Loop Corrected Supercharges from Holomorphic Anomalies

TL;DR

This paper develops a formalism to compute one-loop corrections to supercharges in supersymmetric gauge theories using holomorphic twists and $L_ ablafty$ algebras, providing explicit results for theories like $ abla=4$ SYM.

Contribution

It introduces a novel approach linking supercharge corrections to BRST anomalies via $L_ ablafty$ structures, enabling explicit one-loop calculations in supersymmetric theories.

Findings

Derived complete one-loop supercharge corrections for 4D supersymmetric gauge theories.

Connected supercharge corrections to the holomorphic twist and Konishi anomaly.

Presented compact superfield expressions for $ abla=4$ SYM supercharges.

Abstract

We describe the loop corrections to supercharges in supersymmetric quantum field theories using the holomorphic twist formalism. We begin by reviewing the relation between supercharge corrections and the "twice-generalized" Konishi anomaly, which corrects the semi-chiral ring. In the holomorphic twist, these corrections appear as BRST anomalies and are computed using the higher operations of an underlying $L_\infty$ conformal algebra. We then apply this formalism to obtain the complete one-loop corrections to the supercharge of four-dimensional Lagrangian supersymmetric gauge theories, including $\mathcal{N}=4$ SYM, where it admits a remarkably compact expression in terms of superfields.