Torus reduction of maximal conformal supergravity

TL;DR

This paper explores the dimensional reduction of six-dimensional N=(2,0) conformal supergravity on a two-torus, resulting in a new off-shell N=4 conformal supergravity multiplet in four dimensions, with detailed field relations.

Contribution

It constructs the first explicit off-shell N=4 conformal supergravity multiplet in four dimensions derived from six-dimensional supergravity.

Findings

Reduction of 6D Weyl multiplet to 4D multiplets

Identification of a new off-shell N=4 multiplet

Explicit non-linear relations between fields

Abstract

We consider the dimensional reduction of N=(2,0) conformal supergravity in six dimensions on a two-torus to N=4 conformal supergravity in four dimensions. At the level of kinematics, the six-dimensional Weyl multiplet is shown to reduce to a mixture of the N=4 Weyl and vector multiplets, which can be reinterpreted as a new off-shell multiplet of N=4 conformal supergravity. Similar multiplets have been constructed in other settings and are referred to as dilaton Weyl multiplets. We derive it here for the first time in a maximally supersymmetric context in four dimensions. Furthermore, we present the non-linear relations between all the six- and four-dimensional bosonic and fermionic fields, that are obtained by comparing the off-shell supersymmetry transformation rules.