Three-dimensional Supergravity Research Articles

Microstrata

Microstrata are the non-extremal analogues of superstrata: they are smooth, non-extremal (non-BPS) solitonic solutions to IIB supergravity whose deep-throat limits approximate black holes. Using perturbation theory and numerical methods, we construct families of solutions using a consistent truncation to three-dimensional supergravity. The most general families presented here involve two continuous parameters, or amplitudes, and four quantized parameters that set the angular momenta and energy levels. Our solutions are asymptotic to the vacuum of the D1-D5 system: AdS3 × S3 × \U0001d54b4. Using holography, we show that the they are dual to multi-particle states in the D1-D5 CFT involving a large number of mutually non-BPS supergravitons and we determine the anomalous dimensions of these states from the binding energies in supergravity. These binding energies are uniformly negative and depend non-linearly on the amplitudes of the states. In one family of solutions, smoothness restricts some of the fields to lie on a special locus of the parameter space. Using precision holography we show that this special locus can be identified with the multi-particle states constructed via the standard OPE of the single-particle constituents. Our numerical analysis shows that microstrata are robust at large amplitudes and the solutions can be obtained to very high precision.

Super non-Abelian T-duality

We analyse super non-Abelian T-duality for principal chiral models, symmetric space sigma models, and semi-symmetric space sigma models for general Lie supergroups. This includes T-duality along both bosonic and fermionic directions. As an example, we perform the explicit dualisation of the OSp(1|2) principal chiral model, and, whilst the target superspace of this model is a three-dimensional supergravity background, we find that its super non-Abelian T-dual falls outside the class of such backgrounds.

New superstrata from three-dimensional supergravity

We find a two-parameter family of generalized superstrata that emerge as smooth, supersymmetric solutions in three-dimensional gauged supergravity coupled to additional scalar fields. This new family of generalized superstrata are smooth microstate geometries and may be thought of as supersymmetric Coulomb-branch extensions of the original superstrata in which the underlying supertube undergoes an elliptical deformation. These solutions had already been obtained numerically, and as series solutions, to the equations of motion, and some of them were conjectured to be supersymmetric. Here we prove the supersymmetry of an entire two-parameter family and we obtain a highly non-trivial analytic and smooth solution for a one-parameter limit in which the global symmetry of the metric is enhanced to SO(3). We also confirm that the other known families of microstrata are not supersymmetric. We conclude with a cursory analysis of some of the singular brane distributions that can be accessed from three-dimensional gauged supergravity while preserving the same supersymmetries as the superstratum, and therefore of the three-charge black hole.

Three-dimensional non-relativistic supergravity and torsion

In this paper we present a torsional non-relativi-stic Chern–Simons (super)gravity theory in three spacetime dimensions. We start by developing the non-relativistic limit of the purely bosonic relativistic teleparallel Chern–Simons formulation of gravity. On-shell the latter yields a non-Riemannian setup with non-vanishing torsion, which, at non-relativistic level, translates into a non-vanishing spatial torsion sourced by the cosmological constant. Then we consider the three-dimensional relativistic {mathcal {N}}=2 teleparallel Chern–Simons supergravity theory and obtain its non-relativistic counterpart by exploiting a Lie algebra expansion method. The non-relativistic supergravity theory is characterized, on-shell, by a non-vanishing spatial super-torsion, again sourced by the cosmological constant.

Triality and the consistent reductions on AdS3 \xd7 S3

We study compactifications on AdS3×S3 and deformations thereof. We exploit the triality symmetry of the underlying duality group SO(4,4) of three-dimensional supergravity in order to construct and relate new consistent truncations. For non-chiral D = 6, mathcal{N} 6d = (1, 1) supergravity, we find two different consistent truncations to three-dimensional supergravity, retaining different subsets of Kaluza-Klein modes, thereby offering access to different subsectors of the full nonlinear dynamics. As an application, we construct a two-parameter family of AdS3 × M3 backgrounds on squashed spheres preserving U(1)2 isometries. For generic value of the parameters, these solutions break all supersymmetries, yet they remain perturbatively stable within a non-vanishing region in parameter space. They also contain a one-parameter family of mathcal{N} = (0, 4) supersymmetric AdS3 × M3 backgrounds on squashed spheres with U(2) isometries. Using techniques from exceptional field theory, we determine the full Kaluza-Klein spectrum around these backgrounds.

