Toward Exotic 6D Supergravities

TL;DR

This paper explores exotic 6D supergravity theories with maximal supersymmetry, proposing new actions and a potential unified framework through exceptional field theory, advancing understanding of their structure and relations.

Contribution

It introduces novel actions for (4,0) and (3,1) supergravity theories in 6D and suggests a master exceptional field theory framework unifying these with conventional theories.

Findings

New actions for (4,0) and (3,1) theories derived

Evidence for a master exceptional field theory formulation

Potential for a fully non-linear master theory

Abstract

We investigate exotic supergravity theories in 6D with maximal (4,0) and (3,1) supersymmetry, which were conjectured by C. Hull to exist and to describe strong coupling limits of ${\cal N}=8$ theories in 5D. These theories involve exotic gauge fields with non-standard Young tableaux representations, subject to (self-)duality constraints. We give novel actions in a 5+1 split of coordinates whose field equations reproduce those of the free bosonic (4,0) and (3,1) theory, respectively, including the (self-)duality relations. Evidence is presented for a master exceptional field theory formulation with an extended section constraint that, depending on the solution, produces the (4,0), (3,1) or the conventional (2,2) theory. We comment on the possible construction of a fully non-linear master exceptional field theory.