Superconformal symmetry and maximal supergravity in various dimensions

TL;DR

This paper investigates the connection between conformal superalgebras with 64 supercharges and maximal supergravity theories across three, four, and six dimensions using twistorial oscillator techniques, revealing new multiplet structures.

Contribution

It constructs ultra-short supermultiplets for six-dimensional conformal superalgebras and explores their relation to lower-dimensional supergravity theories, proposing a novel 6D (4,0) supergravity model.

Findings

Maximal supergravity fields fit into supermultiplets of conformal superalgebras.

Constructed the ultra-short supermultiplet of OSp(8*|8) in six dimensions.

Proposed a new 6D (4,0) supergravity theory related to 4D maximal supergravity.

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.