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.
Highlights
Our paper is devoted to a systematic study of the consistent deformations of the gauge invariant actions of the formS0[AIμ, φi] = d4x L0, (1.1)depending on ns uncharged scalar fields φi and nv abelian vector fields AIμ
After establishing general theorems on the BRST cohomology valid without assuming a specific form of the Lagrangian or the rigid symmetries, including the above classification of the deformations and useful triangular properties of their algebra, we turn to various models that have been considered in the literature, for which we completely compute the deformations of U and W -types
By applying the above method, one finds that the local BRST cohomology of the models of section 3.1 can be described along exactly the same lines as given below
Summary
Depending on ns uncharged scalar fields φi and nv abelian vector fields AIμ. We assume that the only gauge symmetries of (1.1) are the standard U(1) gauge transformations for each vector field, so that the gauge algebra is abelian and given by nv copies of u(1). One can investigate the question of gaugings by taking (1.1) as starting point of the deformation procedure, provided one allows the scalar field dependence in the vector piece of the Lagrangian to cover all possible choices of duality frame. It is this task which is carried out here. After establishing general theorems on the BRST cohomology valid without assuming a specific form of the Lagrangian or the rigid symmetries, including the above classification of the deformations and useful triangular properties of their algebra, we turn to various models that have been considered in the literature, for which we completely compute the deformations of U and W -types. Appendix C is devoted to the detailed analysis of the W -component of the commutator of two U -type transformations
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