Localisation with on-shell supersymmetry algebras via the Batalin-Vilkovisky formalism: Localisation as gauge fixing

TL;DR

This paper presents a novel perspective on localization in quantum field theories using the Batalin-Vilkovisky formalism, enabling on-shell supersymmetric localization without auxiliary fields, and unifying gauge fixing and localization as a single operation.

Contribution

It introduces a unified approach to localization and gauge fixing within the BV formalism, allowing on-shell supersymmetric localization with only on-shell supermultiplets.

Findings

First examples of on-shell localization for quantum field theories.

Localization and gauge fixing are unified as a single operation.

Supersymmetric localization achieved without auxiliary fields.

Abstract

The Batalin-Vilkovisky formalism provides a powerful technique to deal with gauge and global (super)symmetries that may only hold on shell. We argue that, since global (super)symmetries and gauge symmetries appear on an equal footing in the Batalin-Vilkovisky formalism, similarly localisation with respect to global (super)symmetries appears on an equal footing with gauge fixing of gauge symmetries; in general, when the gauge-fixing condition is not invariant under the global symmetries, localisation (with respect to a localising fermion) and gauge fixing (with respect to a gauge-fixing fermion) combine into a single operation. Furthermore, this perspective enables supersymmetric localisation using only on-shell supermultiplets, dispensing with auxiliary fields, extending an insight first discovered by Losev and Lysov arXiv:2312.13999. We provide the first examples of on-shell localisation for quantum field theories (together with a companion paper by Arvanitakis arXiv:2511.00144).