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On divergences in non-minimal N=4 conformal supergravity

Abstract

We review the question of quantum consistency of N=4 conformal supergravity in 4 dimensions. The UV divergences and anomalies of the standard ("minimal") conformal supergravity where the complex scalar ϕ\phi is not coupled to the Weyl graviton kinetic term can be cancelled by coupling this theory to N=4 super Yang-Mills with gauge group of dimension 4. The same turns out to be true also for the "non-minimal" N=4 conformal supergravity with the action (recently constructed in arXiv:1609.09083) depending on an arbitrary holomorphic function f(ϕ)f(\phi). The special case of the "non-minimal" conformal supergravity with f=e2ϕf= e^{2\phi} appears in the twistor-string theory. We show that divergences and anomalies do not depend on the form of the function ff and thus can be cancelled just as in the "minimal" f=1f=1 case by coupling the theory to four N=4 vector multiplets.Comment: 6 pages. v2: minor comment and references adde

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