F-theory, T-duality on K3 surfaces, and N = 2 supersymmetric gauge theories in four dimensions

Abstract

We construct T-duality on K3 surfaces. The T-duality exchanges a 4-brane RR charge and a 0-brane RR 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.