On symmetries and dynamics of exotic supermultiplets

TL;DR

This paper explores exotic supermultiplets in six-dimensional extended supersymmetry, analyzing their algebraic structure, embedding in exceptional field theory, and implications for lower-dimensional theories, raising questions about their dynamics and connections to supergravity.

Contribution

It provides an algebraic analysis of exotic supermultiplets, their embedding in exceptional field theory, and proposes a new perspective involving fixed-volume T^3-fibered spacetimes.

Findings

Six-dimensional momenta do not correspond to conventional spacetime sections.

Compactification yields degrees of freedom similar to five-dimensional supergravity.

Anomaly and Chern-Simons analysis cast doubt on direct supergravity correspondence.

Abstract

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 $\mathcal{N}=(4,0)$ 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 spacetime 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 spacetimes play a central role, suggesting that only on compactification to three-dimensions will one make contact with the dynamics of supergravity.