This thesis consists of four research papers and an introduction covering the most important concepts appearing in the papers. The papers deal with applications of gauge/gravity dualities in the study of various physical quantities and systems. Gauge/gravity dualities are equivalences between certain quantum field theories and classical theories of gravity. These dualities can be used as computational tools in a wide range of applications across different fields of physics, and as such they have garnered much attention in the last two decades. The great promise of these new tools is the ability to tackle difficult problems in strongly interacting quantum field theories by translating them to problems in classical gravity, where progress is much easier to make. Quantum information theory studies the information contained in quantum systems. Entanglement is the fundamental property of quantum mechanics that sets it apart from classical theories of physics. Entanglement is commonly quantified by entanglement entropy, a quantity which is difficult to compute in interacting quantum field theories. Gauge/gravity dualities provide a practical way for computing the entanglement entropy via the Ryu-Takayanagi formula. The primary focus of this thesis is to use this formula for computing various entanglement measures in strongly interacting quantum field theories via their gravity duals. The purpose of this thesis is to introduce quantum information theory concepts that have been important in our research. When applicable, quantities of interest are first introduced in the classical setting in order to build intuition about their behaviour. Quantum properties of entanglement measures are discussed in detail, along with their holographic counterparts, and remarks are made concerning their applications.This thesis consists of four research papers and an introduction covering the most important concepts appearing in the papers. The papers deal with applications of gauge/gravity dualities in the study of various physical quantities and systems. Gauge/gravity dualities are equivalences between certain quantum field theories and classical theories of gravity. These dualities can be used as computational tools in a wide range of applications across different fields of physics, and as such they have garnered much attention in the last two decades. The great promise of these new tools is the ability to tackle difficult problems in strongly interacting quantum field theories by translating them to problems in classical gravity, where progress is much easier to make. Quantum information theory studies the information contained in quantum systems. Entanglement is the fundamental property of quantum mechanics that sets it apart from classical theories of physics. Entanglement is commonly quantified by entanglement entropy, a quantity which is difficult to compute in interacting quantum field theories. Gauge/gravity dualities provide a practical way for computing the entanglement entropy via the Ryu-Takayanagi formula. The primary focus of this thesis is to use this formula for computing various entanglement measures in strongly interacting quantum field theories via their gravity duals. The purpose of this thesis is to introduce quantum information theory concepts that have been important in our research. When applicable, quantities of interest are first introduced in the classical setting in order to build intuition about their behaviour. Quantum properties of entanglement measures are discussed in detail, along with their holographic counterparts, and remarks are made concerning their applications.

Työväentutkimus VuosikirjaNov 12, 20190 citations

Gauge theories and holisms

Richard Healey

Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern PhysicsNov 8, 200419 citations

Universal properties of the U(1) current at deconfined quantum critical points: Comparison with predictions from gauge-gravity duality

Flavio S. Nogueira

The deconfined quantum critical point of a two-dimensional $SU(N)$ antiferromagnet is governed by an Abelian Higgs model in $d=2+1$ spacetime dimensions featuring $N$ complex scalar fields. In this context, we derive for $2\ensuremath{\le}d\ensuremath{\le}4$ an exact formula for the central charge of the $U(1)$ current in terms of the gauge coupling at quantum criticality and compare it with the corresponding result obtained using gauge-gravity duality. There is a remarkable similarity precisely for $d=2+1$ . In this case the amplitude of the current correlation function has the same form as predicted by the gauge-gravity duality. We also compare finite temperature results for the charge susceptibility in the large $N$ limit with the result predicted by the gauge-gravity duality. Our results suggest that condensed matter systems at quantum criticality may provide interesting quantitative tests of the gauge-gravity duality even in the absence of supersymmetry.The deconfined quantum critical point of a two-dimensional $SU(N)$ antiferromagnet is governed by an Abelian Higgs model in $d=2+1$ spacetime dimensions featuring $N$ complex scalar fields. In this context, we derive for $2\ensuremath{\le}d\ensuremath{\le}4$ an exact formula for the central charge of the $U(1)$ current in terms of the gauge coupling at quantum criticality and compare it with the corresponding result obtained using gauge-gravity duality. There is a remarkable similarity precisely for $d=2+1$. In this case the amplitude of the current correlation function has the same form as predicted by the gauge-gravity duality. We also compare finite temperature results for the charge susceptibility in the large $N$ limit with the result predicted by the gauge-gravity duality. Our results suggest that condensed matter systems at quantum criticality may provide interesting quantitative tests of the gauge-gravity duality even in the absence of supersymmetry.

arXiv:0902.0364Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsMay 8, 20091 citation

What Can Gauge-Gravity Duality Teach Us About Condensed Matter Physics?

Subir Sachdev A

I discuss the impact of gauge-gravity duality on our understanding of two classes of systems: conformal quantum matter and compressible quantum matter. The first conformal class includes systems, such as the boson Hubbard model in two spatial dimensions, which display quantum critical points described by conformal field theories. Questions associated with nonzero temperature dynamics and transport are difficult to answer using conventional field-theoretic methods. I argue that many of these can be addressed systematically using gauge-gravity duality and discuss the prospects for reliable computation of low-frequency correlations. Compressible quantum matter is characterized by the smooth dependence of the charge density, associated with a global U(1) symmetry, upon a chemical potential. Familiar examples are solids, superfluids, and Fermi liquids, but there are more exotic possibilities involving deconfined phases of gauge fields in the presence of Fermi surfaces. I survey the compressible systems studied using gauge-gravity duality and discuss their relationship to the condensed matter classification of such states. The gravity methods offer hope of a deeper understanding of exotic and strongly coupled compressible quantum states.I discuss the impact of gauge-gravity duality on our understanding of two classes of systems: conformal quantum matter and compressible quantum matter. The first conformal class includes systems, such as the boson Hubbard model in two spatial dimensions, which display quantum critical points described by conformal field theories. Questions associated with nonzero temperature dynamics and transport are difficult to answer using conventional field-theoretic methods. I argue that many of these can be addressed systematically using gauge-gravity duality and discuss the prospects for reliable computation of low-frequency correlations. Compressible quantum matter is characterized by the smooth dependence of the charge density, associated with a global U(1) symmetry, upon a chemical potential. Familiar examples are solids, superfluids, and Fermi liquids, but there are more exotic possibilities involving deconfined phases of gauge fields in the presence of Fermi surfaces. I survey the compressible systems studied using gauge-gravity duality and discuss their relationship to the condensed matter classification of such states. The gravity methods offer hope of a deeper understanding of exotic and strongly coupled compressible quantum states.

arXiv:1108.1197Annual Review of Condensed Matter PhysicsMar 1, 2011246 citations

The deconfined quantum critical point of a two-dimensional

SU(N)

antiferromagnet is governed by an Abelian Higgs model in

d=2+1

spacetime dimensions featuring

N

complex scalar fields. In this context, we derive for $2\ensuremath{\le}d\ensuremath{\le}4$ an exact formula for the central charge of the

U(1)

current in terms of the gauge coupling at quantum criticality and compare it with the corresponding result obtained using gauge-gravity duality. There is a remarkable similarity precisely for

d=2+1

. In this case the amplitude of the current correlation function has the same form as predicted by the gauge-gravity duality. We also compare finite temperature results for the charge susceptibility in the large

N

limit with the result predicted by the gauge-gravity duality. Our results suggest that condensed matter systems at quantum criticality may provide interesting quantitative tests of the gauge-gravity duality even in the absence of supersymmetry.