Dimensional Supergravity Research Articles

SU(1,1) and SU(2) bundles on AdS4 and complex supergravity solutions

We study eleven dimensional supergravity solutions with an AdS7 factor. By writing AdS7 metric as an SU(1,1) bundle over AdS4 we derive new supergravity solutions. The solutions, however, are obtained in Euclidean signature and thus are necessarily complex. We also discuss AdS7 as an SU(2) bundle over AdS4, and observe that the two sets of solutions are related by analytic continuation of the scale factor of the fiber.

Coupling of branes and twisted self-duality in the Maxwell-Chern-Simons theory

We study three approaches to electric-magnetic duality in the 4-dimensional Maxwell theory coupled to a dyonic point charge and in the 5-dimensional Maxwell-Chern-Simons (MCS) theory coupled to an electric point charge and a magnetic string charge. The three approaches have been developed by Dirac, Bunster and Henneaux, and Pasti, Sorokin and Tonin (PST). In Dirac’s formulation, the electric magnetic duality is realized only on the level of the equations of motion. The other two formulations introduce a dual (magnetic) gauge potential to induce manifest twisted self-duality in the action. In particular, we study the relations connecting the three approaches. The main results of this paper are the Bunster-Henneaux and PST formulations of the MCS theory with sources. We compare our result to the PST formulation of 11-dimensional supergravity coupled to the M2- and M5-brane by Bandos, Berkovits, and Sorokin.

Holographic supersymmetric Rényi entropies from hyperbolic black holes with scalar hair

We study holographic supersymmetric Rényi entropies from a family of hyperbolic black holes in an Einstein-Maxwell-dilaton (EMD) system under the BPS condition. We calculate the thermodynamic quantities of these hyperbolic black holes. We find a remarkably simple formula of the supersymmetric Rényi entropy that unifies (interpolates) 11 cases embeddable to 10 or 11 dimensional supergravity. It reproduces many known results in the literature, and gives new results with distinctive features. We show that the supersymmetric version of the modular entropy and the capacity of entanglement cannot be mapped to thermal quantities, due to the dependence of the temperature and the chemical potential by the BPS condition. We also calculate the entanglement spectrum. We derive the potential of the EMD system from a V = 0 solution and obtain two neutral solutions with scalar hair as a byproduct.

Four dimensional topological supergravities from transgression field theory

In this work, we propose a four-dimensional gauged Wess-Zumino-Witten model, obtained as a dimensional reduction from a transgression field theory invariant under the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 Poincaré supergroup. For this purpose, we consider that the two gauge connections on which the transgression action principle depends are given by linear and non-linear realizations of the gauge group respectively. The field content of the resulting four-dimensional theory is given by the gauge fields of the linear connection, in addition to a set of scalar and spinor multiplets in the same representation of the gauge supergroup, which in turn, correspond to the coordinates of the coset space between the gauge group and the five-dimensional Lorentz group. We then decompose the action in terms of four-dimensional quantities and derive the corresponding equations of motion. We extend our analysis to the non- and ultra- relativistic regimes.

Euclidean flows, solitons, and wormholes in AdS space from M-theory

Multiparametric families of nonsupersymmetric EAdS4 flows as well as asymptotically EAdS4 solitons and wormholes are constructed within the four-dimensional SO(8) gauged supergravity that describes the compactification of M-theory on S7. More concretely, the solutions are found within the so-called STU model that describes the U(1)4 invariant sector of the theory. The on-shell action and gravitational free energy are computed for the regular solutions, the latter being zero for the wormholes irrespective of supersymmetry. There are special loci in parameter space yielding solutions with enhanced (super)symmetry. Examples include a supersymmetric EAdS4 flow with SO(4)×SO(4) symmetry dual to a specific real mass deformation of ABJM on S3 as well as a nonsupersymmetric wormhole with SU(3)×U(1)2 symmetry. Uplift formulas for these and other examples to Euclidean solutions of 11-dimensional supergravity are presented and their complex nature discussed. Published by the American Physical Society 2024

