Higgs Mechanism for New Massive Gravity and Weyl Invariant Extensions of Higher Derivative Theories

TL;DR

This paper develops a Weyl invariant extension of New Massive Gravity, demonstrating a Higgs-like mechanism for graviton mass generation and analyzing symmetry breaking via quantum corrections in various backgrounds.

Contribution

It introduces a Weyl invariant formulation of New Massive Gravity and explores symmetry breaking mechanisms, including spontaneous and radiative breaking, in different spacetime backgrounds.

Findings

Weyl invariant version of New Massive Gravity constructed.

Graviton acquires mass through a Higgs-like mechanism when Weyl symmetry breaks.

Radiative corrections can break Weyl symmetry in flat backgrounds.

Abstract

New Massive Gravity provides a non-linear extension of the Fierz-Pauli mass for gravitons in 2+1 dimensions. Here we construct a Weyl invariant version of this theory. When the Weyl symmetry is broken, the graviton gets a mass in analogy with the Higgs mechanism. In (anti)-de Sitter backgrounds, the symmetry can be broken spontaneously, but in flat backgrounds radiative corrections, at the two loop level, break the Weyl symmetry a la Coleman-Weinberg mechanism. We also construct the Weyl invariant extensions of some other higher derivative models, such as the Gauss-Bonnet theory (which reduces to the Maxwell theory in three dimensions) and the Born-Infeld type gravities.