String theory applications in gravitational problems and gauge theories

TL;DR

This paper investigates the stability of string and brane solutions in gauge/gravity duality, analyzing their behavior in various supersymmetric theories and thermal states, to identify physically relevant configurations.

Contribution

It formulates general stability criteria for string and brane solutions in gauge/gravity correspondence and applies these to specific supersymmetric models at finite temperature.

Findings

Unstable configurations are identified as physically irrelevant.

Stability criteria are established for flux tube solutions.

Applications to N=4 SYM and N=1 theories at finite temperature.

Abstract

In this dissertation, we review the study of quark and monopole bound-state potentials within the gauge/gravity correspondence. Their behaviors often differ from what is expected on general physical grounds and field-theory considerations. We identify the configurations of physical interest by examining the stability of the string (brane) solutions dual to the flux tubes between the bound states. In particular, we formulate and prove several general statements concerning the perturbative stability of such string (brane) solutions, relevant for these configurations in a general class of backgrounds. We apply the results to N = 4 SYM and N = 1 at finite temperature and at generic points of the Coulomb branch. In all cases, the problematic regions are found to be unstable and hence physically irrelevant.