IR Dynamics on Branes and Space-Time Geometry

TL;DR

This paper explores how strong coupling effects in three-dimensional gauge theories on branes can be understood through their geometric interpretation as K3 surfaces in M-theory, revealing the moduli space's structure.

Contribution

It demonstrates that IR effects in 3D gauge theories on branes transform their moduli space into a K3 surface, providing a geometric solution to strongly coupled gauge theories.

Findings

Moduli space of the 3D theory is initially T^4/ZZ_2.

Strong coupling IR effects turn the moduli space into a K3 surface.

This geometric interpretation helps solve strongly coupled gauge theories.

Abstract

We consider the type I theory compactified on $T^3$. When the D5-brane wraps the $T^3$ it yields a D2-brane in seven dimensions. In the leading approximation the moduli space of vacua of the three dimensional field theory on the brane is $T^4/\ZZ_2$. The dual M theory description of this theory is a compactification on K3 and our 2-brane is the eleven dimensional 2-brane at a point in K3. We use this fact to conclude that strong coupling IR effects in the three dimensional theory on the brane turn its moduli space into a K3. This interpretation allows us to solve various strongly coupled gauge theories in three dimensions by identifying their Coulomb branch with a piece of a (sometime singular) K3.