Black hole microstates in the D1-D5 orbifold CFT

Abstract

This thesis presents work extending the precision holography calculations for the D1-D5 CFT. The context of these calculations is the fuzzball proposal, which is the most widely accepted string theory answer for black hole microstates. According to this proposal, associated to a black hole there is an exponentially large number of microstates, called fuzzballs, which are regular, horizonless stringy solutions. These account for the whole entropy of the black hole, and solve all the paradoxes arising from the semi-classical study.

The D1-D5 system has an orbifold point in its moduli space, at which it may be described by an N = (4, 4) supersymmetric sigma model with target space MN /S(N), where M is T 4 or K3. In this thesis correlation functions involving chiral operators constructed from twist fields are considered, as well as one and n-point functions. Explicit expressions for processes involving a twist n operator joining n twist operators of arbitrary twist are obtained. One point functions for chiral primary operators are calculated, extending the known CFT results in the literature. The suppression of the long string one point functions with respect to the short string ones is corroborated. Bounds for n-point functions of twist operators are also presented.

On a different direction, work towards the counting of the so-called superstrata subclasses of black hole microstates is presented. To do so, some integer partition results in the context of number theory are introduced. The generating functions for the partitions are obtained, as well as a novel formula to count them exactly. A computer program which implements such formula is described.

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ORCID for Marika Taylor: orcid.org/0000-0001-9956-601X

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