Exceptional algebroids and type IIB superstrings

TL;DR

This paper explores exceptional algebroids in relation to type IIB superstring theory, revealing their local standard form, possible twists, and applications to supersymmetric truncations and U-duality.

Contribution

It introduces a local standard form for IIB-exact exceptional algebroids and links their structure to supersymmetric truncations and U-duality transformations.

Findings

Exceptional algebroids have a standard form given by the exceptional tangent bundle.

Possible twists include a flat $ ext{GL}(2, extbf{R})$-connection, closed 3-forms, and a 5-form.

The approach simplifies the search for maximally supersymmetric truncations and describes Poisson-Lie U-duality.

Abstract

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 $E_{n(n)}\times \mathbb{R}^+$, for $n\le 6$) locally has a standard form given by the exceptional tangent bundle. We derive possible twists, given by a flat $\mathfrak{gl}(2,\mathbb{R})$-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.