From M-theory to F-theory, with Branes

TL;DR

This paper explores the duality between brane configurations in type IIA and IIB string theory via M-theory, elucidating the geometric origins of F-theory backgrounds and their relation to four-dimensional N=2 supersymmetric gauge theories.

Contribution

It demonstrates how non-trivial F-theory backgrounds can be derived from M-theory configurations, clarifying their geometric and physical relationship.

Findings

Duality between IIA and IIB brane configurations established

Spectral curves organize non-perturbative dynamics of N=2 gauge theories

F-theory backgrounds derived from M-theory geometries

Abstract

A duality relationship between certain brane configurations in type IIA and type IIB string theory is explored by exploiting the geometrical origins of each theory in M-theory. The configurations are dual ways of realising the non-perturbative dynamics of a four dimensional N=2 supersymmetric SU(2) gauge theory with four or fewer favours of fermions in the fundamental, and the spectral curve which organizes these dynamics plays a prominent role in each case. This is an illustration of how non-trivial F-theory backgrounds follow from M-theory ones, hopefully demystifying somewhat the origins of the former.