The global formulation of generalized Einstein-Scalar-Maxwell theories

TL;DR

This paper presents a comprehensive geometric framework for Einstein-Scalar-Maxwell theories, incorporating duality, scalar potentials, and quantization conditions, relevant for string/M-theory compactifications with U-fold solutions.

Contribution

It introduces a global geometric formulation of these theories using flat symplectic vector bundles and describes their symmetry groups and quantization conditions.

Findings

Describes the scalar-electromagnetic symmetry group structure.

Defines the Dirac quantization condition involving integral symplectic spaces.

Characterizes models arising from string/M-theory compactifications with U-fold solutions.

Abstract

We summarize the global geometric formulation of Einstein-Scalar-Maxwell theories twisted by flat symplectic vector bundle which encodes the duality structure of the theory. We describe the scalar-electromagnetic symmetry group of such models, which consists of flat unbased symplectic automorphisms of the flat symplectic vector bundle lifting those isometries of the scalar manifold which preserve the scalar potential. The Dirac quantization condition for such models involves a local system of integral symplectic spaces, giving rise to a bundle of polarized Abelian varieties equipped with a symplectic flat connection, which is defined over the scalar manifold of the theory. Generalized Einstein-Scalar-Maxwell models arise as the bosonic sector of the effective theory of string/M-theory compactifications to four-dimensions, and they are characterized by having non-trivial solutions of "U-fold" type.