F-Theory, T-Duality on K3 Surfaces and N=2 Supersymmetric Gauge Theories in Four Dimensions

TL;DR

This paper constructs T-duality on K3 surfaces, explores its effects on brane charges and moduli spaces, and applies these results to dualities in N=2 supersymmetric gauge theories in four dimensions, with extensions to N=1 scenarios.

Contribution

It introduces a novel construction of T-duality on K3 surfaces and applies it to analyze dualities in F-theory compactifications and supersymmetric gauge theories.

Findings

T-duality exchanges 4-brane and 0-brane R-R charges.

The duality acts on the moduli space of branes on K3.

Application to N=2 SU(N_c) gauge theories in four dimensions.

Abstract

We construct T-duality on K3 surfaces. The T-duality exchanges a 4-brane R-R charge and a 0-brane R-R charge. We study the action of the T-duality on the moduli space of 0-branes located at points of K3 and 4-branes wrapping it. We apply the construction to F-theory compactified on a Calabi-Yau 4-fold and study the duality of N=2 SU(N_c) gauge theories in four dimensions. We discuss the generalization to the N=1 duality scenario.