Construction of all N=4 conformal supergravities

TL;DR

This paper constructs all N=4 conformal supergravity theories in four dimensions, detailing their unique off-shell supersymmetry invariance and the role of a holomorphic function in their formulation.

Contribution

It provides the first complete construction of all N=4 conformal supergravities, highlighting their dependence on a holomorphic function and invariance properties.

Findings

All N=4 conformal supergravities are explicitly constructed.

The theories are characterized by a holomorphic function homogeneous of degree zero.

Special cases with constant functions exhibit SU(1,1) invariance.

Abstract

All N=4 conformal supergravities in four space-time dimensions are constructed. These are the only N=4 supergravity theories whose actions are invariant under off-shell supersymmetry. They are encoded in terms of a holomorphic function that is homogeneous of zeroth degree in scalar fields that parametrize an SU(1,1)/U(1) coset space. When this function equals a constant the Lagrangian is invariant under continuous SU(1,1) transformations. The construction of these higher-derivative invariants also opens the door to various applications for non-conformal theories.