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

TL;DR

This paper constructs new asymptotically AdS solutions with S^2 x S^1 boundary, revealing a quantum phase transition in the dual gauge theory as the S^1 radius varies, and proposes a new positive energy conjecture.

Contribution

It introduces novel static AdS solutions with S^2 x S^1 boundary and analyzes their phase structure, including a quantum phase transition and a positive energy conjecture.

Findings

Existence of multiple solution families with different S^1 topologies.

Identification of a quantum phase transition as S^1 radius decreases.

Proposal that the lowest mass solution minimizes energy among all boundary conditions.

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.