Let's Twist Again: N=2 Super Yang Mills Theory Coupled To Matter

TL;DR

This paper presents the twisted formulation of N=2 Super Yang-Mills theory coupled to matter, detailing its quantum fields, symmetries, and algebraic structure, with implications for renormalization and non-renormalization theorems.

Contribution

It provides a comprehensive twisted version of N=2 SYM with matter, including quantum aspects and algebraic constraints, extending previous non-renormalization results.

Findings

Action expressed as a nilpotent variation

Extended Slavnov-Taylor identity established

Framework for algebraic renormalization developed

Abstract

We give the twisted version of N=2 Super Yang Mills theory coupled to matter, including quantum fields, supersymmetry transformations, action and algebraic structure. We show that the whole action, coupled to matter, can be written as the variation of a nilpotent operator, modulo field equations. An extended Slavnov-Taylor identity, collecting gauge symmetry and supersymmetry, is written, which allows to define the web of algebraic constraints, in view of the algebraic renormalization and of the extension of the non-renormalization theorems holding for N=2 SYM theory without matter.