Strings in a 2-d Extremal Black Hole

Abstract

String theory on 2-d charged black holes corresponding to SL(2)×U(1) L U(1)exact asymmetric quotient CFTs are investigated. These backgrounds can be embedded, in particular, in a two dimensional heterotic string. In the extremal case, the quotient CFT description captures the near horizon physics, and is equivalent to strings in AdS 2 with a gauge field. Such string vacua possess an infinite space-time Virasoro symmetry, and hence enhancement of global space-time Lie symmetries to affine symmetries, in agreement with the conjectured AdS 2 /CF T 1 correspondence. We argue that the entropy of these 2-d black holes in string theory is compatible with semi-classical results, and show that in perturbative computations part of an incoming flux is absorbed by the black hole. Moreover, on the way we find evidence that the 2-d heterotic string is closely related to the N = (2, 1) string, and conjecture that they are dual [1]. 07/04

AdS3/CFT2toAdS2/CFT1

“…Since extremal black holes have an AdS 2 factor in their near horizon geometry [7,8], one expects that the underlying quantum gravity theory in this background will have a dual description in terms of a conformal quantum mechanics (CQM) living at the boundary of AdS 2 [9][10][11][12][13][14][15][16][17][18][19][20]. In [19] it was shown that in the classical limit, when Wald's formula is expected to be valid, the Wald entropy computed from the entropy function can be interpreted as the logarithm of the ground state degeneracy of this dual CQM in a fixed charge sector.…”

“…However in that paper the authors interpreted the φ coordinate as the euclidean time direction and the u coordinate as the spatial circle, thereby arriving at a modular transformed version of eq. (16). Since our goal is to identify the CQM living on the boundary of AdS 2 , we must choose u as the time coordinate on the boundary of AdS 3 so that it matches the time coordinate of the CQM.…”

The charged black hole/string transition

“…can be constructed as follows (see [10] for a recent discussion). We start with the supersymmetric SL(2, IR) WZW model at level k, whose central charge is c =c = 3 + 6 k + 3 2 , and add to it a left-moving supersymmetric U (1) current with c = In the coset description, the maximal extension of the background (2.1) -(2.3) splits into different regions, each of which is described by its own set of natural coordinates.…”

“…k 0 is determined by the length of the vector (3.9), 10) and the mass-shell condition for the tachyon,…”

Stringy holography at finite density

“…The metric of the two-dimensional charged black hole [23] with mass M and charge q in suitable coordinates can be written as [26,27]…”