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

Abstract

In $\mathcal{N}=5,6,8$ supergravities there are hidden symmetries of equations of motion, described by duality groups $SU(1,5),S{O}^{\ast }(12),E_{7(7)}$ 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 $\mathcal{N}\ge 5$ 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 $SU(\mathcal{N})$ symmetry of the deformed theory is restored on shell.

30 pages, 1 figure, v2: comments, references added, v3: comments added

References in corpus (7)

• Stringy KLT relations, global symmetries, and E_7(7) violation
• E7(7) symmetry in perturbatively quantised N=8 supergravity
• d=4 Attractors, Effective Horizon Radius and Fake Supergravity
• Explicit Action of E7(7) on N=8 Supergravity Fields
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Cited by in corpus (3)

• Supersymmetry constraints on U-duality invariant deformations of $N\ge 5$ Supergravity
• The Action with Manifest E7 Type Symmetry
• Deformation of d=4, N> 4 Supergravities Breaks Nonlinear Local Supersymmetry