Seven-dimensional Sasaki-Einstein Manifold Research Articles

Uplifting dyonic AdS4 black holes on seven-dimensional Sasaki-Einstein manifolds

We revisit non-rotating, dyonically charged, and supersymmetric AdS4 black holes, which are solutions of mathcal{N} = 2 gauged supergravity with vector- and hyper-multiplets. Uplifting the near horizon solutions to D = 11 supergravity on seven-dimensional Sasaki-Einstein manifolds, we show that dyonic AdS4 black holes correspond to AdS2 solutions with electric and magnetic baryonic fluxes in D = 11 supergravity. We identify the off-shell AdS4 black hole solutions with parameters of D = 11 AdS2 solutions without imposing the equations of motion. We calculate the entropy of dyonic black holes, carefully analyzing the Page charge quantization conditions.

Black holes with baryonic charge and mathcal{I} -extremization

Recently it was discovered that twisted superconformal index mathcal{I} can be used to understand the Bekenstein-Hawking entropy of magnetically charged black holes in AdS spacetime. In this paper we apply the so-called mathcal{I} -extremization procedure to three-dimensional gauge field theories and their geometric dual, focusing in particular on the seven-dimensional Sasaki-Einstein manifold M1,1,1. We generalize recent studies on relations among toric geometry, variational principles, and black hole entropy to the case of AdS2× Y9, where Y9 is a fibration of toric Sasaki-Einstein manifold M1,1,1 over a two-dimensional Riemann surface Σg. The nine-dimensional variational problem is given in terms of an entropy functional. In order to illustrate the computations as explicitly as possible, we consider cases where either only mesonic or baryonic fluxes are turned on. By employing the operator counting method, we calculate the S3 free energy and the topologically twisted index mathcal{I} at large-N. The result for mathcal{I} , it turns out, can be also obtained from the variational principle of the entropy functional with mesonic fluxes. We also study asymptotically AdS4 black holes which are magnetically charged with respect to the vector field in the Betti multiplet. By extremizing the entropy functional with baryonic flux, we compute the entropy and find that it agrees with the entropy of an explicit solution in a four-dimensional gauged supergravity which is a consistent truncation of eleven-dimensional supergravity in AdS4× M1,1,1.

Aspects of AdS2 classification in M-theory: solutions with mesonic and baryonic charges

We construct necessary and sufficient geometric conditions for a class of AdS2 solutions of M-theory with, at least, minimal supersymmetry to exist. We generalize previous results in the literature for mathcal{N} = (2, 0) supersymmetry in AdS2 to mathcal{N} = (1, 0). When the solution can be locally described as AdS2× Σg× SE7 with Σg a Riemann surface of genus g and SE7 a seven-dimensional Sasaki-Einstein manifold, we clarify and unify various solutions present in the literature. In the case of SE7 = Q1,1,1 we find a new solution with baryonic and mesonic charges turned on simultaneously.

MULTISPIN MEMBRANE SOLUTIONS IN AdS4 ×Q1, 1, 1

We study several types of classical rotating membrane solutions in AdS 4 ×Q1, 1, 1 and discuss their field theory duals. Q1, 1, 1 is a seven-dimensional Sasaki–Einstein manifold given as a nontrivial U(1) fibration over S2×S2×S2, equipped with SU(2)3 ×U(1) isometry. It is recently suggested that there exist quiver Chern–Simons theories which are dual to M-theory in certain orbifolds of Q1, 1, 1. The membrane solutions we consider have in general nonvanishing angular momenta both in AdS 4 and Q1, 1, 1 spaces. We present solutions for folded and wrapped membranes. According to the AdS/CFT correspondence, such classical solutions are dual to long operators of the dual conformal field theories in the large coupling limit. We analyze the asymptotic behaviour of the dispersion relation between energy (conformal dimension) and angular momenta (global charges).