Three-dimensional teleparallel Chern-Simons supergravity theory

In this work we present a gauge-invariant three-dimensional teleparallel supergravity theory using the Chern-Simons formalism. The present construction is based on a supersymmetric extension of a particular deformation of the Poincaré algebra. At the bosonic level the theory describes a non-Riemannian geometry with a non-vanishing torsion. In presence of supersymmetry, the teleparallel supergravity theory is characterized by a non-vanishing super-torsion in which the cosmological constant can be seen as a source for the torsion. We show that the teleparallel supergravity theory presented here reproduces the Poincaré supergravity in the vanishing cosmological limit. The extension of our results to {mathcal {N}}=p+q supersymmetries is also explored.

Non-relativistic three-dimensional supergravity theories and semigroup expansion method

In this work we present an alternative method to construct diverse non-relativistic Chern-Simons supergravity theories in three spacetime dimensions. To this end, we apply the Lie algebra expansion method based on semigroups to a supersymmetric extension of the Nappi-Witten algebra. Two different families of non-relativistic superalgebras are obtained, corresponding to generalizations of the extended Bargmann superalgebra and extended Newton-Hooke superalgebra, respectively. The expansion method considered here allows to obtain known and new non-relativistic supergravity models in a systematic way. In particular, it immediately provides an invariant tensor for the expanded superalgebra, which is essential to construct the corresponding Chern-Simons supergravity action. We show that the extended Bargmann supergravity and its Maxwellian generalization appear as particular subcases of a generalized extended Bargmann supergravity theory. In addition, we demonstrate that the generalized extended Bargmann and generalized extended Newton-Hooke supergravity families are related through a contraction process.

Mathcal{N} = (8, 0) AdS vacua of three-dimensional supergravity

We give a classification of fully supersymmetric chiral mathcal{N} = (8, 0) AdS3 vacua in general three-dimensional half-maximal gauged supergravities coupled to matter. These theories exhibit a wealth of supersymmetric vacua with background isometries given by the supergroups OSp(8|2, ℝ), F(4), SU(4|1, 1), and OSp(4∗|4), respectively. We identify the associated embedding tensors and the structure of the associated gauge groups. We furthermore compute the mass spectra around these vacua. As an off-spin we include results for a number of mathcal{N} = (7, 0) vacua with supergroups OSp(7|2, ℝ) and G(3), respectively. We also comment on their possible higher-dimensional uplifts.

Quarter-BPS solutions in three-dimensionalN=16supergravity and the Liouville equation

We show how by assuming at least 8 real timelike supersymmetries in the maximally supersymmetric three-dimensional ungauged supergravity and a further simplifying Ansatz, we are naturally led to a pair of Liouville field equations. We also show that there are no solutions that preserve only 6 real timelike supersymmetries. The solution relies on the classification of complex spinors of Spin(8) to which the problem quickly reduces.