The cosmological constant problem and the extra dimensions of [formula omitted]=2 [formula omitted]=5 supergravity

We propose an interpretation for the cosmological constant problem based on modeling the universe as a 3-brane embedded in the bulk of 5-dimensional supergravity with hypermultiplets. When solving the modified Friedmann equations the complex structure moduli of the Calabi-Yau manifold cancel the large value of the vacuum energy density on the brane, wherein this value transfers to an Anti-de Sitter fifth dimensional bulk compactified on a scale (∼10−26m). An effective dark energy density is produced on the brane which equals the observed value responsible for the late-time acceleration of the universe. The bulk undergoes a decelerated contraction while we show that cosmic expansion of the brane-universe consists with the recent observed data of the ΛCDM model. On the other hand, through this model, the hierarchy between the electroweak scale (MEW=100GeV) and the Planck scale (Mpl∼1018GeV) is interpreted by compactifying the 6-extra dimensions of D=5 supergravity on a sub-millimeters scale, where the fundamental scale of gravity within these extra dimensions is MEW.

Higgs-like (pseudo)scalars in AdS4, marginal and irrelevant deformations in CFT3, and instantons on S 3

Employing a 4-form ansatz of 11-dimensional supergravity over a non-dynamical background and setting the internal space as an Hopf fibration on , we obtain a consistent truncation. The (pseudo)scalars, in the resulting scalar equations in Euclidean AdS space, may be considered to arise from (anti)M-branes wrapping around the internal directions in the (Wick-rotated) skew-whiffed M2-brane background (as the resulting theory is for anti-M2-branes), thus realizing the modes after swapping the three fundamental representations , , and of . Taking the backreaction on the external and internal spaces, we obtain the massless and massive modes, corresponding to exactly marginal and marginally irrelevant deformations on the boundary CFT , respectively. Subsequently, we obtain a closed solution for the bulk equation and compute its correction with respect to the background action. Next, considering the Higgs-like (breathing) mode , having all supersymmetries as well as parity and scale-invariance broken, solving the associated bulk equation with mathematical methods, specifically the Adomian decomposition method, and analyzing the behavior near the boundary of the solutions, we realize the boundary duals in the -singlet sectors of the ABJM model. Then, introducing the new dual deformation operators made of bi-fundamental scalars, fermions, and gauge fields, we obtain the -invariant solutions as small instantons on a three-sphere with the radius at infinity, which correspond to collapsing bulk bubbles leading to big-crunch singularities.

Asymptotic dynamics of three dimensional supergravity and higher spin gravity revisited

We reconsider the Hamiltonian reduction of the action for three dimensional AdS supergravity and W3 higher spin AdS gravity in the Chern-Simons formulation under asymptotically anti-de Sitter boundary conditions. We show that the reduction gives two copies of chiral bosons on the boundary. In particular, we take into account the holonomy of the Chern-Simons connection which manifests itself as zero mode of the momentum of the boundary chiral boson. We provide an equivalent formulation of the boundary action which we claim to be the geometric action on symplectic leaves of a (super-)Virasoro or a higher spin WN Poisson manifold in the case of supergravity or higher spin gravity respectively, where the intersection of leaves (given in terms of leaves representatives) can be identified as the bulk holonomy. This concludes the extension to non-linear algebras where the notion of coadjoint representation is not well-defined. The boundary Hamiltonian depends on a choice of boundary conditions and is equivalent to the Schwarzian action for corresponding Brown-Henneaux boundary conditions. We make this connection explicit in the extended supersymmetric case. Moreover, we discuss the geometric action in the case of W3 AdS3 gravity in both mathfrak{sl} (3) highest weight representations based on principal and diagonal mathfrak{sl} (2) embeddings.

