Exotic potentials and Bianchi identities in SL(5) exceptional field theory

TL;DR

This work extends the flux formulation to SL(5) exceptional field theory by defining a complete flux algebra including the embedding tensor $\Theta$ and additional fluxes, and by rewriting the SL(5) ExFT Lagrangian entirely in terms of fluxes $\mathcal{F}_{\mu\nu}{}^{MN}$, $\mathcal{F}_{\mu\nu ho M}$, $\mathcal{F}_{\mu\nu\rho\sigma}{}^{M}$, and related objects. It derives the full set of Bianchi identities, in curved and flat indices, linking them to the tensor hierarchy and quadratic constraints, and identifies magnetic potentials that couple to magnetically charged branes in M-theory, including exotic branes. The paper also analyzes external and internal diffeomorphisms, discusses dual formulations of fluxes in the DFT/ExFT context, and presents a detailed account of exotic potentials and their brane interpretations, providing a framework for non-geometric backgrounds and duality-invariant reductions in seven dimensions. These results enable systematic construction and analysis of flux backgrounds, tadpole cancellation conditions, and SL(5) duality multiplets relevant for M-theory compactifications and their deformations. Overall, the study offers a comprehensive, flux-centered description of SL(5) ExFT, connecting higher-form potentials, brane spectra, and duality structures in a covariant seven-dimensional setting.

Abstract

Tensor hierarchy of Exceptional Field Theories contains gauge fields satisfying certain Bianchi identities. We define the full set of fluxes of the SL(5) exceptional field theory containing known gauge field strengths, generalized anholonomy coefficients and two new fluxes. It is shown that the full SL(5) ExFT Lagrangian can be written in terms of the listed fluxes. We derive the complete set of Bianchi identities and identify magnetic potentials of the theory and the corresponding (wrapped) membranes of M-theory.