In this paper we explore the relation between conformal superalgebras with 64 supercharges and maximal supergravity theories in three, four and six dimensions using twistorial oscillator techniques. The massless fields of N = 8 supergravity in four dimensions were shown to fit into a CPT-self-conjugate doubleton supermultiplet of the conformal superalgebra SU(2, 2|8) a long time ago. We show that the fields of maximal supergravity in three dimensions can similarly be fitted into the super singleton multiplet of the conformal superalgebra OSp(16|4,R), which is related to the doubleton supermultiplet of SU(2, 2|8) by dimensional reduction. Moreover, we construct the ultra-short supermultiplet of the six-dimensional conformal superalgebra OSp(8*|8) and show that its component fields can be organized in an on-shell superfield. The ultra-short OSp(8*|8) multiplet reduces to the doubleton supermultiplet of SU(2, 2|8) upon dimensional reduction. We discuss the possibility of a novel non-metric based (4, 0) six-dimensional supergravity theory with USp(8) R-symmetry that reduces to maximal supergravity in four dimensions and is different from six-dimensional metric based (2, 2) maximal supergravity, whose fields cannot be fitted into a unitary supermultiplet of a simple conformal superalgebra. Such an interacting (4, 0) theory would be the non-metric gravitational analog of the interacting (2, 0) theory.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics