Deformations of vector-scalar models

TL;DR

This paper systematically classifies consistent deformations of vector-scalar models with non-minimal couplings, using algebraic methods and BRST cohomology, with implications for supergravity gaugings.

Contribution

It provides a comprehensive algebraic framework for identifying all possible gaugings of vector-scalar models, including higher-order constraints, extending previous approaches.

Findings

Explicit parametrization of BRST cohomology classes

Identification of global symmetries and Noether currents

Analysis of linear and quadratic consistency constraints

Abstract

Abelian vector fields non-minimally coupled to uncharged scalar fields arise in many contexts. We investigate here through algebraic methods their consistent deformations ("gaugings"), i.e., the deformations that preserve the number (but not necessarily the form or the algebra) of the gauge symmetries. Infinitesimal consistent deformations are given by the BRST cohomology classes at ghost number zero. We parametrize explicitly these classes in terms of various types of global symmetries and corresponding Noether currents through the characteristic cohomology related to antifields and equations of motion. The analysis applies to all ghost numbers and not just ghost number zero. We also provide a systematic discussion of the linear and quadratic constraints on these parameters that follow from higher-order consistency. Our work is relevant to the gaugings of extended supergravities.