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

Understand

In ${\cal N}=5, 6, 8$ 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 ${\cal N}\geq 5$ supergravities using the universality of the symplectic structure of extended supergravities.