Quantum corrections to the generalized Proca theory via a matter field

TL;DR

This paper investigates quantum corrections in the generalized Proca theory caused by matter loops, finding nonlinear interactions are safe while linear ones introduce ghosts, and determines the energy scale where the theory remains consistent.

Contribution

It analyzes quantum corrections in the generalized Proca theory with matter loops, highlighting the effects of linear and nonlinear interactions and establishing the theory's valid energy range.

Findings

Nonlinear matter-vector interactions are harmless and only renormalize the theory.

Linear interactions introduce ghost degrees of freedom.

The theory remains healthy up to a specific energy scale.

Abstract

We study the quantum corrections to the generalized Proca theory via matter loops. We consider two types of interactions, linear and nonlinear in the vector field. Calculating the one-loop correction to the vector field propagator, three- and four-point functions, we show that the non-linear interactions are harmless, although they renormalize the theory. The linear matter-vector field interactions introduce ghost degrees of freedom to the generalized Proca theory. Treating the theory as an effective theory, we calculate the energy scale up to which the theory remains healthy.