Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions

TL;DR

This paper demonstrates how holomorphic quantities in supersymmetric gauge theories can be computed using intersecting D-brane configurations, linking them to topological strings and non-commutative geometry.

Contribution

It introduces a novel framework connecting D-brane setups, chiral fermions, and topological string theory, incorporating quantum corrections via D-modules and non-commutative geometry.

Findings

Holomorphic gauge theory quantities are computed through D-brane configurations.

The system maps to topological string theory on non-compact Calabi-Yau manifolds.

Quantum corrections are incorporated using D-modules and non-commutative geometry.

Abstract

We show that various holomorphic quantities in supersymmetric gauge theories can be conveniently computed by configurations of D4-branes and D6-branes. These D-branes intersect along a Riemann surface that is described by a holomorphic curve in a complex surface. The resulting I-brane carries two-dimensional chiral fermions on its world-volume. This system can be mapped directly to the topological string on a large class of non-compact Calabi-Yau manifolds. Inclusion of the string coupling constant corresponds to turning on a constant B-field on the complex surface, which makes this space non-commutative. Including all string loop corrections the free fermion theory is elegantly formulated in terms of holonomic D-modules that replace the classical holomorphic curve in the quantum case.