Constraints on Non-Holomorphic correction in N=2 superspace

TL;DR

This paper investigates quantum corrections to four-derivative terms in N=2 supersymmetric Yang-Mills theory, revealing a splitting of corrections and extending non-renormalization theorems to mixed Coulomb-Higgs branches.

Contribution

It demonstrates the splitting of quantum corrections between hypermultiplets and vector multiplets and extends non-renormalization theorems to more general vacua.

Findings

Quantum correction splitting at four-derivative order.

Extension of non-renormalization theorem to mixed branches.

Validation of corrections despite hypermultiplet VEVs.

Abstract

We study quantum corrections on four derivative term of vector multiplets in ${\cal{N}}=2$ supersymmetric Yang-Mills theory. We first show splitting of quantum correction on gauge neutral hypermultiplets from U(1) vector multiplets at four derivative order. We then revisit the non-renormalization theorem given by N. Seiberg and M. Dine and show the non-renormalization theorem in mixed (coulomb plus Higgs) branch even though gauge neutral hypermultiplet develops the vacuum expectation value.