F-theory, Geometric Engineering and N=1 Dualities

TL;DR

This paper explores the geometric engineering of N=1 supersymmetric QFTs via F-theory on Calabi-Yau fourfolds, revealing dualities and quantum effects through brane configurations and instanton moduli spaces.

Contribution

It introduces a geometric framework for N=1 supersymmetric gauge theories using F-theory, identifying Higgs branches with instanton moduli spaces and linking Seiberg duality to T-duality.

Findings

Higgs branch corresponds to instanton moduli space.

Euclidean 3-branes generate superpotential and quantum corrections.

Seiberg duality maps to T-duality exchanging branes.

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 worldvolume. Moreover we show that the Euclidean 3-branes wrapped around the compact part of the 7-brane worldvolume 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.