Aspects of holographic string theory

Abstract

In this thesis we study several aspects of gauge/gravity dualities. We start by analyzing the structure of the UV divergences of the Wilson loop for a general gauge/gravity duality. We find that, due to the presence of a nontrivial NSNS B-field and metric, new divergences that cannot be subtracted out by the conventional Legendre transform may arise. We also derive conditions on the B-field and the metric, which when satisfied, the leading UV divergence will become linear, and can be canceled out by choosing the boundary condition of the string appropriately. Our results, together with the result of [15], where the effect of a nontrivial dilaton on the structure of UV divergences in Wilson loop is analyzed, allow us to conclude that Legendre transform is at best capable of canceling the linear UV divergences arising from the area of the worldsheet, but is incapable to handle the divergences associated with the dilaton or the B-field in general. We also solve the conditions for the cancelation of the leading linear divergences generally and find that many well-known super gravity backgrounds are of these kinds, including examples such as the Sakai-Sugimoto QCD model or N = 1 duality with Sasaki-Einstein spaces. We also point out that Wilson loop in the Klebanov-Strassler background have a divergence associated with the B-field which cannot be canceled away with the Legendre transform. Moreover, our results indicate that the finiteness of the expectation value of the Wilson loop does not depend on the supersymmetry. In the next chapter, we propose a definition of the Wilson loop operator in the N = 1 ß-deformed supersymmetric Yang-Mills theory. Although the operator is not BPS, it has a finite expectation value, result that come from the work in the previous chapter but also from the field theory calculations at least up to order (9(^2)N)(^2). We also derive the general form of the boundary condition satisfied by the dual string worldsheet and find that it is deformed. Finiteness of the expectation value of the Wilson loop, together with some rather remarkable properties of the Lunin-Maldacena metric and the B-field, fixes the boundary condition to be one which is characterized by the vielbein of the deformed supergravity metric. The Wilson loop operators provide natural candidates as dual descriptions to some of the existing D-brane configurations in the Lunin-Maldacena background. We also construct the string dual configuration for a near-1/4 BPS circular Wilson loop operator. The string lies on a deformed three-sphere instead of a two-sphere as in the undeformed case. The expectation value of the Wilson loop operator is computed using the AdS/CFT correspondence and is found to be independent of the deformation. In the next chapter we focus on a different topic, and find point-like and classical string solutions on the AdS(_5) x X(^5), where are the 5-dimensional Sasaki-Einstein manifolds Y(^p,q) and L(^p.q.r). The number of acceptable solutions is limited drastically in order to satisfy the constraints on the parameters and coordinates of the manifolds. We find the energy-spin relations of the above solutions and see that they depend on the parameters of the Sasaki-Einstein manifolds. A discussion on BPS solutions is presented as well. In the last chapter we present a general discussion on topics which related closely to all previous chapters. Among other things we also give some comments on the form of the Wilson loop operator in the ABJM superconformal Chern-Simons theory.