“Induced” N=4 conformal supergravity

AbstractWe 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 N=4 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