Comment on "The N = 3 Weyl Multiplet in Four Dimensions"

N = 3 Weyl multiplet in four dimensions was first constructed in J van Muiden et al (2017) where the authors used the current multiplet approach to obtain the linearized transformation rules and completed the nonlinear variations using the superconformal algebra. The multiplet of currents was obtained by a truncation of the multiplet of currents for the N = 4 vector multiplet. While the procedure seems to be correct, the result suffers from several inconsistencies. The inconsistencies are observed in the transformation rules as well as the field dependent structure constants in the corresponding soft algebra. We take a different approach, and compute the transformation rule as well as the corresponding soft algebra by demanding consistency.Comment: 7 pages, text revision

AdS_3, Black Holes and Higher Derivative Corrections

Using AdS/CFT correspondence and the Euclidean action formalism for black hole entropy Kraus and Larsen have argued that the entropy of a BTZ black hole in three dimensional supergravity with (0,4) supersymmetry does not receive any correction from higher derivative terms in the action. We argue that as a consequence of AdS/CFT correspondence the action of a three dimensional supergravity with (0,4) supersymmetry cannot receive any higher derivative correction except for those which can be removed by field redefinition. The non-renormalization of the entropy then follows as a consequence of this and the invariance of Wald's formula under a field redefinition.Comment: LaTeX file, 12 pages; v2: reference adde

Curvature squared action in four dimensional N=2N=2 supergravity using the dilaton Weyl multiplet

In this paper we derive the most general curvature squared action coupled to an arbitrary number of vector multiplets in four dimensional $N=2$ supergravity using the dilaton Weyl multiplet. The action that we derive is encoded in a single holomorphic prepotential.Comment: 40 Pages Latex, minor change

N=2N=2 dilaton Weyl multiplet in 4D supergravity

We construct the dilaton Weyl multiplet for $N=2$ conformal supergravity in four dimensions. Beginning from an on-shell vector multiplet coupled to the standard Weyl multiplet, the equations of motion can be used to eliminate the supergravity auxiliary fields, following a similar pattern as in five and six dimensions. The resulting 24+24 component multiplet includes two gauge vectors and a gauge two-form and provides a variant formulation of $N=2$ conformal supergravity. We also show how this dilaton Weyl multiplet is contained in the minimal 32+32 Poincare supergravity multiplet introduced by Muller in superspace.Comment: 15 page

N=4 conformal supergravity: the complete actions

The most general class of 4D N=4 conformal supergravity actions depends on a holomorphic function of the scalar fields that parametrize an SU(1,1)/U(1) coset space. The bosonic sector of these actions was presented in a letter [arXiv:1609.09083]. Here we provide the complete actions to all orders in the fermion fields. They rely upon a new N=4 density formula, which permits a direct but involved construction. This density formula also recovers the on-shell action for vector multiplets coupled to conformal supergravity. Applications of these results in the context of Poincar\'e supergravity are briefly discussed.Comment: v2: 44 pages, supplementary file added to ancillary file