Spontaneous Conformal Symmetry Breaking and Quantum Quadratic Gravity

TL;DR

This paper explores how conformal symmetry can be spontaneously broken in quadratic gravity, leading to mass generation for ghost fields and discussing conditions for unitarity in the quantum theory.

Contribution

It introduces a Higgs mechanism within quadratic gravity, demonstrating spontaneous conformal symmetry breaking and analyzing the resulting mass spectrum and unitarity conditions.

Findings

Conformal symmetry breaking can give mass to ghost fields.

A Higgs mechanism is possible in conformally invariant quadratic gravity.

Conditions for unitarity in the quantum theory are discussed.

Abstract

We investigate several quantum phenomena related to quadratic gravity after rewriting the general fourth-order action in a more convenient form that is second-order in derivatives and produces only first-class constraints in phase space. We find that a Higgs mechanism may occur in the conformally invariant subset of the general quadratic action if the theory is conformally coupled to a scalar field that acquires a non-zero vacuum expectation value and spontaneously breaks the conformal symmetry. Then, in the broken phase, the originally massless spin-2 ghost may absorb both the scalar and vector fields to become massive. We also perform a BRST quantization of second-order quadratic gravity in the covariant operator formalism and discuss conditions under which unitarity of the full interacting quantum theory may be established.