Exceptional Algebroids and Type IIA Superstrings

Abstract

We study exceptional algebroids in the context of warped compactifications of type IIA string theory down to n dimensions, with n≤6$n\le 6$. 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.

Maximal D = 2 supergravities from higher dimensions

“…This is a daunting task even in D > 2. Progress has been made in recent years, by identifying necessary and sufficient conditions for the existence of an uplift of a gauged supergravity and by devising a general procedure for constructing the twist matrix [79][80][81][82][83]. In order to carry out an explicit classification of all gauged maximal supergravities admitting a higher-dimensional origin, one would need to classify duality orbits of inequivalent embedding tensors satisfying the uplift conditions found in these works, as well as the standard gauged supergravity quadratic constraints.…”

“…The D = 9, 8 cases are treated in [84]. It would be highly desirable to extend the analyses of [79][80][81][82] to D ≤ 3. The simple observation [29] that the internal space must be a coset space G/H with G the gauge group of the D dimensional theory applies also to the lower-dimensional cases, as the presence of ancillary transformations in the gauge structure of E 8 and E 9 ExFTs does not enter JHEP01(2024)046 in the argument.…”