On the Relation Between the Holomorphic Prepotential and the Quantum Moduli in SUSY Gauge Theories

TL;DR

This paper proves a fundamental relation connecting the holomorphic prepotential and quantum moduli in N=2 supersymmetric gauge theories, extending the understanding to various gauge groups and massive hypermultiplets.

Contribution

It provides a simple proof of a key relation in N=2 SUSY QCD and explores its generalizations to theories with massive hypermultiplets and N=1 models.

Findings

Established a proof of the prepotential-moduli relation for various gauge groups.

Extended the relation to theories with massive hypermultiplets.

Discussed generalizations to N=1 supersymmetric models.

Abstract

We give a simple proof of the relation $\Lambda\p_artial{\Lambda}\F= {i\over2\pi}b_1\langle\Tr\phi^2\rangle$, which is valid for $N=2$ supersymmetric QCD with massless quarks. We consider $SU(N_c)$ gauge theories as well as $SO(N_c)$ and $SP(N_c)$. Aa analogous relation which corresponds to massive hypermultiplets is written down. We also discuss the generalizations to $N=1$ models in the Coulomb phase.