One-loop divergences in the Galileon model

TL;DR

This paper calculates the one-loop UV divergences in the flat-space Galileon model using Schwinger-DeWitt and Feynman diagram techniques, revealing the need for a $ox^4$ term and implications for superrenormalizability and ghost states.

Contribution

It provides the first detailed one-loop divergence analysis of the Galileon model, highlighting the UV completion and potential for superrenormalizability with ghost states.

Findings

UV divergences include a $ox^4$ term in the effective action.

The theory can be modified to be superrenormalizable but introduces ghosts.

Non-renormalization theorem remains valid at low energies.

Abstract

The investigation of UV divergences is a relevant step in better understanding of a new theory. In this work the one-loop divergences in the free field sector are obtained for the popular Galileons model. The calculations are performed by the generalized Schwinger-DeWitt technique and also by means of Feynman diagrams. The first method can be directly generalized to curved space, but here we deal only with the flat-space limit. We show that the UV completion of the theory includes the $\pi \Box^4\pi$ term. According to our previous analysis in the case of quantum gravity, this means that the theory can be modified to become superrenormalizable, but then its physical spectrum includes two massive ghosts and one massive scalar with positive kinetic energy. The effective approach in this theory can be perfectly successful, exactly as in the higher derivative quantum gravity, and in this case the non-renormalization theorem for Galileons remains valid in the low-energy region.