The TCFHs of D = 11 AdS backgrounds and hidden symmetries

We present the TCFHs of all AdS backgrounds of 11-dimensional supergravity and explore some of the properties of the associated connections. Therefore, we demonstrate that all Killing spinor bilinears satisfy a generalisation of the conformal Killing-Yano equations with respect to the TCFH connection. In addition, we explore the hidden symmetries of spinning particle probes propagating on these backgrounds. We give several examples of hidden symmetries for probes on the maximal supersymmetric AdS backgrounds as well as on some AdS backgrounds that arise as near horizon geometries of intersecting M-branes.

Kaluza-Klein spectrometry beyond consistent truncations: the squashed S7

We show how to use Exceptional Field Theory to compute the full Kaluza-Klein spectra of 10- and 11-dimensional supergravity around deformations of backgrounds of maximal gauged supergravity by scalar modes that do not form part of the consistent truncation. This includes deformations of AdS4 × S7 and AdS5 × S5 by modes that are not part of the mathcal{N} = 8 supermultiplet. As an application, we compute the full Kaluza-Klein spectrum of the mathcal{N} = 1 and mathcal{N} = 0 squashed S7. In this example, all conformal dimensions are captured by a universal formula in terms of the Casimir operators and additional quantum numbers which organise the spectrum.

Mysterious Triality and Rational Homotopy Theory

Mysterious Duality has been discovered by Iqbal, Neitzke, and Vafa (Adv Theor Math Phys 5:769–808, 2002) as a convincing, yet mysterious correspondence between certain symmetry patterns in toroidal compactifications of M-theory and del Pezzo surfaces, both governed by the root system series $$E_k$$ . It turns out that the sequence of del Pezzo surfaces is not the only sequence of objects in mathematics that gives rise to the same $$E_k$$ symmetry pattern. We present a sequence of topological spaces, starting with the four-sphere $$S^4$$ , and then forming its iterated cyclic loop spaces $$\mathscr {L}_c^k S^4$$ , within which we discover the $$E_k$$ symmetry pattern via rational homotopy theory. For this sequence of spaces, the correspondence between its $$E_k$$ symmetry pattern and that of toroidal compactifications of M-theory is no longer a mystery, as each space $$\mathscr {L}_c^k S^4$$ is naturally related to the compactification of M-theory on the k-torus via identification of the equations of motion of $$(11-k)$$ -dimensional supergravity as the defining equations of the Sullivan minimal model of $$\mathscr {L}_c^k S^4$$ . This gives an explicit duality between algebraic topology and physics. Thereby, we extend Iqbal-Neitzke-Vafa’s Mysterious Duality between algebraic geometry and physics into a triality, also involving algebraic topology. Via this triality, duality between physics and mathematics is demystified, and the mystery is transferred to the mathematical realm as duality between algebraic geometry and algebraic topology. Now the question is: Is there an explicit relation between the del Pezzo surfaces $$\mathbb {B}_k$$ and iterated cyclic loop spaces of $$S^4$$ which would explain the common $$E_k$$ symmetry pattern?

β Symmetry of Supergravity.

Continuous O(d,d) global symmetries emerge in Kaluza-Klein reductions of D-dimensional string supergravities to D-d dimensions. We show that the nongeometric elements of this group effectively act in the D-dimensional parent theory as a hidden bosonic symmetry that fixes its couplings: the β symmetry. We give the explicit β transformations to first order in α^{'} and verify the invariance of the action as well as the closure of the transformation rules.

Instantons in AdS$$_4$$ from (anti)membranes wrapping $$S^7$$ to Bose–Fermi duality in CFT$$_3$$’s

