On infrared problems of effective Lagrangians of massive spin 2 fields coupled to gauge fields

TL;DR

This paper investigates the infrared issues in effective Lagrangians for massive spin-2 fields coupled to gauge fields, revealing gauge fixing ambiguities similar to Gribov problems, with implications for theoretical consistency.

Contribution

It identifies and analyzes the gauge fixing ambiguities in massive spin-2 field theories, proposing a potential approach to mitigate these issues.

Findings

Infrared problems and gauge fixing ambiguities are present in the theory.

Vacuum copies can be explicitly found on a four-dimensional torus.

Large gauge potentials are necessary for the emergence of gauge copies.

Abstract

In this paper we analyze the interactions of a massive spin-2 particles charged under both Abelian and non-Abelian group using the Porrati-Rahman Lagrangian. This theory is valid up to an intrinsic cutoff scale. Phenomenologically a theory valid up to a cutoff scale is sensible as all known higher spin particles are non-fundamental and it is shown that indeed this action can be used to estimate some relevant cross section. Such action necessarily includes Stuckelberg field and therefore it is necessary to fix the corresponding gauge symmetry. We show that this theory, when the Stuckelberg symmetry is gauge-fixed, possesses a non-trivial infrared problem. A gauge fixing ambiguity arises which is akin to the Gribov problem in QCD in the Abelian case as well. In some cases (such as when the space-time is the four-dimensional torus) the vacuum copies can be found analytically. A similar phenomenon also appears in the case of Proca fields. A very interesting feature of these copies is that they arise only for "large enough" gauge potentials. This opens the possibility to avoid the appearance of such gauge fixing ambiguities by using a Gribov-Zwanziger like approach.