Study of behaviour of fermions in some holographic theories using gauge gravity duality

Abstract

Gauge/Gravity duality relates a strongly coupled d-dimensional field theory to a weakly coupled d + 1-dimensional gravity theory and vice versa. This holographic duality provides extremely powerful machinery to unravel and explore strongly coupled regimes giving rise to wide applications in diverse areas, such as gauge theory,hydrodynamics, condensed matter theories etc.This thesis is based on the application of Gauge/Gravity duality in some aspects of strongly coupled condensed matter systems. Though these kinds of systems are not amenable to perturbative techniques of quantum field theory, there are formalisms, within the framework of condensed matter theory, such as Fermi liquid theory, which can capture its dynamics in most of the cases. However, vaious materials have been discovered in the eighties, which exhibit behaviour different newlinefrom predictions of Fermi liquid theory and dubbed as non-Fermi liquid. Examples of such materials are high (Tc) cuprates superconductors and heavy fermions near a quantum phase transition. In the present work, we aim at understanding the behaviour of such systems using the Gauge/Gravity duality. We have adopted a top-down approach, where one considers a well established theory following from String theory on the gravity side with an exactly known dual field theory. We begin with maximally gauged supergravity theory in seven dimension. The dual of this theory is conjectured to be (2,0) conformal field theory in six dimension. newlineThis theory admits asymptotically AdS blackhole solution characterised by newlinetwo chemical potentials. The extremal limit of this blackhole corresponds to a one parameter family of solutions. We consider analysis of the fermionic modes in this background that reveals existence of the Fermi surface. Depending on the fermionic mode we have obtained a pair of Fermi surfaces or a single Fermi surface. Study of fermionic excitations shows that they mostly belong to the non-Fermi regime. We newlinehave obtained excitations belonging to Fermi regime as well.