Unfolding the Exotic Supergravity Multiplet

Abstract

We provide an unfolded formulation of linearised 6D exotic supergravity with manifest superconformal symmetry including conformal duality transformations. The construction is based on a superoscillator realisation of the metaplectic supergroup $MOSp(16|16)$ containing the Howe dual pair $MOSp(8^\ast|8)\times SU(2)$. Exotic graviton potentials arise in conformally dual pairs of two-forms in direct products of $SU(2)$-triplets and supertraceless graded-symmetric rank-two supertensors of $OSp(8^\ast|8)$ generated from a hypercharge by the supercharges, providing an analogue of the adjoint representation of $\mathfrak{psu}(2,2|4)$. The potentials are sourced via relative Chevalley-Eilenberg cocycles by a conformally dual pair of chiral and anti-chiral Weyl zero-forms valued in $SO(1,1)\times Spin(1,5)\times USp(8)$-covariant monomorphic restrictions of an extended supersingleton, i.e., an infinite-dimensional $SU(2)$-invariant Hermitian left-module of $MOSp(8^\ast|8)$ containing various irreps associated with different boundary conditions, including the unitarizable exotic supergravity multiplet. Two natural quadratic observables are i) an on-shell closed zero-form built from the chiral Weyl zero-form and its dual, akin to the on-shell value of the second Chern class on the internal twistor $Z$-space of 4D Vasiliev systems; and ii) an off-shell topological six-form built from the conformally dual pair of two-form potentials, reducing on-shell to a generating function for chiral two-point functions in super-Poincar\'e backgrounds.