Abelian gauge symmetries and fluxed instantons in compactifications of type IIB and F-theory

TL;DR

This paper explores how Abelian gauge symmetries, especially massive U(1)s, are incorporated into F-theory compactifications using non-harmonic forms, and analyzes their effects on instanton physics and zero modes.

Contribution

It proposes a method to include geometrically massive U(1)s in F-theory via non-harmonic forms and matches the effective actions with type IIB results, advancing understanding of fluxed instantons.

Findings

Effective F-theory action includes non-harmonic forms for massive U(1)s.

Matching of M5-instanton partition functions with D3-instantons in type IIB.

Selection rules for zero modes on M5-instantons with G_4 flux are established.

Abstract

We discuss the role of Abelian gauge symmetries in type IIB orientifold compactifications and their F-theory uplift. Particular emphasis is placed on U(1)s which become massive through the geometric St\"uckelberg mechanism in type IIB. We present a proposal on how to take such geometrically massive U(1)s and the associated fluxes into account in the Kaluza-Klein reduction of F-theory with the help of non-harmonic forms. Evidence for this proposal is obtained by working out the F-theory effective action including such non-harmonic forms and matching the results with the known type IIB expressions. We furthermore discuss how world-volume fluxes on D3-brane instantons affect the instanton charge with respect to U(1) gauge symmetries and the chiral zero mode spectrum. The classical partition function of M5-instantons in F-theory is discussed and compared with the type IIB results for D3-brane instantons. The type IIB match allows us to determine the correct M5 partition function. Selection rules for the absence of chiral charged zero modes on M5-instantons in backgrounds with G_4 flux are discussed and compared with the type IIB results. The dimensional reduction of the democratic formulation of M-theory is presented in the appendix. This article is based on the author's PhD thesis but includes minor modifications.