Branes, U-folds and hyperelliptic fibrations

TL;DR

This paper constructs supersymmetric type IIB string theory vacua involving complex brane configurations, utilizing hyperelliptic fibrations and U-duality monodromies to generalize F-theory models with genus two surfaces.

Contribution

It introduces a novel class of vacua characterized by hyperelliptic fibrations, extending F-theory frameworks to include genus two Riemann surfaces and non-perturbative brane instanton effects.

Findings

Generalization of F-theory elliptic fibrations to genus two surfaces

Explicit construction of supersymmetric vacua with brane monodromies

Encoding fluxes and axio-dilaton in hyperelliptic fibrations

Abstract

We construct a class of supersymmetric vacua of type IIB string theory describing systems of three- and seven-branes non-perturbatively completed by brane instantons. The vacua are specified by a set of holomorphic functions defined over a complex plane up to non-trivial U-duality monodromies around the brane locations. In the simplest setting, the solutions can be seen as a generalization of F-theory elliptic fibrations, where the torus fiber is replaced by a genus two Riemann surface with periods encoding the information on the axio-dilaton, the warp factor and the NS-NS and R-R fluxes.