase transition were to occur.

Low energy effective theory on a regularized brane in 6D gauged chiral supergravity

We derive the low energy effective theory on a brane in six-dimensional chiral supergravity.The conical 3-brane singularities are resolved by introducing cylindrical 4-branes ofco-dimension 1 whose interiors are capped by a regular spacetime. The effective theoryis described by the Brans–Dicke (BD) theory with the BD parameter given byωBD = 1/2. The BD field originates from a modulus which is associated with the scaling symmetry ofthe system. If the dilaton potentials on the branes preserve the scaling symmetry, the scalarfield has an exponential potential in the Einstein frame. We show that the time dependentsolutions driven by the modulus in the four-dimensional effective theory can be lifted up tothe six-dimensional exact solutions found in the literature. On the basis of theeffective theory, we discuss a possible way to stabilize the modulus to recoverstandard cosmology and also study the implication for the cosmological constantproblem.

UV caps and modulus stabilization for 6D gauged chiral supergravity

We describe an explicit UV regularization of the brane singularities for all 4D flat configurations of 6D gauged chiral supergravity compactified on axially symmetric internal spaces (for which the general solutions are known). All such solutions have two or fewer co-dimension two singularities, which we resolve in terms of microscopic co-dimension one cylindrical 4-branes, whose interiors are capped using the most general possible 4D flat solution of the 6D field equations. By so doing we show that such a cap is always possible for any given bulk geometry, and obtain an explicit relationship between the properties of the capped 4-branes and the various parameters which describe the bulk solution. We show how these branes generically stabilize the size of the extra dimensions by breaking the scale invariance which relates classical solutions to 6D supergravity, and we compute the scalar potential for this modulus in the 4D effective theory. The lifting of this marginal direction provides a natural realization of the Goldberger-Wise stabilization mechanism in six dimensions.

Brane cosmological solutions in six-dimensional warped flux compactifications

We study cosmology on a conical brane in the six-dimensional Einstein–Maxwell-dilatonsystem, where the extra dimensions are compactified by a magnetic flux. We systematicallyconstruct exact cosmological solutions using the fact that the system is equivalently described by(6+n)-dimensional pure Einstein–Maxwell theory via dimensional reduction. In particular, wefind a power-law inflationary solution for a general dilatonic coupling. When the dilatoniccoupling is given by that of Nishino–Sezgin chiral supergravity, this reduces to the knownsolution which is not inflating. The power-law solution is shown to be the late-timeattractor. We also investigate cosmological tensor perturbations in this model using the(6+n)-dimensional description. We obtain the separable equation of motion and findthat there always exists a zero mode, while tachyonic modes are absent in thespectrum. The mass spectrum of Kaluza–Klein modes is obtained numerically.

Kicking the rugby ball: perturbations of 6D gauged chiral supergravity

We analyse the axially symmetric scalar perturbations of 6D chiral gauged supergravitycompactified on the general warped geometries in the presence of two source branes. Wefind that all of the conical geometries are marginally stable for normalizable perturbations(in disagreement with some recent calculations) and the non-conical ones for regularperturbations, even though none of them are supersymmetric (apart from the trivialSalam–Sezgin solution, for which there are no source branes). The marginal direction is theone whose presence is required by the classical scaling property of the field equations, andall other modes have positive squared mass. In the special case of the conicalsolutions, including (but not restricted to) the unwarped ‘rugby-ball’ solutions, wefind closed-form expressions for the mode functions in terms of Legendre andhypergeometric functions. In so doing we show how to match the asymptotic near-braneform for the solution to the physics of the source branes, and thereby how tophysically interpret perturbations which can be singular at the brane positions.