Dilaton: Saving Conformal Symmetry

TL;DR

This paper develops a method to maintain a massless dilaton, the Goldstone boson of spontaneously broken conformal symmetry, in quantum theories without gravitational anomalies, ensuring consistent coupling and quantum corrections.

Contribution

It introduces an approach that preserves a massless dilaton at all orders in perturbation theory for anomaly-free systems, enabling consistent conformal symmetry breaking.

Findings

Dilaton remains massless at all perturbative orders.

The method applies to systems without gravitational anomalies.

Provides a framework for spontaneous conformal symmetry breaking.

Abstract

The characteristic feature of the spontaneous symmetry breaking is the presence of the Goldstone mode(s). For the conformal symmetry broken spontaneously the corresponding Goldstone boson is the dilaton. Coupling an arbitrary system to the dilaton in a consistent (with quantum corrections) way has certain difficulties due to the trace anomaly. In this paper we present the approach allowing for an arbitrary system without the gravitational anomaly to keep the dilaton massless at all orders in perturbation theory, i.e. to build a theory with conformal symmetry broken spontaneously.