Brst Structure Of Two Dimensional Conformal Field Theories PDF Download

In this thesis, we study aspects of three-dimensional gravity in Anti de Sitter (AdS) space by studying the holographically dual two-dimensional conformal field theory (CFT). We begin by describing general constraints on the elliptic genus of a two-dimensional supersymmetric conformal field theory which has a gravity dual with large radius in Planck units. We discuss the distinction between theories with supergravity duals and those whose duals have strings at the scale set by the AdS curvature, using symmetric orbifolds as a case study. We then move on to study extremal theories, conjectured to be dual to "pure" three-dimensional gravity. We first provide an example of an extremal chiral N=2 superconformal field theory at c=24. We then consider extremal CFTs at large central charge, and consider the quantum corrections to the classical spectrum. Our conjecture passes various consistency checks, especially when generalized to include theories with supersymmetry. Finally, we examine a specific top-down construction of AdS3/CFT2 from string theory, called the D1/D5 system. We examine the low-lying quarter BPS spectrum of the K3 symmetric orbifold CFT at various points in moduli space, and look at a more refined count than the ordinary elliptic genus. We do a decomposition of the spectra into N=4 characters, and show that at large N the character decomposition satisfies an unusual property, in which the degeneracy only depends on a certain linear combination of left- and right-moving quantum numbers, suggesting deeper symmetry structure.