Deformations of global symmetries in the extended antifield formalism

TL;DR

This paper explores how to classify and construct deformations of global symmetries in field theories using cohomological methods within the extended antifield formalism, including applications to supersymmetry and BRST-invariant models.

Contribution

It introduces a cohomological framework for deforming and extending global symmetries, with specific focus on subsets of symmetries and their algebraic structures.

Findings

Deformations can lead to nontrivial extensions of symmetry algebras.

Application to a D=4, N=2 supersymmetric model shows emergence of central charges.

Discussion of deformations in gauge-fixed actions, exemplified by the Curci-Ferrari model.

Abstract

It is outlined how deformations of field theoretical rigid symmetries can be constructed and classified by cohomological means in the extended antifield formalism. Special attention is devoted to deformations referring only to a subset of the rigid symmetries of a given model and leading to a nontrivial extension of the graded Lie algebra associated with that subset. The method is illustrated for a D=4, N=2 supersymmetric model where the central extension of the supersymmetry algebra emerges via a deformation. Deformations of gauge fixed actions with a BRST symmetry are discussed too and illustrated by the Curci-Ferrari model.