F-theory, geometric engineering and N = 1 dualities

Abstract

We consider geometric engineering of N = 1 supersymmetric QFTs with matter in terms of a local model for compactification of F-theory on Calabi-Yau fourfold. By bringing 3-branes near 7-branes we engineer N = 1 supersymmetric SU( N c ) gauge theory with N f flavors in the fundamental. We identify the Higgs branch of this system with the instanton moduli space on the compact four-dimensional space of the 7-brane world-volume. Moreover we show that the Euclidean 3-branes wrapped around the compact part of the 7-brane world-volume can generate superpotential for N f = N c − 1 as well as lead to quantum corrections to the moduli space for N f = N c . Finally we argue that Seiberg's duality for N = 1 supersymmetric QCD may be mapped to T-duality exchanging 7-branes with 3-branes.