Ward Identities for N=2 Rigid and Local Supersymmetry in Euclidean Space

TL;DR

This paper derives and verifies Ward identities for N=2 supersymmetric theories in Euclidean space using the Batalin-Vilkovisky formalism, highlighting the role of specific field pairs in supergravity.

Contribution

It provides explicit construction and verification of BRST Ward identities for N=2 super Yang-Mills and supergravity in Euclidean space without auxiliary fields, employing the BV formalism.

Findings

Verified Ward identities through Feynman diagram calculations

Identified necessary field pairs for supergravity gauge fixing

Extended formalism to include Nielsen-Kallosh ghosts

Abstract

We construct and check by explicit Feynman diagram calculations the BRST Ward identities for N=2 rigid super Yang-Mills theory and N=2 extended supergravity in four-dimensional Euclidean space without auxiliary fields. We use the Batalin-Vilkovisky formalism. In the supergravity case we need one new contractible pair of complex spinor fields to obtain the usual gauge-fixing term and corresponding Nielsen-Kallosh ghosts.