Torsion and the Gravity Dual of Parity Symmetry Breaking in AdS4/CFT3 Holography

TL;DR

This paper explores a gravity model with torsion in AdS4, finding an exact solution called the torsion vortex that models a transition between parity-breaking vacua and draws an analogy with superconducting vortices.

Contribution

It introduces the torsion vortex solution in AdS4 gravity with torsion and proposes its holographic dual as a domain wall between distinct parity-breaking vacua.

Findings

The torsion vortex solution supports two asymptotic AdS4 regimes.

It models a transition between different parity-breaking vacua.

Analogy with Abrikosov vortices in superconductors.

Abstract

We study four dimensional gravity with a negative cosmological constant deformed by the Nieh-Yan torsional topological invariant with a spacetime-dependent coefficient. We find an exact solution of the Euclidean system, which we call the torsion vortex, having two asymptotic AdS4 regimes supported by a pseudoscalar with a kink profile. We propose that the torsion vortex is the holographic dual of a three dimensional system that exhibits distinct parity breaking vacua. The torsion vortex represents a (holographic) transition between these distinct vacua. We expect that from the boundary point of view, the torsion vortex represents a `domain wall' between the two distinct vacua. From a bulk point of view, we point out an intriguing identification of the parameters of the torsion vortex with those of an Abrikosov vortex in a Type I superconductor. Following the analogy, we find that external Kalb-Ramond flux then appears to support bubbles of flat spacetime within an asymptotically AdS geometry.