Non-holomorphic terms in N=2 SUSY Wilsonian actions and RG equation

TL;DR

This paper investigates non-holomorphic corrections in N=2 supersymmetric gauge theories, deriving a non-perturbative RG equation for these terms and computing instanton contributions to validate the proposed Ansatz.

Contribution

It introduces a non-perturbative RG equation for non-holomorphic terms in N=2 theories and computes instanton effects to test the Ansatz's validity.

Findings

Derived a fully non-perturbative RG equation for K(Psi,Psi)

Computed instanton contributions for winding numbers 1 and 2

Confirmed a non-renormalisation theorem for N_F=4

Abstract

In this paper we first investigate the Ansatz of one of the present authors for K(\Psi,\bar\Psi), the adimensional modular invariant non-holomorphic correction to the Wilsonian effective Lagrangian of an N=2 globally supersymmetric gauge theory. The renormalisation group beta-function of the theory crucially allows us to express K(\Psi,\bar\Psi) in a form that easily generalises to the case in which the theory is coupled to N_F hypermultiplets in the fundamental representation of the gauge group. This function satisfies an equation which should be viewed as a fully non-perturbative ``non-chiral superconformal Ward identity". We also determine its renormalisation group equation. Furthermore, as a first step towards checking the validity of this Ansatz, we compute the contribution to K(\Psi,\bar\Psi) from instantons of winding number k=1 and k=2. As a by-product of our analysis we check a non-renormalisation theorem for N_F=4.