Noether's variational theorem II and the BV formalism

TL;DR

This paper revisits Noether's Second Theorem within the Lagrangian framework, illustrating its application through the Cattaneo-Felder sigma model and connecting it to the Batalin-Vilkovisky formalism.

Contribution

It modernizes the presentation of Noether's Second Theorem and explicitly demonstrates its relation to the BV formalism using a specific sigma model example.

Findings

Explicit derivation of Noether identities for the Cattaneo-Felder sigma model

Demonstration of how anti-ghosts encode Noether identities in BV formalism

Clarification of the connection between symmetries and the BV anti-bracket structure

Abstract

We review the basics of the Lagrangian approach to field theory and recast Noether's Second Theorem formulated in her language of dependencies using a slight modernization of terminology and notation. We then present the Cattaneo-Felder sigma model and work out the Noether identities or dependencies for this model. We review the description of the Batalin-Vilkovisky formalism and show explicitly how the anti-ghosts encode the Noether identities in this example.