"Induced" N=4 conformal supergravity

TL;DR

This paper analyzes the quantum properties of N=4 super Yang-Mills coupled to conformal supergravity, demonstrating SU(1,1) invariance of the divergent effective action and deriving the full non-linear bosonic supergravity action.

Contribution

It provides the first explicit derivation of the non-linear bosonic N=4 conformal supergravity action with manifest SU(1,1) invariance based on quantum divergence calculations.

Findings

The divergent part of the effective action is SU(1,1) invariant.

The divergence is one-loop exact and related to the conformal anomaly.

The full non-linear bosonic action with SU(1,1) symmetry is determined.

Abstract

We consider an abelian N=4 super Yang-Mills theory coupled to background N=4 conformal supergravity fields. At the classical level, this coupling is invariant under global SU(1,1) transformation of the complex ("dilaton-axion") supergravity scalar combined with an on-shell vector-vector duality. We compute the divergent part of the corresponding quantum effective action found by integrating over the super Yang-Mills fields and demonstrate its SU(1,1) invariance. This divergent part related to the conformal anomaly is one-loop exact and should be given by the N=4 conformal supergravity action containing the Weyl tensor squared term. This allows us to determine the full non-linear form of the bosonic part of the N=4 conformal supergravity action which has manifest SU(1,1) invariance.