On symmetries and dynamics of exotic supermultiplets

© 2021 The Author(s). This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0 - https://creativecommons.org/licenses/by/4.0/), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.Among the allowed representations of extended supersymmetry in six dimensions there are exotic chiral multiplets that, instead of a graviton, contain mixed-symmetry spin-2 tensor fields. Notably, an N = (4, 0) multiplet has a four index exotic graviton and it was conjectured that an interacting theory based on this multiplet could arise as a strong coupling limit of M theory compactified on T 6. We present an algebraic study of these multiplets and their possible embedding into the framework of exceptional field theory, finding in particular that the six-dimensional momenta do not correspond to a conventional space-time section. When compactified on a circle, the six-dimensional multiplets give rise to the same degrees of freedom as five-dimensional supergravity theories with the same number of supersymmetries. However, by considering anomalies (computed using the product multiplets construction) and the generation of Chern-Simons couplings, we find reason to doubt that their dynamics will agree with the five-dimensional gravity theories. We propose an alternative picture, similar to F-theory, in which particular fixed-volume T 3-fibered space-times play a central role, suggesting that only on compactification to three-dimensions will one make contact with the dynamics of supergravity.Peer reviewe