Super Background Field Method for N=2 SYM

TL;DR

This paper develops a systematic background field method within the BV formalism for N=2 Super-Yang-Mills theory, simplifying multiloop calculations and aiding in the identification of observables, with potential applications to the MSSM.

Contribution

It introduces a novel construction of the background field method for N=2 SYM in the BV formalism, including background transformations and gauge fixing via canonical transformations.

Findings

Derived the BFM for N=2 SYM in Wess-Zumino gauge.

Established linear Ward-Takahashi identities for background invariance.

Facilitated the identification of observables through equivariant cohomology.

Abstract

The implementation of the Background Field Method (BFM) for quantum field theories is analysed within the Batalin-Vilkovisky (BV) formalism. We provide a systematic way of constructing general splittings of the fields into classical and quantum parts, such that the background transformations of the quantum fields are linear in the quantum variables. This leads to linear Ward-Takahashi identities for the background invariance and to great simplifications in multiloop computations. In addition, the gauge fixing is obtained by means of (anti)canonical transformations generated by the gauge-fixing fermion. Within this framework we derive the BFM for the N=2 Super-Yang-Mills theory in the Wess-Zumino gauge viewed as the twisted version of Donaldson-Witten topological gauge theory. We obtain the background transformations for the full BRST differential of N=2 Super-Yang-Mills (including gauge transformations, SUSY transformations and translations). The BFM permits all observables of the supersymmetric theory to be identified easily by computing the equivariant cohomology of the topological theory. These results should be regarded as a step towards the construction of a super BFM for the Minimal Supersymmetric Standard Model.