What is the $R$-symmetry group for ${\cal N}=6$ supergravity in $D=4$ dimensions? What is the $R$-symmetry group for ${\cal N}=6$ supergravity in $D=4$ dimensions?
 A: In $D=4$ the $R$-symmetry group is $U({\cal N})$, cf. Ref. 1, which also lists $R$-symmetry groups in other spacetime dimensions $D$.
References:


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*D.Z. Freedman & A. Van Proeyen, SUGRA, 2012; Table 12.1 p. 240.

A: This is an old post, but I would like to clarify this for others who, like me, stumble upon this question now. As Qmechanic noted, the $R$-symmetry group in $D = 4$ is $U(\mathcal{N})$, which is Table 12.1 on page 240 of Ref. [1]. However, in supergravity theories, the kinetic terms for the scalars are non-trivial and determine the scalar manifold (see section 12.5 of Ref. [1]). Scalar manifolds of all supergravities with more than 8 real-component supersymmetries are symmetric spaces, i.e. they are spaces $G/H$, with $G$ non-compact (the isometry group) and $H$ its maximal compact subgroup (the isotropy group). An overview of the scalar manifolds for various supergravity theories is given in Table 12.3, page 250 of Ref. [1]. Ash's comment on $\mathcal{N} = 8, D = 4$ supergravity actually refers to the isotropy group being $\text{SU}(8)$, as given in that table, probably explaining the confusion. The $R$-symmetry group is always a factor of the isotropy group.
References:

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*D.Z. Freedman & A. Van Proeyen, Supergravity, 2012

