Exceptional algebroids and type IIA superstrings

TL;DR

This paper classifies exceptional algebroids in type IIA string theory compactifications, revealing multiple scalar deformations and twisting possibilities, and connects these to supersymmetric truncations and dualities in lower dimensions.

Contribution

It provides a detailed classification of exceptional algebroids in type IIA string theory, including scalar deformations and twisting mechanisms, and relates these to supersymmetric truncations and dualities.

Findings

Identification of 5 distinct points in the moduli space of algebroids.

Classification of possible twists using differential forms.

Translation of Leibniz parallelisable spaces into algebraic problems.

Abstract

We study exceptional algebroids in the context of warped compactifications of type IIA string theory down to $n$ dimensions, with $n\le 6$. In contrast to the M-theory and type IIB case, the relevant algebroids are no longer exact, and their locali moduli space is no longer trivial, but has $5$ distinct points. This relates to two possible scalar deformations of the IIA theory. The proof of the local classification shows that, in addition to these scalar deformations, one can twist the bracket using a pair of $1$-forms, a $2$-form, a $3$-form, and a $4$-form. Furthermore, we use the analysis to translate the classification of Leibniz parallelisable spaces (corresponding to maximally supersymmetric consistent truncations) into a tractable algebraic problem. We finish with a discussion of the Poisson-Lie U-duality and examples given by tori and spheres in $2$, $3$, and $4$ dimensions.