Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics

The structure

We review black-hole solutions of higher-dimensional vacuum gravity and higher-dimensional supergravity theories. The discussion of vacuum gravity is pedagogical, with detailed reviews of Myers-Perry solutions, black rings, and solution-generating techniques. We discuss black-hole solutions of maximal supergravity theories, including black holes in anti-de Sitter space. General results and open problems are discussed throughout.

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Black Holes in Higher Dimensions

We analyze various aspects of the recently proposed holographic theories with general dynamical critical exponent z and hyperscaling violation exponent θ. We first find the basic constraints on z, θ from the gravity side, and compute the stress-energy tensor expectation values and scalar two-point functions. Massive correlators exhibit a nontrivial exponential behavior at long distances, controlled by θ. At short distance, the two-point functions become power-law, with a universal form for θ > 0. Next, the calculation of the holographic entanglement entropy reveals the existence of novel phases which violate the area law. The entropy in these phases has a behavior that interpolates between that of a Fermi surface and that exhibited by systems with extensive entanglement entropy. Finally, we describe microscopic embeddings of some θ ≠ 0 metrics into full string theory models — these metrics characterize large regions of the parameter space of Dp-brane metrics for p ≠ 3. For instance, the theory of N D2-branes in IIA super gravity has z = 1 and θ = −1/3 over a wide range of scales, at large g
 s
 N.

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Aspects of holography for theories with hyperscaling violation

Non-relativistic versions of the AdS/CFT conjecture have recently been investigated in some detail These have primarily been in the context of the Schrodinger symmetry group Here we initiate a study based on a different non-relativistic conformal symmetry: one obtained by a parametric contraction of the relativistic conformal group The resulting Galilean conformal symmetry has the same number of generators as the relativistic symmetry group and thus is different from the Schrodinger group (which has fewer) One of the interesting features of the Galilean Conformal Algebra is that it admits an extension to an infinite dimensional symmetry algebra (which can potentially be dynamically realised) The latter contains a Virasoro-Kac-Moody subalgebra We comment on realisations of this extended symmetry in a boundary field theory We also propose a somewhat unusual geometric structure for the bulk gravity dual to any realisation of this symmetry This involves taking a Newton-Cartan like limit of Einstein's equations in anti de Sitter space which singles out an AdS2 comprising of the time and radial direction The infinite dimensional Virasoro extension is identified with the asymptotic isometries of this AdS2

http://hep.physics.uoc.gr/mideast5/talks/Saturday/Gopakumar.pdf

Galilean Conformal Algebras and AdS/CFT

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.

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Consistent supersymmetric Kaluza-Klein truncations with massive modes

We study how to generate new Lie algebras $\mathcal{G}(N_0,..., N_p,...,N_n)$ from a given one $\mathcal{G}$. The (order by order) method consists in expanding its Maurer-Cartan one-forms in powers of a real parameter $\lambda$ which rescales the coordinates of the Lie (super)group $G$, $g^{i_p} \to \lambda^p g^{i_p}$, in a way subordinated to the splitting of $\mathcal{G}$ as a sum $V_0 \oplus ... \oplus V_p \oplus ... \oplus V_n$ of vector subspaces. We also show that, under certain conditions, one of the obtained algebras may correspond to a generalized \.In\"on\"u-Wigner contraction in the sense of Weimar-Woods, but not in general. The method is used to derive the M-theory superalgebra, including its Lorentz part, from $osp(1|32)$. It is also extended to include gauge free differential (super)algebras and Chern-Simons theories, and then applied to D=3 CS supergravity.

Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity

At the level of the bosonic fields, we construct consistent Kaluza-Klein reductions of D = 11 supergravity on Σ3 × S4, where Σ3 = H
 3/Γ, S
 3/Γ or R
 3/Γ where Γ is a discrete group of isometries. The result is the bosonic content of an N = 2 D = 4 gauged supergravity with a single vector multiplet and two hypermultiplets, whose scalar fields parametrise SU(1,1)/U(1) × G
 2(2)/SO(4). When Σ3 = H
 3/Γ the D = 4 theory has an AdS
 4 vacuum which uplifts to the known supersymmetric AdS
 4 × H
 3/Γ × S
 4 solution of D = 11 supergravity that describes the N = 2 d = 3 SCFT arising when M5-branes wrap SLag 3-cycles H
 3/Γ in Calabi-Yau three-folds. We use the KK reduction for Σ3 = H
 3/Γ to construct D = 11 black hole solutions that describe these d = 3 SCFTs at finite temperature and charge density and show that there is a superconducting instability involving a charged scalar field, and another instability involving neutral fields including both scalar and vector fields. We also use this KK reduction to construct a D = 11 Lifshitz solution that is dual to a d = 3 field theory with dynamical exponent z ∼ 39.

https://pure.mpg.de/pubman/item/item_529206_2/component/file_529205/1009.3805

Wrapped M5-branes, consistent truncations and AdS/CMT

We construct explicit consistent Kaluza–Klein reductions of type IIB supergravity on HK
 4 ×S
 1, where HK
 4 is an arbitrary four-dimensional hyper-Kahler manifold, and on SE
 5, an arbitrary five-dimensional Sasaki–Einstein manifold. In the former case we obtain the bosonic action of D = 5 N = 4 (ungauged) supergravity coupled to two vector multiplets. For the SE
 5 case we extend a known reduction, which leads to minimal D = 5 N = 2 gauged supergravity, to also include a multiplet of massive fields, containing the breathing mode of the SE
 5. We show that the resulting D = 5 action is also consistent with N = 4 gauged supergravity coupled to two vector multiplets. This theory has a supersymmetric AdS
 5 vacuum, which uplifts to the class of supersymmetric AdS
 5 × SE
 5 solutions, that spontaneously breaks N = 4 to N = 2, and also a non-supersymmetric AdS
 5 vacuum which uplifts to a class of solutions first found by Romans.

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Universal Kaluza-Klein reductions of type IIB to N=4 supergravity in five dimensions

By studying classes of supersymmetric solutions of D = 11 supergravity with AdS5 factors, we determine some properties of the dual four-dimensional N = 1 superconformal field theories. For some explicit solutions we calculate the central charges and also the conformal dimensions of certain chiral primary operators arising from wrapped membranes. For the most general class of solutions we show that there is a consistent Kaluza-Klein truncation to minimal D = 5 gauged supergravity. This latter result allows us to study some aspects of the dual strongly coupled thermal plasma with a non-zero R-charge chemical potential and, in particular, we show that the ratio of the shear viscosity to the entropy density has the universal value of 1/4π.

https://digital.csic.es/bitstream/10261/9175/2/jhep022007049.pdf

Oscar Varela

Papers

Consistent supersymmetric Kaluza-Klein truncations with massive modes

Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity

Wrapped M5-branes, consistent truncations and AdS/CMT

Universal Kaluza-Klein reductions of type IIB to N=4 supergravity in five dimensions

Properties of some conformal field theories with M-theory duals