Generalized Einstein-Scalar-Maxwell theories and locally geometric U-folds

TL;DR

This paper develops a global framework for four-dimensional scalar sigma models coupled with Abelian gauge fields, describing classical locally geometric U-folds and duality symmetries without relying on duality frames or supersymmetry.

Contribution

It introduces a global formulation using flat symplectic vector bundles and tamings, capturing inverse gauge couplings and theta angles without local duality frames, and extends mathematical structures from supergravity to purely bosonic models.

Findings

Global solutions correspond to classical locally geometric U-folds.

Duality groups involve lifting isometries to flat automorphisms of the bundle.

Dirac quantization involves a smooth bundle of polarized Abelian varieties.

Abstract

We give a global formulation of the coupling of four-dimensional scalar sigma models to Abelian gauge fields for the generalized situation when the "duality structure" of the Abelian gauge theory is described by a flat symplectic vector bundle $(\mathcal{S},D,\omega)$ defined over the scalar manifold $\mathcal{M}$. The construction uses a taming of $(\mathcal{S}, \omega)$, which encodes globally the inverse gauge couplings and theta angles of the "twisted" Abelian gauge theory in a manner that makes no use of duality frames. We show that global solutions of the equations of motion of such models give classical locally geometric U-folds. We also describe the groups of duality transformations and scalar-electromagnetic symmetries arising in such models, which involve lifting isometries of $\mathcal{M}$ to a particular class of flat automorphisms of the bundle $\mathcal{S}$ and hence differ from expectations based on local analysis. The appropriate version of the Dirac quantization condition involves a discrete local system defined over $\mathcal{M}$ and gives rise to a smooth bundle of polarized Abelian varieties, endowed with a flat symplectic connection. This shows that a generalization of part of the mathematical structure familiar from $\mathcal{N}=2$ supergravity is already present in such purely bosonic models, without any coupling to fermions and hence without any supersymmetry.