Fermions and D = 11 supergravity on squashed Sasaki-Einstein manifolds

We discuss the dimensional reduction of fermionic modes in a recently found class of consistent truncations of D = 11 supergravity compactified on squashed seven-dimensional Sasaki-Einstein manifolds. Such reductions are of interest, for example, in that they have (2 + 1)-dimensional holographic duals, and the fermionic content and their interactions with charged scalars are an important aspect of their applications. We derive the lower-dimensional equations of motion for the fermions and exhibit their couplings to the various bosonic modes present in the truncations under consideration, which most notably include charged scalar and form fields. We demonstrate that our results are consistent with the expected supersymmetric structure of the lower dimensional theory, and apply them to a specific example which is relevant to the study of (2 + 1)-dimensional holographic superconductors.

Solutions of type IIB and D=11 supergravity with Schrödinger (z) symmetry

We construct families of supersymmetric solutions of type IIB and D=11 supergravity that are invariant under the non-relativistic Schrodinger(z) algebra for various values of the dynamical exponent z. The new solutions are based on five- and seven-dimensional Sasaki-Einstein manifolds, respectively, and include supersymmetric solutions with z=2.

Consistent supersymmetric Kaluza-Klein truncations with massive modes

We construct consistent Kaluza-Klein reductions of D = 11 supergravity to four dimensions using an arbitrary seven-dimensional Sasaki-Einstein manifold. At the level of bosonic fields, we extend the known reduction, which leads to minimal N = 2 gauged supergravity, to also include a multiplet of massive fields, containing the breathing mode of the Sasaki-Einstein space, and still consistent with N = 2 supersymmetry. In the context of flux compactifications, the Sasaki-Einstein reductions are generalizations of type IIA SU(3)-structure reductions which include both metric and form-field flux and lead to a massive universal tensor multiplet. We carry out a similar analysis for an arbitrary weak G2 manifold leading to an N = 1 supergravity with massive fields. The straightforward extension of our results to the case of the seven-sphere would imply that there is a four-dimensional Lagrangian with N = 8 supersymmetry containing both massless and massive spin two fields. We use our results to construct solutions of M-theory with non-relativistic conformal symmetry.

Supersymmetric solutions for non-relativistic holography

We construct families of supersymmetric solutions of type IIB and D=11 supergravity that are invariant under the non-relativistic conformal algebra for various values of dynamical exponent z greater than or equal to 4 and 3, respectively. The solutions are based on five- and seven-dimensional Sasaki-Einstein manifolds and generalise the known solutions with dynamical exponent z=4 for the type IIB case and z=3 for the D=11 case, respectively.

Consistent Kaluza-Klein reductions for general supersymmetricAdSsolutions

For the most general supersymmetric solutions of type IIB supergravity consisting of a warped product of $Ad{S}_{5}$ with a five-dimensional manifold ${M}_{5}$, we construct an explicit consistent Kaluza-Klein reduction on ${M}_{5}$ to minimal $D=5$ gauged supergravity. Thus, any solution of the gauged supergravity can be uplifted on ${M}_{5}$ to obtain an exact solution of type IIB supergravity. We also show that for general $Ad{S}_{4}\ifmmode\times\else\texttimes\fi{}S{E}_{7}$ solutions, where $S{E}_{7}$ is a seven-dimensional Sasaki-Einstein manifold, and for a general class of supersymmetric solutions that are a warped product of $Ad{S}_{4}$ with a seven-dimensional manifold ${N}_{7}$, there is an analogous consistent reduction to minimal $D=4$ gauged supergravity.

Dual giant gravitons in AdSm× Yn(Sasaki-Einstein)

We consider BPS motion of dual giant gravitons on AdS5 × Y5 where Y5 represents a five-dimensional Sasaki-Einstein manifold. We find that the phase space for the BPS dual giant gravitons is symplectically isomorphic to the Calabi-Yau cone over Y5, with the Kahler form identified with the symplectic form. The quantization of the dual giants therefore coincides with the Kahler quantization of the cone which leads to an explicit correspondence between holomorphic wavefunctions of dual giants and gauge-invariant operators of the boundary theory. We extend the discussion to dual giants in AdS4 × Y7 where Y7 is a seven-dimensional Sasaki-Einstein manifold; for special motions the phase space of the dual giants is symplectically isomorphic to the eight-dimensional Calabi-Yau cone.