A large-D Weyl invariant string model in anti-de sitter space

Abstract

In this thesis we present a novel scheme for calculating the bosonic string partition function on certain curved backgrounds related to Anti-de Sitter [AdS] space. We take the concept of a large expansion from nonlinear sigma models in particle physics and apply it to the bosonic string theory sigma model, where the analogous large dimensionless parameter is the dimension of the target space, D. We then perform a perturbative expansion in negative powers of D, rather than in positive powers of α/ι(^2)(the conventional expansion parameter).As a specific example of a curved geometry of interest, we focus on an example of the metric proposed by Polyakov [1] to describe the dynamics of the Wilson loop of pure SU(N) Yang-Mills theory, namely AdS space. Using heat kernel methods, we find that within the large-D scheme one can obtain different conditions for Weyl invariance than those found in [2]. This is because our scheme is valid for backgrounds where a is no longer small. In particular, we find that it is possible to have a dilaton that depends on the holographic coordinate only, provided one allows mixing of the ghost and matter sectors of the worldsheet theory. This field preserves Poincare invariance in the gauge theory, unlike the conventional dilaton. We also compute a simple string amplitude by constructing certain vertex operators for a scalar field in AdS, and discuss the consequences for the string spectrum.