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.
Highlights
The cohomological antifield method goes one step further as it unifies into a purely algebraic framework the problems of deforming consistently both the gauge symmetry and the action functional of a theory
In this paper we have initiated the study of the consistent deformations of massive field theories using the BRST-BV formalism as a tool
Such theories do not possess any gauge invariance in their usual parametrizations, it is well known that gauge symmetries can be straightforwardly introduced via the Stueckelberg procedure
Summary
The cohomological reformulation of the deformation procedure exposed in [5] was proposed in [6]. For concreteness we will take both the fields φi and the gauge parameters α to be bosonic, thereby excluding the discussion of supergravity theories, the general case can be treated in much the same way modulo some obvious changes, see for example the pedagogical review [55]. In this situation the ghost antifields are Grassmann-even or commuting variables as well, while the ghosts Cα and antifields φ∗i are Grassmann-odd or anticommuting. The formalism is not restricted to this case, since for instance one can apply it to known models which are themselves already interacting, see for example [17, 18] for recent analyses
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