Confining Phase Superpotentials for SO/Sp Gauge Theories via Geometric Transition

TL;DR

This paper explores the duality between large N gauge theories and geometric transitions, specifically analyzing confining superpotentials for SO/Sp gauge theories with classical quartic superpotentials, showing precise agreement up to the 4th order.

Contribution

It provides an exact analysis of confining phase superpotentials for SO/Sp gauge theories with classical superpotentials using geometric transition and Seiberg-Witten theory.

Findings

Exact agreement of superpotentials up to 4th order for SO(6), SO(8), and Sp(4) gauge theories.

Demonstrates the duality between gauge theories and geometric transitions for specific classical superpotentials.

Abstract

We examine a large N duality via geometric transition for N=1 SO/Sp gauge theories with superpotential for adjoint chiral superfield. In this paper, we find that the large N gauge theories are exactly analyzed for the classical quartic superpotentials by the finite rank SO/Sp gauge theories. With this classical superpotentials, we evaluate the confining phase superpotentials using the Seiberg-Witten theory. In the dual theory, we calculate the superpotential generated by the R-R and NS-NS 3-form fluxes. As the non-trivial examples, we discuss for SO(6), SO(8) and Sp(4) gauge theories. In these cases we have the perfect agreement of the confining phase superpotentials up to the 4th order of the glueball superfields.