Microscopic formulation of black holes in string theory

Abstract

In this Report we review the microscopic formulation of the five dimensional black hole of type IIB string theory in terms of the D1-D5 brane system. The emphasis here is more on the brane dynamics than on supergravity solutions. We show how the low energy brane dynamics, combined with crucial inputs from AdS/CFT correspondence, leads to a derivation of black hole thermodynamics and the rate of Hawking radiation. Our approach requires a detailed exposition of the gauge theory and conformal field theory of the D1-D5 system. We also discuss some applications of the AdS/CFT correspondence in the context of black hole formation in three dimensions by thermal transition and by collision of point particles.

Worldsheet correlators in AdS3/CFT2

“…There are also different chiral primary operators that can be obtained by multiplying Σ (n) with appropriate combinations of spinors ψ i A [5], the superpartners of the X i A . However, in this paper we shall only consider the chiral primaries Σ…”

“…The situation is different for the AdS 3 /CFT 2 duality for which both the ten-dimensional string theory as well as the two-dimensional boundary conformal field theory are explicitly known (for a review see [5]). Starting from the intersection of N 1 D1-branes and N 5 D5-branes compactified on a four-torus T 4 , one finds AdS 3 × S 3 × T 4 as the corresponding near-horizon geometry.…”

A general black string and its microscopics

“…This means that the solution has already been boosted along the z-direction as a result of the intricate action of the g 2(2) generators. 3 It is however straightforward to find the boost γ = γ c (β, δ) one has to apply to reach the non-boosted frame. Solving for P z = 0, one finds…”

“…Following [1], a number of different types of black holes have been studied and the agreement between the statistical mechanical entropy and the Bekenstein-Hawking entropy has been shown to hold in each case (see e.g. reviews [2][3][4] and references therein). In particular, references [5][6][7] extended the success of [1] to the five-dimensional near-extremal setting.…”

Warped AdS3 black holes in higher derivative gravity theories

“…The reason for this seemingly unreasonable effectiveness was clarified in [14] (see also [15][16][17] for related earlier works): for CFTs with a large central charge (corresponding to the semi-classical limit on the gravity side) and a sparse light spectrum, the Cardy regime extends all the way down to where the condition L + 0 + L − 0 ≥ c 12 is satisfied. This behavior puts constraints on the precise nature of 2d CFTs potentially dual to AdS 3 theories of gravity, examples of which include symmetric orbifolds [14,[17][18][19][20][21] and extremal CFTs [22,23]. Other CFTs potentially dual to AdS 3 gravity have recently been discussed in [24] The key property responsible for the existence of a simple and elegant formula like (1.1) is modular invariance.…”