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

TL;DR

The paper addresses how to encode data from globally non-geometric F-theory compactifications into four-dimensional gauged supergravity algebras. By starting from a non-geometric IIB flux algebra and systematically applying SL(2,Z)^7 dualities, the authors construct a complete flux algebra that includes RR/NSNS, geometric, and dual fluxes, with Jacobi identities reproducing Bianchi and tadpole constraints. Incorporating brane gaugings, they show Freed-Witten anomalies and brane tadpole conditions arise as Jacobi identities mixing bulk and brane generators, and they connect the construction to N=4 gauged supergravity via embedding tensors, with a detailed discussion of N=1 structure in the D3-brane sector. The framework provides a cohesive algebraic lens on moduli stabilization and open-string–closed-string consistency in non-geometric F-theory settings, while highlighting avenues for further exploration in vacuum structure and exceptional generalized geometry.

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.