One-loop divergences in massive gravity theory

TL;DR

This paper computes the one-loop divergences in a ghost-free massive gravity theory involving metric and external tensor fields, revealing that quantum corrections produce counterterms differing from the classical action and forming a power series in the tensor field.

Contribution

It provides the first calculation of one-loop divergences in a ghost-free massive gravity model with auxiliary fields, highlighting quantum corrections' structure.

Findings

Counterterms differ from the classical action.

Quantum corrections form a power series in the external tensor field.

The non-polynomial structure is simplified using auxiliary fields.

Abstract

The one-loop divergences are calculated for the recently proposed ghost-free version of massive gravity, where the action depends on both metric and external tensor field f. The non-polynomial structure of the massive term is reduced to a more standard form by means of auxiliary tensor field, which is settled on-shell after quantum calculations are performed. As one should expect, the counterterms do not reproduce the form of the classical action. Moreover, the result has the form of the power series in f.