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

TL;DR

This paper investigates how counterterm deformations affect duality symmetries in extended supergravities, constructing a deformed action with higher derivatives that restores symmetry at the on-shell level.

Contribution

It introduces a universal approach to incorporate counterterm effects into supergravity actions, restoring duality symmetries through an infinite series of higher derivative terms.

Findings

Deformed action maintains duality symmetry with deformation parameter λ.

On-shell SU(N) symmetry is restored in the λ² approximation.

Constructs a compact form of the deformed supergravity action.

Abstract

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. We construct a compact form of a deformed action with infinite number of higher derivative terms and restored duality symmetry with deformation parameter $\lambda$. We find, in $\lambda^2$ approximation, that the $SU({\cal N})$ symmetry of the deformed theory is restored on shell.