Dilaton: Saving Conformal Symmetry

TL;DR

The paper addresses whether conformal symmetry can survive quantum corrections when mass scales are present. It proposes coupling a dilaton field $X$ and using a conformally invariant regulator within dimensional regularization, enabling scales to originate from the dilaton vev $X\to v$ and preserving Weyl symmetry; the analysis requires the theory to be free of gravitational (Diff) anomalies. A general iterative argument shows that the pole part of the effective action can be made conformally invariant at each order, allowing conformally invariant counterterms to-renormalize the theory in a symmetry-preserving way. The authors illustrate the approach with two toy models in 4D and 8D, demonstrating that while conformal invariance can be maintained, the resulting theories acquire an infinite set of conformally invariant counterterms (including higher-derivative ones), signaling non-renormalizability but offering a consistent framework for quantum conformal symmetry with spontaneous breaking via the dilaton.

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.

Figures (1)

• Figure 1: One and two loop UV divergent topologies and their leading divergence.