One-loop corrections to vector Galileon theory

TL;DR

This paper calculates one-loop quantum corrections in vector Galileon theory, revealing that unlike scalar Galileons, the vector version's propagator is renormalized, affecting its mass and generating new terms.

Contribution

It provides the first detailed one-loop analysis of vector Galileon interactions, showing their renormalization properties and deriving explicit counterterms.

Findings

The vector Galileon propagator is renormalized at one-loop.

Divergences are removed using dimensional regularization.

Finite corrections modify the propagator and generate new terms.

Abstract

The effective action of the recently proposed vector Galileon theory is considered. Using the background field method, we obtain the one-loop correction to the propagator of the Proca field from vector Galileon self-interactions. Contrary to the so-called scalar Galileon interactions, the two-point function of the vector field gets renormalized at the one-loop level, indicating that there is no non-renormalization theorem in the vector Galileon theory. Using dimensional regularization, we remove the divergences and obtain the counterterms of the theory. The finite term is analytically calculated, which modifies the propagator and the mass term and generates some new terms also.