On the BPS Sector in AdS₃/CFT₂ Holography

Abstract

The BPS sector in AdS3/CFT2$AdS_3/CFT_2$ duality has been fertile ground for the exploration of gauge/gravity duality, from the match between black hole entropy and the CFT elliptic genus to the construction of large families of geometrical microstates and the identification of the corresponding states in the CFT. Worldsheet methods provide a tool to further explore the relation between string theory in the bulk and corresponding CFT quantities. We show how to match individual BPS strings to their counterparts in the symmetric product orbifold CFT. In the process, we find an exact match between known constructions of microstate geometries and condensates of BPS supergraviton strings, and discuss their role in the broader collection of BPS states. In particular, we explore how microstate geometries develop singularities; and how string theory resolves these singularities through the appearance of “tensionless” string dynamics, which is the continuation of structures found in the weak‐coupling CFT into the strongly coupled regime described by string theory in the bulk. We argue that such “tensionless” strings are responsible for black hole microstructure in the bulk description.

NS5-brane backgrounds and coset CFT partition functions

“…(6.69) and (6.88)) gives us confidence in the result, and confirms the analysis of the spectrum carried out in e.g. [14,20].…”

“…Recently, a large class of 1/2-BPS "supertube" geometries [12] have been shown to be described by the cosets [13][14][15][16][17][18][19][20] SL(2, R) n 5 × SU (2)…”

A proof for string three-point functions in AdS3

“…The interest in correlation functions of the SL(2,R)-WZW model is explained by their important holographic applications, especially in the context of superstring theory in AdS 3 ×S 3 ×T 4 (or K3) [6][7][8][9], and for the dynamics of light probes in black hole microstates [10][11][12][13][14][15][16][17]. Worldsheet vertex operators are functions of the worldsheet coordinate z, and of an additional continuous parameter x, which plays the role of the holomorphic coordinate on the conformal boundary.…”

The chiral ring of a symmetric orbifold and its large N limit

“…8 This is a consequence of the fact that the multiplication of conjugacy classes is upper triangular in an appropriate sense. 9 Finding closed expressions however can remain hard. The generic three-point functions we obtained are our main result.…”