Higher derivative couplings and massive supergravity in three dimensions

We develop geometric superspace settings to construct arbitrary higher derivative couplings (including R^n terms) in three-dimensional supergravity theories with N=1,2,3 by realising them as conformal supergravity coupled to certain compensators. For all known off-shell supergravity formulations, we construct supersymmetric invariants with up to and including four derivatives. As a warming-up exercise, we first give a new and completely geometric derivation of such invariants in N=1 supergravity. Upon reduction to components, they agree with those given in arXiv:0907.4658 and arXiv:1005.3952. We then carry out a similar construction in the case of N=2 supergravity for which there exist two minimal formulations that differ by the choice of compensating multiplet: (i) a chiral scalar multipet; (ii) a vector multiplet. For these formulations all four derivative invariants are constructed in completely general and gauge independent form. For a general supergravity model (in the N=1 and minimal N=2 cases) with curvature-squared and lower order terms, we derive the superfield equations of motion, linearise them about maximally supersymmetric backgrounds and obtain restrictions on the parameters that lead to models for massive supergravity. We use the non-minimal formulation for N = 2 supergravity (which corresponds to a complex linear compensator) to construct a novel consistent theory of massive supergravity. In the case of N = 3 supergravity, we employ the off-shell formulation with a vector multiplet as compensator to construct for the first time various higher derivative invariants. These invariants may be used to derive models for N = 3 massive supergravity. As a bi-product of our analysis, we also present superfield equations for massive higher spin multiplets in (1,0), (1,1) and (2,0) anti-de Sitter superspaces.

From U(1) to E8: soft theorems in supergravity amplitudes

It is known that for $$ \mathcal{N}=8 $$ supergravity, the double-soft-scalar limit of a n-point amplitude is given by a sum of local SU(8) rotations acting on a (n−2)-point amplitude. For $$ \mathcal{N}<8 $$ supergravity theories, complication arises due to the presence of a U(1) in the U( $$ \mathcal{N} $$ ) isotropy group, which introduces a soft-graviton singularity that obscures the action of the duality symmetry. In this paper, we introduce an anti-symmetrised extraction procedure that exposes the full duality group. We illustrate this procedure for tree-level amplitudes in 4 ≤ $$ \mathcal{N}<8 $$ supergravity in four dimensions, as well as $$ \mathcal{N}=16 $$ supergravity in three dimensions. In three dimensions, as all bosonic degrees of freedom transform under the E8 duality group, supersymmetry ensures that the amplitude vanishes in the single-soft limit of all particle species, in contrast to its higher dimensional siblings. Using recursive formulas and generalized unitarity cuts in three dimensions, we demonstrate the action of the duality group for any tree-level and one-loop amplitudes. Finally we discuss the implications of the duality symmetry on possible counter terms for this theory. As a preliminary application, we show that the vanishing of single-soft limits of arbitrary component fields in three-dimensional supergravity rules out the direct dimensional reduction of D 8 R 4 as a valid counter term.

EquivalentD=3Supergravity Amplitudes from Double Copies of Three-Algebra and Two-Algebra Gauge Theories

We show that three-dimensional supergravity amplitudes can be obtained as double copies of either three-algebra super-Chern-Simons matter theory or two-algebra super-Yang-Mills theory when either theory is organized to display the color-kinematics duality. We prove that only helicity-conserving four-dimensional gravity amplitudes have nonvanishing descendants when reduced to three dimensions, implying the vanishing of odd-multiplicity S-matrix elements, in agreement with Chern-Simons matter theory. We explicitly verify the double-copy correspondence at four and six points for N = 12,10,8 supergravity theories and discuss its validity for all multiplicity.

Super Virasoro algebra from supergravity

We investigate three dimensional anti--de sitter $({\mathrm{AdS}}_{3})/{\mathrm{CFT}}_{2}$ correspondence in three-dimensional supergravity. We construct a current for the general coordinate invariance and that for local supersymmetry via the covariant approach. The Hamiltonian and supercharge are well defined in terms of vielbein and spin connection. After discussing the asymptotic supersymmetry group at the boundary of $\mathrm{Ad}{\mathrm{S}}_{3}$ geometry, we show that there exists a direct product of Virasoro algebras at the boundary. We also show that one of them is extended to super Virasoro algebra.

New Relations for Three-Dimensional Supersymmetric Scattering Amplitudes

We provide evidence for a duality between color and kinematics in three-dimensional supersymmetric Chern-Simons matter theories. We show that the six-point amplitude in the maximally supersymmetric N=8 theory can be arranged so that the kinematic factors satisfy the fundamental identity of three-algebras. We further show that the four- and six-point N=8 amplitudes can be squared into the amplitudes of N=16 three-dimensional supergravity, thus providing evidence for a hidden three-algebra structure in the dynamics of the supergravity.

