On quantum compatibility of counterterm deformations and duality symmetries in $$ \mathcal{N}\ge 5 $$ supergravities

Abstract

Abstract In $$ \mathcal{N}=5 $$ N = 5 , 6, 8 supergravities there are hidden symmetries of equations of motion, described by duality groups SU(1, 5), SO*(12), E 7(7) respectively. UV divergences and known candidate counterterms violate the deformed duality symmetry current conservation. Extra higher derivative terms in the action are required to restore duality. We study the effect of a two-vector part of the counterterm for $$ \mathcal{N}\ge 5 $$ N ≥ 5 supergravities using the universality of the symplectic structure of extended supergravities. We construct a compact form of a deformed action with infinite number of higher derivative terms and restored duality symmetry with deformation parameter λ. We find, in λ 2 approximation, that the $$ \mathrm{S}\mathrm{U}\left(\mathcal{N}\right) $$ S U N symmetry of the deformed theory is restored on shell.