From F/M-theory to K-theory and back

TL;DR

This paper explores the relationship between K-theory charge cancellation in type IIB string theory with 7-branes and its geometric realization via F-/M-theory, revealing new discrete constraints and flux quantization modifications.

Contribution

It demonstrates how K-theory constraints are naturally encoded in F-/M-theory flux quantization, uncovering previously unnoticed discrete conditions and flux modifications.

Findings

K-theory charge constraints are implied by 4-form flux quantization in F-/M-theory.

New discrete constraints on magnetic fluxes on 7-branes are identified.

Flux quantization conditions are altered in the presence of 3-form fluxes.

Abstract

We consider discrete K-theory tadpole cancellation conditions in type IIB orientifolds with magnetised 7-branes. Cancellation of K-theory charge constrains the choices of world-volume magnetic fluxes on the latter. We describe the F-/M-theory lift of these configurations, where 7-branes are encoded in the geometry of an elliptic fibration, and their magnetic quanta correspond to supergravity 4-form field strength fluxes. In a K3 compactification example, we show that standard quantization of 4-form fluxes as integer cohomology classes in K3 automatically implies the K-theory charge cancellation constraints on the 7-brane worldvolume magnetic fluxes in string theory (as well as new previously unnoticed discrete constraints, which we also interpret). Finally, we show that flux quantization in F-/M-theory implies that 7-brane world-volume flux quantization conditions are modified in the presence of 3-form fluxes.