Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Domain Wall Holography for Finite Temperature Scaling Solutions

Eric Perlmutter

TL;DR

This work identifies finite-temperature, charged scaling solutions in a bulk Einstein-Maxwell-scalar theory with exponential couplings and shows how these IR geometries, which possess zero extremal entropy, can be consistently glued to UV domain-wall vacua via domain-wall holography. By transforming to the domain-wall conformal frame, the IR sector exhibits a generalized scale invariance related to Lifshitz physics despite lacking Einstein-frame scale invariance, and this structure is inherited from the domain-wall (DW) geometry. The authors construct a global interpolating solution numerically, demonstrating an IR generalized Lifshitz behavior that flows to a UV domain-wall AdS-like regime in the conformal frame, and they argue that DW holography provides a robust EFT-style holographic tool even when a UV AdS fixed point is present. They also discuss the broader applicability of domain-wall holography to theories with approximate domain-wall regions, outlining criteria for when this approach yields a faithful holographic map and connecting the construction to nonconformal D-branes and their generalized conformal structure.

Abstract

We investigate a class of near-extremal solutions of Einstein-Maxwell-scalar theory with electric charge and power law scaling, dual to charged IR phases of relativistic field theories at low temperature. These are exact solutions of theories with domain wall vacua; hence, we use nonconformal holography to relate the bulk and boundary theories. We numerically construct a global interpolating solution between the IR charged solutions and the UV domain wall vacua for arbitrary physical choices of Lagrangian parameters. By passing to a conformal frame in which the domain wall metric becomes that of AdS, we uncover a generalized scale invariance of the IR scaling solution, indicating a connection to the physics of Lifshitz fixed points. Finally, guided by effective field theoretic principles and the physics of nonconformal D-branes, we argue for the applicability of domain wall holography even in theories with AdS critical points, namely those theories for which a scalar potential is dominated by a single exponential term over a large range.

Domain Wall Holography for Finite Temperature Scaling Solutions

TL;DR

This work identifies finite-temperature, charged scaling solutions in a bulk Einstein-Maxwell-scalar theory with exponential couplings and shows how these IR geometries, which possess zero extremal entropy, can be consistently glued to UV domain-wall vacua via domain-wall holography. By transforming to the domain-wall conformal frame, the IR sector exhibits a generalized scale invariance related to Lifshitz physics despite lacking Einstein-frame scale invariance, and this structure is inherited from the domain-wall (DW) geometry. The authors construct a global interpolating solution numerically, demonstrating an IR generalized Lifshitz behavior that flows to a UV domain-wall AdS-like regime in the conformal frame, and they argue that DW holography provides a robust EFT-style holographic tool even when a UV AdS fixed point is present. They also discuss the broader applicability of domain-wall holography to theories with approximate domain-wall regions, outlining criteria for when this approach yields a faithful holographic map and connecting the construction to nonconformal D-branes and their generalized conformal structure.

Abstract

We investigate a class of near-extremal solutions of Einstein-Maxwell-scalar theory with electric charge and power law scaling, dual to charged IR phases of relativistic field theories at low temperature. These are exact solutions of theories with domain wall vacua; hence, we use nonconformal holography to relate the bulk and boundary theories. We numerically construct a global interpolating solution between the IR charged solutions and the UV domain wall vacua for arbitrary physical choices of Lagrangian parameters. By passing to a conformal frame in which the domain wall metric becomes that of AdS, we uncover a generalized scale invariance of the IR scaling solution, indicating a connection to the physics of Lifshitz fixed points. Finally, guided by effective field theoretic principles and the physics of nonconformal D-branes, we argue for the applicability of domain wall holography even in theories with AdS critical points, namely those theories for which a scalar potential is dominated by a single exponential term over a large range.

Paper Structure

This paper contains 12 sections, 109 equations, 2 figures.

Table of Contents

  1. Introduction and summary
  2. Construction of the action and scaling solution
  3. Extremal solution
  4. Near-extremal solution
  5. Domain walls
  6. Geometry
  7. Holography
  8. Numerical construction of interpolating solution
  9. Generalized scale invariance
  10. Domain wall holography and effective field theory
  11. Discussion and prospects
  12. Numerical study of finite temperature modified Lifshitz solution

Figures (2)

  • Figure 1: Behavior of fields in the interpolating solution. a. Upper: The metric component $V(r)=g_{ii}$, as well as the ratio $\frac{U(r)}{V(r)}=\frac{-g_{tt}}{g_{ii}}$, rescaled to fit on the same graph. The turnover in the slope of the former curve, and the flatness of the latter, indicate the domain wall asymptotics. b. Lower left: The field strength, multiplied by its asymptotic domain wall power of $r$. c. Lower right: The exponentiated scalar field, multiplied by its asymptotic domain wall power of $r$.
  • Figure 2: Low-temperature power law scaling of entropy density with temperature, including the coefficient. The entropy density displays true Lifshitz power law behavior as the IR asymptotics approach those of the zero temperature case. All quantities are dimensionless.