Superconformal symmetry and maximal supergravity in various dimensions

Abstract

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 chiral maximal (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 (2,2) maximal supergravity, whose fields cannot be fitted into a unitary supermultiplet of a simple conformal superalgebra. Such an interacting theory would be the gravitational analog of the (2,0) theory.

54 pages, PDFLaTeX, Section 5 and several references added. Version accepted for publication in JHEP

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• The Mile High Magic Pyramid
• The Action of the (free) $(4,0)$-theory
• The Magic Star of Exceptional Periodicity
• Supersymmetry constraints on U-duality invariant deformations of $N\ge 5$ Supergravity
• A Kind of Magic
• Conformal higher-spin symmetries in twistor string theory
• Obstruction to E_{7(7)} Deformation in N=8 Supergravity
• The complete unitary dual of non-compact Lie superalgebra su(p,q|m) via the generalised oscillator formalism, and non-compact Young diagrams
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