Super Yang-Mills, Matrix Models and Geometric Transitions

TL;DR

This paper explores the connections between supersymmetric gauge theories, matrix models, and string theory geometric transitions, revealing insights into BPS states and a new method for summing planar diagrams via open/closed string duality.

Contribution

It introduces a geometric approach to sum planar diagrams exactly and demonstrates the interpolation between D-brane and closed string states in N=1 theories.

Findings

Interpolation between D-brane and closed string states with different tension scalings

A new geometric method for summing planar diagrams

Insights into N=1 quantum parameter spaces

Abstract

I explain two applications of the relationship between four dimensional N=1 supersymmetric gauge theories, zero dimensional gauged matrix models, and geometric transitions in string theory. The first is related to the spectrum of BPS domain walls or BPS branes. It is shown that one can smoothly interpolate between a D-brane state, whose weak coupling tension scales as Nc or 1/gs, and a closed string solitonic state, whose weak coupling tension scales as Nc^2 or 1/gs^2. This is part of a larger theory of N=1 quantum parameter spaces. The second is a new purely geometric approach to sum exactly over planar diagrams in zero dimension. It is an example of open/closed string duality.