The Super-potential and Holomorphic properties of the MQCD

TL;DR

This paper investigates the holomorphic properties of MQCD, proposing a new superpotential definition that overcomes limitations of the traditional integral approach, and verifies its consistency across various gauge groups and quark configurations.

Contribution

It introduces a new superpotential formulation for MQCD that applies to brane configurations with 90-degree rotation, including true SQCD, and relates it to previous definitions.

Findings

The traditional superpotential integral is inadequate for generic quark configurations.

A new superpotential definition is proposed that does not require an auxiliary surface.

Explicit calculations confirm the new definition's consistency for SU(N), SO(N), Sp(N) groups.

Abstract

We study the holomorphic properties of the MQCD by comparing the super-potentials in MQCD and the gauge theory. First we show that the super-potential defined as an integral of three form is NOT appropriate for generic situation with quarks. We report a resolution of the problem which works for the brane configurations of 90 degree rotation, including the true SQCD. The new definition does not need auxiliary surface and can be reduced to a contour integral for some cases. We find relation beetween the new and old definitions, which is verified by explicit calculation for SU(N), SO(N), Sp(N) simple groups with $F$ of massive quarks.