Shubho Roy

A Grassmann path from AdS3 to flat space

A bstractWe show that interpreting the inverse AdS3 radius 1/l as a Grassmann variable results in a formal map from gravity in AdS3 to gravity in flat space. The underlying reason for this is the fact that ISO(2, 1) is the Inonu-Wigner contraction of SO(2, 2). We show how this works for the Chern-Simons actions, demonstrate how the general (Banados) solution in AdS3 maps to the general flat space solution, and how the Killing vectors, charges and the Virasoro algebra in the Brown-Henneaux case map to the corresponding quantities in the BMS3 case. Our results straightforwardly generalize to the higher spin case: the recently constructed flat space higher spin theories emerge automatically in this approach from their AdS counterparts. We conclude with a discussion of singularity resolution in the BMS gauge as an application.

Higher spin resolution of a toy big bang

Diffeomorphisms preserve spacetime singularities, whereas higher spin symmetries need not. Since three-dimensional de Sitter space has quotients that have big-bang/big-crunch singularities and since dS(3)-gravity can be written as an SL(2, C) Chern-Simons theory, we investigate SL(3, C) Chern-Simons theory as a higher-spin context in which these singularities might get resolved. As in the case of higher spin black holes in AdS(3), the solutions are invariantly characterized by their holonomies. We show that the dS(3) quotient singularity can be desingularized by an SL(3, C) gauge transformation that preserves the holonomy: this is a higher spin resolution the cosmological singularity. Our work deals exclusively with the bulk theory, and is independent of the subtleties involved in defining a CFT2 dual to dS(3) in the sense of dS/CFT.

Desingularization of the Milne Universe

Resolution of cosmological singularities is an important problem in any full theory of quantum gravity. The Milne orbifold is a cosmology with a big-bang/big-crunch singularity, but being a quotient of flat space it holds potential for resolution in string theory. It is known, however, that some perturbative string amplitudes diverge in the Milne geometry. Here we show that flat space higher spin theories can effect a simple resolution of the Milne singularity when one embeds the latter in 2 + 1 dimensions. We explain how to reconcile this with the expectation that non-perturbative string effects are required for resolving Milne. Along the way, we introduce a Grassmann realization of the inonfi-Wigner contraction to export much of the AdS technology to -our flat space computation

Punctuated eternal inflation via AdS/CFT

The work is an attempt to model a scenario of inflation in the framework of anti-de Sitter/conformal field theory duality, a potentially complete nonperturbative description of quantum gravity. We study bubble geometries with de Sitter interiors within an ambient Schwarzschild anti-de Sitter black hole spacetime and the properties of the corresponding states in the dual conformal field theory. It is argued the viable bubble states can be identified with a subset of the black hole microstates. Consistency checks are performed and a number of implications regarding cosmology are discussed including how the key problems or paradoxes of conventional eternal inflation are overcome in this scenario.

Higher spin cosmology

We construct cosmological solutions of higher spin gravity in 2 + 1 dimensional de Sitter space. We show that a consistent thermodynamics can be obtained for their horizons by demanding appropriate holonomy conditions. This is equivalent to demanding the integrability of the Euclidean boundary conformal field theory partition function, and it reduces to Gibbons-Hawking thermodynamics in the spin-2 case. By using the prescription of Maldacena, we relate the thermodynamics of these solutions to those of higher spin black holes in AdS(3).

Holographic description of asymptotically AdS{sub 2} collapse geometries

The mapping between bulk supergravity fields in anti\char21{}de Sitter space and operators in the dual boundary conformal field theory usually relies heavily on the available global symmetries. In the present work, we study a generalization of this mapping to time dependent situations, for the simple case of collapsing shock waves in two spacetime dimensions. The construction makes use of analyticity of the conformal field theory and the properties of the asymptotic bulk geometry to reconstruct the nonanalytic bulk observables. Many of the features of this construction are expected to apply to higher dimensional asymptotically anti\char21{}de Sitter spacetimes and their conformal field theory duals.

Black Hole Formation at the Correspondence Point

We study the process of bound state formation in a D-brane collision. We consider two mechanisms for bound state formation. The first, operative at weak coupling in the worldvolume gauge theory, is pair creation of W-bosons. The second, operative at strong coupling, corresponds to formation of a large black hole in the dual supergravity. These two processes agree qualitatively at intermediate coupling, in accord with the correspondence principle of Horowitz and Polchinski. We show that the size of the bound state and time scale for formation of a bound state agree at the correspondence point. The time scale involves matching a parametric resonance in the gauge theory to a quasinormal mode in supergravity.

Black hole formation in fuzzy sphere collapse

We study the collapse of a fuzzy sphere, that is a spherical membrane built out of D0-branes, in the Banks-Fischler-Shenker-Susskind model. At weak coupling, as the sphere shrinks, open strings are produced. If the initial radius is large then open string production is not important and the sphere behaves classically. At intermediate initial radius the backreaction from open string production is important but the fuzzy sphere retains its identity. At small initial radius the sphere collapses to form a black hole. The crossover between the later two regimes is smooth and occurs at the correspondence point of Horowitz and Polchinski.

Chiral geometries of (2+1)-d AdS gravity

Abstract Pure gravity in ( 2 + 1 )-dimensions with negative cosmological constant is classically equivalent Chern–Simons gauge theory with gauge group SO ( 2 , 2 ) , which may be realized on chiral and anti-chiral gauge connections. This Letter looks at half-AdS geometries i.e. those with a trivial right-moving gauge connection while the left-moving connection is a standard (Banados–Teitelboim–Zanelli) BTZ connection. These are shown to be related by diffeomorphism to a BTZ geometry with different mass and angular momentum. Generically this is over-spinning, leading to a naked closed timelike curves. Other closely related solutions are also studied. These results suggest that the measure of the Chern–Simons path integral cannot factorize in a chiral way, if it is to represent a sum over physically sensible states.

Holographic bulk reconstruction with

We outline a holographic recipe to reconstruct α corrections to AdS (quantum) gravity from an underlying CFT in the strictly planar limit (N → ∞). Assuming that the boundary CFT can be solved in principle to all orders of the ’t Hooft coupling λ, for scalar primary operators, the λ expansion of the conformal dimensions can be mapped to higher curvature corrections of the dual bulk scalar field action. Furthermore, for the metric perturbations in the bulk, the AdS/CFT operator-field isomorphism forces these corrections to be of the Lovelock type. We demonstrate this by reconstructing the coefficient of the leading Lovelock correction, aka the Gauss-Bonnet term in a bulk AdS gravity action using the expression of stress-tensor two-point function up to sub-leading order in λ.