We present new SO(4)-invariant and non-supersymmetric instanton solutions for the conformally coupled m^2=-2 and massive m^2=+4 (pseudo)scalars arising from a consistent truncation of 11-dimensional supergravity over AdS_4 x S^7/Z_k when the internal space is a S^1 Hopf fibration on CP^3, and we consider backreaction. In fact, the bulk configurations associate with (anti)membranes wrapped around mixed internal (and external) directions, which in turn probe the Wick-rotated or skew-whiffed background, break all supersymmetries as well as parity invariance. From near the boundary behavior of the closed solution for the coupled bulk (pseudo)scalar, we get a marginal triple-trace deformation with mixed boundary condition (valid also for the bulk massless m^2=0 (pseudo)scalar, raised when considering the external space backreaction, with Dirichlet boundary condition) and as a result, the corresponding boundary effective potential is unbounded from below and causes an instability because of the Fubini-like instanton. Presenting dual effective actions, we see that the boundary solutions and counterparts realize in singlet sectors of three-dimensional U(N) and O(N) Chern--Simons-matter field theories. In particular, we use versions of massless and mass-deformed regular and critical boson and fermion models, find instantons and confirm state-operator AdS_4/CFT_3 correspondence and also Bose-Fermi duality at the level of the solutions. In addition, we discuss on relations of our setups with Vasiliev's Higher-Spin theories, deformations of the Aharony-Bergman-Jafferis-Maldacena model and other related studies.

Generalized 11D supergravity equations from tri-vector deformations

In Bakhmatov et al. (Phys. Rev. D 105(8): L081904, 2022) we presented a modification of 11-dimensional supergravity field equations which upon dimensional reduction yields generalized supergravity equations in 10-dimensions. In this paper we provide full technical details of that result which is based on SL(5) exceptional field theory. The equations are obtained by making a non-unimodular tri-vector Yang-Baxter deformation which breaks the initial local diffeomorphism symmetry in 11 dimensions down to separate coordinate transformations in external 7 and internal 4 directions. We also give some non-trivial solutions to these equations.

Generalised U-dual solutions via ISO(7) gauged supergravity

We study a solution generating technique in supergravity which can be viewed as a generalised version of U-duality, taking solutions of type IIA supergravity on a 6-sphere with RR flux to new solutions of 11-dimensional supergravity. The new solutions are characterised by an underlying 6-algebra structure. Our construction provides an 11-dimensional uplift of four-dimensional ISO(7) gauged supergravity, using E7 exceptional geometry techniques. We focus on an example where we start with the D2 solution in type IIA supergravity and construct a new frac{1}{2} -BPS 11-dimensional solution.

TCFHs, hidden symmetries and M-theory backgrounds

We present the twisted covariant form hierarchy (TCFH) of 11-dimensional supergravity and so demonstrate that the form bilinears of supersymmetric solutions satisfy a generalisation of the conformal Killing-Yano equation with resepct to the TCFH connection. We also compute the Killing-Stäckel, KY and closed conformal Killing-Yano tensors of all spherically symmetric M-branes that include the M2-brane, M5-brane, KK-monopole and pp-wave and demonstrate that their geodesic flows are completely integrable by giving all independent conserved charges in involution. We then find that all form bilinears of pp-wave and KK-monopole solutions generate (hidden) symmetries for spinning particle probes propagating on these backgrounds. Moreover, there are Killing spinors such that some of the 1-, 2- and 3-form bilinears of the M2-brane solution generate symmetries for spinning particle probes. We also explore the question on whether the form bilinears are sufficient to prove the integrability of particle probe dynamics on 11-dimensional supersymmetric backgrounds.

Linearized off-shell 4+7 supergeometry of 11D supergravity

We describe the linearized supergeometry of eleven dimensional supergravity with four off-shell local supersymmetries. We start with a background Minkowski 11D, N=1 superspace, and an additional ingredient of a global, constant, G2-structure which facilitates the definition of a 4|4 + 7 background superspace. A bottom-up construction of linear fluctuations of the geometric constituents (such as supervielbein, spin connection, and the super 3-form of 11D supergravity) is given in terms of 4D, N=1 prepotential superfields. This is complemented by a top-down description of the linearized supergeometry of the 4|4 + 7 superspace dealing directly with torsion, curvature, and Bianchi identities. Torsion constraints that (combined with the Bianchi identities) lead to the preceding prepotential expressions of the gauge fields are identified. All irreducible consequences of the torsion and 4-form Bianchi identities are systematically derived except for dimension 2 Bianchi identities of the 4-form, and dimension frac{5}{2} Bianchi identities of torsion, which set bosonic curls of components of one lower dimension to zero.

