Superconformal invariance from N=2 supersymmetry Ward identities

TL;DR

This paper proves that N=2 supersymmetric gauge theories with a vanishing one-loop beta function have no higher-order corrections to the beta function or anomalous dimensions, confirming superconformal invariance through algebraic methods.

Contribution

It extends the algebraic proof of beta function cancellation from N=4 to N=2 supersymmetric gauge theories using Slavnov-Taylor identities.

Findings

Beta function cancels at all perturbation orders.

Anomalous dimensions of BPS operators vanish at all orders.

Confirms superconformal invariance in N=2 theories.

Abstract

We algebraically prove the cancellation of the beta function at all order of perturbation theory of N=2 supersymmetric gauge theories with a vanishing one-loop beta function. The proof generalises that recently given for the N=4 case. It uses the consistent Slavnov-Taylor identities of the shadow dependent formulation. We also demonstrate the cancellation at all orders of the anomalous dimensions of vector and hypermultiplet one half BPS operators.