Consistent deformations of free massive field theories in the Stueckelberg formulation

Abstract

Cohomological techniques within the Batalin-Vilkovisky (BV) extension of the Becchi-Rouet-Stora-Tyutin (BRST) formalism have proved invaluable for classifying consistent deformations of gauge theories. In this work we investigate the application of this idea to massive field theories in the Stueckelberg formulation. Starting with a collection of free massive vectors, we show that the cohomological method reproduces the cubic and quartic vertices of massive Yang-Mills theory. In the same way, taking a Fierz-Pauli graviton on a maximally symmetric space as the starting point, we are able to recover the consistent cubic vertices of nonlinear massive gravity. The formalism further sheds light on the characterization of Stueckelberg gauge theories, by demonstrating for instance that the gauge algebra of such models is necessarily Abelian and that they admit a Born-Infeld-like formulation in which the action is simply a combination of the gauge-invariant structures of the free theory.

General method for including Stueckelberg fields

“…One of the motivations for introducing the Stueckelberg fields is the idea to provide consistent inclusion of interactions by controlling compatibility of Stueckelberg gauge symmetry when the free theory is deformed. This idea works well in various examples, see [3] and references therein. However, it does not seem a consistent general scheme, as it controls just algebraic consistency of the Stueckelberg symmetry, not the number of propagating DoF's, while the artificial symmetry is not necessarily reasonably related to the structure of the dynamics.…”

“…In this article, the class of field theories is considered such that the action does not admit gauge symmetry 3 , while the Lagrangian equations are not involutive. The involutive closure ( 3) is non-Lagrangian as such, though it is equivalent to the original Lagrangian system (1).…”

“…In this gauge, the Stueckelberg theory reduces to the original one. This pattern of inclusion the Stueckelberg fields, sometimes referred to as the "Stueckelberg trick", is summarized and studied in very general form in the article [3] where one can also find a review of the vast contemporary literature on this topic.…”

Theory for multiple partially massless spin-2 fields

“…We refer the reader to the Section 2 of [27] and to [28] for pedagogical introductions. The case of deformations of massive theories was analyzed in the same framework in [29].…”

Gauged galileons

“…This is completely analogous to the treatment of massive field theories in the Stückelberg formulation, see e.g [48,49]…”