Holomorphic Effective Action of N=2 SYM Theory from Harmonic Superspace with Central Charges

TL;DR

This paper calculates the one-loop holomorphic effective action in N=2 supersymmetric Yang-Mills theory using harmonic superspace techniques, revealing its dependence on central charges and its relation to Seiberg's action.

Contribution

It introduces a method to compute the holomorphic effective action in N=2 SYM with central charges using harmonic superspace diagram techniques, extending previous approaches.

Findings

The holomorphic effective action is proportional to central charges.

It reproduces Seiberg's action from U(1) R-anomaly integration.

The action vanishes for N=4 SYM theory.

Abstract

We compute the one-loop holomorphic effective action of the massless Cartan sector of N=2 SYM theory in the Coulomb branch, taking into account the contributions both from the charged hypermultiplets and off-diagonal components of the gauge superfield. We use the manifestly supersymmetric harmonic superfields diagram techniques adapted to N=2 supersymmetry with the central charges induced by Cartan generators. The (anti)holomorphic part proves to be proportional to the central charges and it has the generic form of Seiberg's action obtained by integrating U(1) R-anomaly. It vanishes for N=4 SYM theory, i.e. the coupled system of N=2 gauge superfield and hypermultiplet in the adjoint representation.