On quantum compatibility of counterterm deformations and duality symmetries in N≥ 5 supergravities

In N= 5 , 6, 8 supergravities there are hidden symmetries of equations of motion, described by duality groups SU(1, 5), SO^*(12), E₇₍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 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 λ² approximation, that the S U (N) symmetry of the deformed theory is restored on shell.