Flux algebra, Bianchi identities and Freed-Witten anomalies in F-theory compactifications

TL;DR

This paper develops a comprehensive algebraic framework for understanding fluxes, Bianchi identities, and Freed-Witten anomalies in F-theory compactifications, linking higher-dimensional theories with 4D gauged supergravity.

Contribution

It derives a full gauge algebra incorporating geometric and non-geometric fluxes, and encodes tadpole and Bianchi constraints as algebraic Jacobi identities.

Findings

Derived a complete gauge algebra for F-theory fluxes.

Connected algebraic identities to tadpole and Bianchi constraints.

Integrated brane gauge symmetries and Freed-Witten conditions into the algebra.

Abstract

We discuss the structure of 4D gauged supergravity algebras corresponding to globally non-geometric compactifications of F-theory, admitting a local geometric description in terms of 10D supergravity. By starting with the well known algebra of gauge generators associated to non-geometric type IIB fluxes, we derive a full algebra containing all, closed RR and NSNS, geometric and non-geometric dual fluxes. We achieve this generalization by a systematic application of SL(2,Z) duality transformations and by taking care of the spinorial structure of the fluxes. The resulting algebra encodes much information about the higher dimensional theory. In particular, tadpole equations and Bianchi identities are obtainable as Jacobi identities of the algebra. When a sector of magnetized (p,q) 7-branes is included, certain closed axions are gauged by the U(1) transformations on the branes. We indicate how the diagonal gauge generators of the branes can be incorporated into the full algebra, and show that Freed-Witten constraints and tadpole cancellation conditions for (p,q) 7-branes can be described as Jacobi identities satisfied by the algebra mixing bulk and brane gauge generators.