Conjecture on Hidden Superconformal Symmetry of N=4 Supergravity

TL;DR

This paper proposes that the UV finiteness observed in 3-loop extended supergravities could be due to an underlying hidden local superconformal symmetry in N=4 supergravity, which might be confirmed by future loop calculations.

Contribution

It introduces the conjecture that a hidden local superconformal symmetry underlies N=4 supergravity, potentially explaining its UV finiteness and absence of certain invariants.

Findings

Arguments for the existence of hidden superconformal symmetry in N=4 supergravity.

Analysis of superconformal invariants and anomalies in the model.

Potential support for the conjecture through future loop computations.

Abstract

We argue that the observed UV finiteness of the 3-loop extended supergravities may be a manifestation of a hidden local superconformal symmetry of supergravity. We focus on the SU(2,2|4) dimensionless superconformal model. In Poincare gauge where the compensators are fixed to phi^2= 6 M_P^2 this model becomes a pure classical N=4 Einstein supergravity. We argue that in N=4 the higher-derivative superconformal invariants like phi^{-4}W^2 \bar W^2 and the consistent local anomaly delta (ln phi W^2) are not available. This conjecture on hidden local N=4 superconformal symmetry of Poincare supergravity may be supported by subsequent loop computations.