Holography for the practical person

Langley, Brandon W.

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https://hdl.handle.net/2142/104841 Copy

Description

Title

Holography for the practical person

Author(s)

Langley, Brandon W.

Issue Date

2019-04-17

Director of Research (if dissertation) or Advisor (if thesis)

Phillips, Philip W.

Doctoral Committee Chair(s)

Faulkner, Thomas

Committee Member(s)

• Abbamonte, Peter
• Cooper, Lance

Department of Study

Physics

Discipline

Physics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• holography
• condensed matter
• AdS/CFT
• gauge/gravity
• Lifshitz
• diffusion
• transport
• conductivity
• general relativity
• duality

Abstract

"This article opens with a pedagogical discussion of holography aimed at calculating the thermodynamics and transport coefficients in condensed matter systems. Therein, we will discuss the duality of thermodynamics to classical field theory, construct the associated dual action at the field theory's boundary, and divulge the numerical techniques of the Einstein-DeTurck equations. The latter allows a numerical treatment of linear response theory in highly nontrivial gravitational backgrounds. We will use these techniques in the analysis of two major problems. In the first, we will discuss the specific implementation of the numerical methodology in the exploration of holographic lattices. Particularly, we construct generalizations of AdS-Reissner-Nordstr\""om that interpolate between those used in two previous studies --- one that reports power-law scaling for the mid-frequency regime of the optical conductivity and one that does not. We find no evidence for power-law scaling of the conductivity, thereby corroborating the previous negative result that gravitational crystals are insufficient to generate the power-law mid-infrared conductivity observed in cuprate superconductors. In the second problem, we present the full charge and energy diffusion coefficients for the Einstein-Maxwell dilaton (EMD) action for Lifshitz spacetime characterized by a dynamical critical exponent $z$. We compute the fully renormalized static Lifshitz thermodynamic potential explicitly, which confirms the forms of all thermodynamic quantities including the Bekenstein-Hawking and Smarr-like relationships. For transport, we target our analysis at finite chemical potential and include axion fields to generate momentum dissipation. Beyond analysis of the bounds, we find deviation from universal transport obtains when either the chemical potential or momentum dissipation are large relative to temperature, an echo of strong thermoelectric interactions. We also find that regardless of what is diffusing, energy or charge, the diffusion constant is independent of matter content when $z=2$. This state of affairs obtains because the diffusion equation is scale invariant when $z=2$."

Graduation Semester

2019-05

Type of Resource

text

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http://hdl.handle.net/2142/104841

Copyright and License Information

Copyright 2019 by Brandon W. Langley. All rights reserved.

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