Phase transitions and linear response in strongly coupled systems: A holographic approach
File(s)
Author(s)
Banks, Elliot
Type
Thesis
Abstract
Understanding strongly coupled systems is an important area of theoretical physics,
and has wide ranging applications from quantum chromodynamics to condensed matter
physics. This thesis uses holographic methods to understand two particular aspects
of strongly coupled systems - linear response and phase transitions.
Firstly, we consider a general class of electrical black holes in Einstein-Maxwell-scalar
theory, that are holographically dual to conformal eld theories at nite charge density
and explicitly break translational invariance. By considering the linearised perturbations
of these background black holes, we show that the DC thermoelectric conductivity of
these systems can be determined by solving a set of linearised Navier-Stokes equations on
the event horizon of the dual black hole. We demonstrate how to apply this framework
in practice with several examples.
Next, we consider this framework in the hydrodynamic limit, for the simpler case of
Einstein gravity. We show that the full stress-energy response, rather than just the
thermal conductivity, can be determined in this limit, and compare the results with
the
uid/gravity correspondence. We then consider more general hydrodynamics, and
demonstrate that periodically deformed eld theories exhibit thermal back
ow when a
DC thermal source is applied
Finally, we study black hole solutions of type IIB supergravity that describe N=4 supersymmetric
Yang-Mills plasma with an anisotropic spatial deformation. We show that,
by preserving additional scalar modes from the consistent truncation of IIB supergravity
on the ve-sphere, these black holes have low temperature instabilities. We construct new
thermodynamically preferred black hole solutions, and show that the phase transition between
these black hole solution has unusual critical exponents that is not captured by
the normal Landau-Ginzburg exponents. We consider various extensions to this, such as
introducing a chemical potential, and construct a more complete phase diagram for the
theory.
and has wide ranging applications from quantum chromodynamics to condensed matter
physics. This thesis uses holographic methods to understand two particular aspects
of strongly coupled systems - linear response and phase transitions.
Firstly, we consider a general class of electrical black holes in Einstein-Maxwell-scalar
theory, that are holographically dual to conformal eld theories at nite charge density
and explicitly break translational invariance. By considering the linearised perturbations
of these background black holes, we show that the DC thermoelectric conductivity of
these systems can be determined by solving a set of linearised Navier-Stokes equations on
the event horizon of the dual black hole. We demonstrate how to apply this framework
in practice with several examples.
Next, we consider this framework in the hydrodynamic limit, for the simpler case of
Einstein gravity. We show that the full stress-energy response, rather than just the
thermal conductivity, can be determined in this limit, and compare the results with
the
uid/gravity correspondence. We then consider more general hydrodynamics, and
demonstrate that periodically deformed eld theories exhibit thermal back
ow when a
DC thermal source is applied
Finally, we study black hole solutions of type IIB supergravity that describe N=4 supersymmetric
Yang-Mills plasma with an anisotropic spatial deformation. We show that,
by preserving additional scalar modes from the consistent truncation of IIB supergravity
on the ve-sphere, these black holes have low temperature instabilities. We construct new
thermodynamically preferred black hole solutions, and show that the phase transition between
these black hole solution has unusual critical exponents that is not captured by
the normal Landau-Ginzburg exponents. We consider various extensions to this, such as
introducing a chemical potential, and construct a more complete phase diagram for the
theory.
Version
Open Access
Date Issued
2017-03
Date Awarded
2017-06
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Gauntlett, Jerome
Sponsor
Imperial College London
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)