More on massive 3D supergravity

Completing earlier work on three-dimensional (3D) supergravity with curvature-squared terms, we construct the general supergravity extension of ‘cosmological’ massive gravity theories. In particular, we show that all adS vacua of ‘new massive gravity’ (NMG) correspond to supersymmetric adS vacua of a ‘super-NMG’ theory that is perturbatively unitary whenever the corresponding NMG theory is perturbatively unitary.

Massive three-dimensional supergravity from R + R 2 action in six dimensions

We obtain a three-parameter family of massive N=1 supergravities in three dimensions from the 3-sphere reduction of an off-shell N=(1,0) six-dimensional Poincare supergravity that includes a curvature squared invariant. The three-dimensional theory contains an off-shell supergravity multiplet and an on-shell scalar matter multiplet. We then generalise this in three dimensions to an eight-parameter family of supergravities. We also find a duality relationship between the six-dimensional theory and the N=(1,0) six-dimensional theory obtained through a T^4 reduction of the heterotic string effective action that includes the higher-order terms associated with the supersymmetrisation of the anomaly-cancelling \tr(R\wedge R) term.

Quantum gravity partition functions in three dimensions

We consider pure three-dimensional quantum gravity with a negative cosmological constant. The sum of known contributions to the partition function from classical geometries can be computed exactly, including quantum corrections. However, the result is not physically sensible, and if the model does exist, there are some additional contributions. One possibility is that the theory may have long strings and a continuous spectrum. Another possibility is that complex geometries need to be included, possibly leading to a holomorphically factorized partition function. We analyze the subleading corrections to the Bekenstein-Hawking entropy and show that these can be correctly reproduced in such a holomorphically factorized theory. We also consider the Hawking-Page phase transition between a thermal gas and a black hole and show that it is a phase transition of Lee-Yang type, associated with a condensation of zeros in the complex temperature plane. Finally, we analyze pure three-dimensional supergravity, with similar results.

Massive 3D supergravity

We construct the three-dimensional supergravity theory with cosmological, Einstein–Hilbert, Lorentz Chern–Simons, and general curvature squared terms. We determine the general supersymmetric configuration, and find a family of supersymmetric adS vacua with the supersymmetric Minkowski vacuum as a limiting case. Linearizing about the Minkowski vacuum, we find three classes of unitary theories; one is the supersymmetric extension of the recently discovered ‘massive 3D gravity’. Another is a ‘new topologically massive supergravity’ (with no Einstein–Hilbert term) that propagates a single helicity supermultiplet.

Three-dimensional supergravity reloaded

The locally supersymmetric extension of the most general gravity theory in three dimensions leading to first-order field equations for the vielbein and the spin connection is constructed. Apart from the Einstein–Hilbert term with cosmological constant, the gravitational sector contains the Lorentz–Chern–Simons form and a term involving the torsion each with arbitrary couplings. The supersymmetric extension is carried out for vanishing and negative effective cosmological constant, and it is shown that the action can be written as a Chern–Simons theory for the supersymmetric extension of the Poincaré and AdS groups, respectively. Here we introduce a duality map between different gravity theories that greatly simplifies the construction. This map relies on the different ways to make geometry emerge from a single gauge potential. The extension for gravitini is also performed.

Effective actions for massive Kaluza-Klein states onAdS3×S3×S3

We construct the effective supergravity actions for the lowest massive Kaluza-Klein states on the supersymmetric background AdS_3 x S^3 x S^3. In particular, we describe the coupling of the supergravity multiplet to the lowest massive spin-3/2 multiplet which contains 256 physical degrees of freedom and includes the moduli of the theory. The effective theory is realized as the broken phase of a particular gauging of the maximal three-dimensional supergravity with gauge group SO(4) x SO(4). Its ground state breaks half of the supersymmetries leading to 8 massive gravitinos acquiring mass in a super Higgs effect. The holographic boundary theory realizes the large N=(4,4) superconformal symmetry.