Heterotic strings on mathbbm{T} 3/ℤ2, Nikulin involutions and M-theory

We first describe the low energy dynamics of ten dimensional heterotic supergravity compactified on the smooth, flat 3-manifold mathbbm{T} 3/ℤ2, without supersymmetry, and explain how it arises from flat heterotic gauge fields. The semi-classical theory has both Coulomb and Higgs branches of non-supersymmetric vacua. We then give an exact worldsheet description as asymmetric orbifolds of mathbbm{T} 3, where the orbifold generator involves a Nikulin non-symplectic involution θ of the even self-dual lattice Γ(19,3). Along the way we briefly compare our findings with M-theory on K3/θ. Our construction gives a novel CFT description of the semi-classical field theory moduli space. In particular, the Wilson line parameters in the lattice I ⊂ Γ(19,3) of signature (19 − s, 1) which is invariant under θ, and in its orthogonal complement N , correspond respectively to Coulomb and Higgs branch moduli. There is a rich pattern of transitions amongst Higgs and Coulomb branches which we describe using the worldsheet theory.

Non-isometric U-dualities

I study generalisations of U-duality transformations which do not rely on the existence of isometries. I start by providing more details of a recently proposed generalised U-duality map between solutions of type IIA supergravity of the form M7× S3, with NSNS flux, and solutions of 11-dimensional supergravity, in which the three-sphere is replaced by a four-dimensional geometry which encodes three-algebra structure constants. I then show that when M7 admits two abelian isometries, TsT deformations on the IIA side become six-vector deformations in the 11-dimensional setting. These six-vector deformations involve an action of E6(6) on both isometric and non-isometric directions. I discuss the algebraic interpretation of these deformations, and compare and contrast them with (generalised) Yang-Baxter deformations in supergravity.

Consistent truncations to 3-dimensional supergravity

We show how to construct consistent truncations of 10-/11-dimensional supergravity to 3-dimensional gauged supergravity, preserving various amounts of supersymmetry. We show, that as in higher dimensions, consistent truncations can be defined in terms of generalised G-structures in Exceptional Field Theory, with G ⊂ E8(8) for the 3-dimensional case. Differently from higher dimensions, the generalised Lie derivative of E8(8) Exceptional Field Theory requires a set of “covariantly constrained” fields to be well-defined, and we show how these can be constructed from the G-structure itself. We prove several general features of consistent truncations, allowing us to rule out a higher-dimensional origin of many 3-dimensional gauged supergravities. In particular, we show that the compact part of the gauge group can be at most SO(9) and that there are no consistent truncations on a 7-or 8-dimensional product of spheres such that the full isometry group of the spheres is gauged. Moreover, we classify which matter-coupled mathcal{N} ≥ 4 gauged supergravities can arise from consistent truncations. Finally, we give several examples of consistent truncations to three dimensions. These include the truncations of IIA and IIB supergravity on S7 leading to two different mathcal{N} = 16 gauged supergravites, as well as more general IIA/IIB truncations on Hp,7−p. We also show how to construct consistent truncations of IIB supergravity on S5 fibred over a Riemann surface. These result in 3-dimensional mathcal{N} = 4 gauged supergravities with scalar manifold mathcal{M}=frac{mathrm{S}mathrm{O}left(6,4right)}{mathrm{S}mathrm{O}(6)times mathrm{SO}(4)}times frac{mathrm{S}mathrm{U}left(2,1right)}{mathrm{S}left(mathrm{U}(1)times mathrm{U}(2)right)} with a ISO(3) × U(1)4 gauging and for hyperboloidal Riemann surfaces contain mathcal{N} = (2, 2) AdS3 vacua.