Effective Dilaton Potential in Linearized Gravity

TL;DR

This paper investigates the semiclassical generation of an effective potential for the dilaton in linearized gravity with matter, exploring implications for symmetry breaking and the physical behavior of the dilaton in different frames.

Contribution

It introduces a method to derive the dilaton potential via one-loop matter contributions and examines the resulting symmetry structure and potential for spontaneous symmetry breaking.

Findings

Effective potential for the dilaton is generated semiclassically.

The gauge fixing leads to volume-preserving diffeomorphism symmetry.

Spontaneous diffeomorphism symmetry breaking is a possibility.

Abstract

Considering the linearized gravity with matter fields, the effective potential of the ``conformal dilaton'' in the string frame is generated semiclassically by one-loop contribution of heavy matter fields. This in turn generates a nontrivial potential for the physical dilaton in the Einstein frame with the trace of the graviton in the Einstein frame gauged away. The remaining manifest local spacetime symmetry is only the volume preserving diffeomorphism symmetry. The consistency of this procedure is examined and the possibility of spontaneous diffeomorphism symmetry breaking is suggested.