Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Gravity Dual of Gauge Theory on S^2 x S^1 x R

Keith Copsey, Gary T. Horowitz

TL;DR

This work addresses the gravity dual of a gauge theory on $S^2 × S^1 × R$ by numerically constructing static, asymptotically AdS solutions with that conformal boundary. The authors show the existence of a noncontractible S^1 family and, for small S^1, bubble solutions where the circle pinches off, indicating a quantum phase transition for antiperiodic fermions; they also formulate a positive energy conjecture stating that the lowest-energy static solution minimizes energy for fixed circle size. Extending the analysis, they generalize to time-symmetric initial data that yield a minimum-energy bubble consistent with the Casimir energy of the boundary theory and relate these geometries to the AdS soliton in a specific limit. A simple analytic continuation reveals AdS black strings with horizon topology S^2 × S^1, linking the high-temperature phase of the dual gauge theory to these new bulk solutions and supporting a lower-energy bound for asymptotically locally AdS spacetimes.

Abstract

We (numerically) construct new static, asymptotically AdS solutions where the conformal infinity is the product of time and S^2 x S^1. There always exist a family of solutions in which the S^1 is not contractible and, for small S^1, there are two additional families of solutions in which the S^1 smoothly pinches off. This shows that (when fermions are antiperiodic around the S^1) there is a quantum phase transition in the gauge theory as one decreases the radius of the S^1 relative to the S^2. We also compare the masses of our solutions and argue that the one with lowest mass should minimize the energy among all solutions with conformal boundary S^2 x S^1 x R. This provides a new positive energy conjecture for asymptotically locally AdS metrics. A simple analytic continuation produces AdS black holes with topology S^2 x S^1.

Gravity Dual of Gauge Theory on S^2 x S^1 x R

TL;DR

This work addresses the gravity dual of a gauge theory on by numerically constructing static, asymptotically AdS solutions with that conformal boundary. The authors show the existence of a noncontractible S^1 family and, for small S^1, bubble solutions where the circle pinches off, indicating a quantum phase transition for antiperiodic fermions; they also formulate a positive energy conjecture stating that the lowest-energy static solution minimizes energy for fixed circle size. Extending the analysis, they generalize to time-symmetric initial data that yield a minimum-energy bubble consistent with the Casimir energy of the boundary theory and relate these geometries to the AdS soliton in a specific limit. A simple analytic continuation reveals AdS black strings with horizon topology S^2 × S^1, linking the high-temperature phase of the dual gauge theory to these new bulk solutions and supporting a lower-energy bound for asymptotically locally AdS spacetimes.

Abstract

We (numerically) construct new static, asymptotically AdS solutions where the conformal infinity is the product of time and S^2 x S^1. There always exist a family of solutions in which the S^1 is not contractible and, for small S^1, there are two additional families of solutions in which the S^1 smoothly pinches off. This shows that (when fermions are antiperiodic around the S^1) there is a quantum phase transition in the gauge theory as one decreases the radius of the S^1 relative to the S^2. We also compare the masses of our solutions and argue that the one with lowest mass should minimize the energy among all solutions with conformal boundary S^2 x S^1 x R. This provides a new positive energy conjecture for asymptotically locally AdS metrics. A simple analytic continuation produces AdS black holes with topology S^2 x S^1.

Paper Structure

This paper contains 3 sections, 45 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Static solutions
  3. Generalizing the Witten AdS bubble

Figures (4)

  • Figure 1: $g_{\chi \chi}$ for $r_0 = l$ bubble (dashed line) and background (solid line)
  • Figure 2: $g_{rr}$ for $r_0 = l$ bubble (dashed line) and background (solid line)
  • Figure 3: $g_{tt}$ for $r_0 = l$ bubble (dashed line) and background (solid line)
  • Figure 4: Energy for solutions (\ref{['alphaconstr']}) (solid line) and static solution (dashed line) for $s = 1.021741$