Medium Generated Gap in Gravity and a 3d Gauge Theory

TL;DR

This paper explores how a medium that breaks Lorentz symmetry induces a mass gap in gravity, and demonstrates that in 3D, gravity can be described as a massive Chern-Simons gauge theory with ghost-free properties.

Contribution

It introduces a novel approach to modeling massive gravity in 3D as a Chern-Simons gauge theory with an unusual mass term that avoids ghosts and tachyons.

Findings

Mass gap in gravity due to Lorentz-breaking medium.

Reformulation of 3D gravity as a massive Chern-Simons theory.

Novel gauge invariance in flat space Chern-Simons theory.

Abstract

It is well known that a physical medium that sets a Lorentz frame generates a Lorentz-breaking gap for a graviton. We examine such generated "mass" terms in the presence of a fluid medium whose ground state spontaneously breaks spatial translation invariance in $d = D+1$ spacetime dimensions, and for a solid in $D = 2$ spatial dimensions. By requiring energy positivity and subluminal propagation, certain constraints are placed on the equation of state of the medium. In the case of $D = 2$ spatial dimensions, classical gravity can be recast as a Chern-Simons gauge theory and motivated by this we recast the massive theory of gravity in AdS$_3$ as a massive Chern-Simons gauge theory with an unusual mass term. We find that in the flat space limit the Chern-Simons theory has a novel gauge invariance that mixes the kinetic and mass terms, and enables the massive theory with a non-compact internal group to be free of ghosts and tachyons.