Aspects of Gauge-Gravity Duality

TL;DR

This thesis explores various gauge-gravity dualities, analyzing phase structures, spectra, and walking behaviors in supergravity backgrounds, revealing insights into metastable states, flavor effects, and potential dilaton particles.

Contribution

It provides new holographic models and detailed computations of spectra and phase transitions, including the emergence of a light dilaton in walking backgrounds.

Findings

Metastable states at critical chemical potential and temperature.

Scalar glueball mass dependence on flavor number.

Identification of a light scalar in walking backgrounds.

Abstract

In this Ph.D. thesis, we study various backgrounds in Type IIB supergravity which admit interpretations in terms a dual field theory, and compute properties such as effective potentials and spectra, using both holographic and field theoretic methods. First, we study the phase structure of beta-deformed N=4 SYM on S3 at weak and strong 't Hooft coupling. We compute the one-loop effective potential, and find that at near critical chemical potential and small finite temperature, there is a metastable state at the origin of moduli space. We derive the gravitational background describing the theory at strong coupling, and by performing a probe-brane calculation, we find qualitative agreement between the weak and strong coupling results. Next, we study gravitational backgrounds obtained by wrapping Nc D5 color branes on an S2 inside a CY3-fold, and Nf D5 backreacting flavor branes on a non-compact two-cycle inside the same CY3-fold. These backgrounds are believed to be dual to certain SQCD-like theories. We compute how the spectrum depends on the number of flavors, and find that the mass of the lightest scalar glueball increases with the number of flavors until the point Nf=2Nc is reached after which the opposite behaviour is observed. Finally, we consider a class of backgrounds that exhibit walking behaviour, i.e. a suitably defined four-dimensional gauge coupling stays nearly constant in an intermediate energy regime. The breaking of approximate scale invariance has been conjectured to lead to the existence of a light scalar in the spectrum. This so-called dilaton would be the pseudo-Goldstone boson of dilatations. Using holographic techniques, we compute the spectrum and find a light state whose mass is suppressed by the length of the walking region, suggesting that this might be the dilaton.