Exceptional algebroids and Type IIB superstrings

In this note we study exceptional algebroids, focusing on their relation to type IIB superstring theory. We show that a IIB-exact exceptional algebroid (corresponding to the group urn:x-wiley:00158208:media:prop202100104:prop202100104-math-0001, for urn:x-wiley:00158208:media:prop202100104:prop202100104-math-0002) locally has a standard form given by the exceptional tangent bundle. We derive possible twists, given by a flat urn:x-wiley:00158208:media:prop202100104:prop202100104-math-0003-connection, a covariantly closed pair of 3-forms, and a 5-form, and comment on their physical interpretation. Using this analysis we reduce the search for Leibniz parallelisable spaces, and hence maximally supersymmetric consistent truncations, to a simple algebraic problem. We show that the exceptional algebroid perspective also gives a simple description of Poisson–Lie U-duality without spectators and hence of generalised Yang–Baxter deformations.