Extended antifield-formalism

TL;DR

This paper extends the antifield formalism to include rigid symmetries and higher order conservation laws, revealing an algebraic structure and enabling systematic analysis of anomalies and deformations.

Contribution

It introduces global ghosts for all conservation laws, extending the master equation to incorporate higher order symmetries and their algebraic relations.

Findings

Higher order conservation laws define additional rigid symmetries.

The extended master equation captures gauge and rigid symmetries uniformly.

Independent Ward identities are derived for all symmetries.

Abstract

The antifield formalism is extended so as to incorporate the rigid symmetries of a given theory. To that end, it is necessary to introduce global ghosts not only for the given rigid symmetries, but also for all the higher order conservation laws, associated with conserved antisymmetric tensors. Otherwise, one may encounter obstructions of the type discussed in [13]. These higher order conservation laws are shown to define additional rigid symmetries of the master equation and to form -- together with the standard symmetries -- an interesting algebraic structure. They lead furthermore to independent Ward identities which are derived in the standard manner, because the resulting master ("Zinn-Justin") equation capturing both the gauge symmetries and the rigid symmetries of all orders takes a known form. Issues such as anomalies or consistent deformations of the action preserving some set of rigid symmetries can be also systematically analysed in this framework.