Entanglement and Excitations in Gauge/Gravity Duality

Abstract

In this thesis, we study a variety of phenomena in strongly coupled quantum field theories by performing calculations in their gravitational duals. We compute entanglement entropy in a variety of holographic systems, paying particular attention to its long-distance behaviour, characterised by a term proportional to surface area. This term is known to decrease along Lorentz-invariant renormalisation group flows, suggesting that it may count massless degrees of freedom. We find that more general deformations may increase this area term, possibly indicating an enhanced number of long-distance degrees of freedom. We observe a correlation between this enhancement and the emergence of new scaling symmetry at long distances. Next, we study the spectrum of collective excitations in a holographic model of a non-Fermi liquid. At high temperatures, the spectrum of collective excitations includes hydrodynamic sound waves. As in similar models, we observe that sound-like modes also exist at low temperatures. Such modes are known as holographic zero sound. We study the changing properties of holographic zero sound and the emergence of hydrodynamic behaviour at high temperatures as we vary the parameters of the model. We find that for certain values of the parameters, the temperature-dependence of holographic zero sound qualitatively resembles that of a normal Fermi liquid. Finally, we study the entanglement entropy contribution of surface defects in a six-dimensional quantum field theory of relevance to M-theory, which is a candidate theory of quantum gravity. We find that the entanglement entropy does not montonically decrease along renormalisation group flows on these defects, ruling it out as a potential measure of degrees of freedom. On the other hand, we find that two of the contributions of the defect to the Weyl anomaly of the quantum field theory decrease along all of the flows that we study.

PhD thesis, 185 pages

References in corpus (36)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Towards a derivation of holographic entanglement entropy
• Minkowski-space correlators in AdS/CFT correspondence: recipe and applications
• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• Ab-initio Determination of Light Hadron Masses
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Schwinger-Keldysh Propagators from AdS/CFT Correspondence
• Entanglement as a Probe of Confinement
• Causality & holographic entanglement entropy
• Seeing a c-theorem with holography
• A holographic proof of the strong subadditivity of entanglement entropy
• Thermodynamical Property of Entanglement Entropy for Excited States
• Entanglement Entropy, Trace Anomalies and Holography
• Topological order in a 3D toric code at finite temperature
• Zero Sound from Holography
• 1/2-BPS states in M theory and defects in the dual CFTs
• The Shear Viscosity to Entropy Density Ratio of Trapped Fermions in the Unitarity Limit
• Shear Modes, Criticality and Extremal Black Holes
• Holographic Responses of Fermion Matter
• Quasinormal spectrum and the black hole membrane paradigm
• M5-branes and Wilson Surfaces
• Comments on Fermi Liquid from Holography
• Entanglement density and gravitational thermodynamics
• Fluctuations and instabilities of a holographic metal
• Zero Sound in Strange Metallic Holography
• Conductivity of weakly disordered strange metals: from conformal to hyperscaling-violating regimes
• Origin of the Drude peak and of zero sound in probe brane holography
• Boundary F-maximization
• BPS Soliton Solutions of a D3-brane Action
• The Self-dual String Soliton in AdS_4\times S^7 spacetime
• Holographic torus entanglement and its RG flow
• On Holographic Entanglement Density
• Probing $\eta$ deformed backgrounds with $Dp$ branes