From M-theory to F-theory, with branes

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 realizing the non-perturbative dynamics of four-dimensional N=2 supersymmetric SU(2) gauge theory with four or fewer flavours of quark, 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. (orig.)