N =2 three dimensional Supergravity with internal R−symmetry generators can be understood as a two dimensional chiral Wess-Zumino-Witten model. In this paper, we present the reduced phase space description of the theory, which turns out to be flat limit of a generalised Liouville theory, up to zero modes. The reduced phase space description can also be explained as a gauged chiral Wess-Zumino-Witten model. We show that both these descriptions possess identical gauge and global (quantum N =2 superBMS 3 ) symmetries.1 nabamita@iiserb.ac.in (on lien from IISER Pune) 2 ks.saurish@gmail.com 3 paritars8@gmail.com 4 Higher spin and Supersymmetric generalisations were performed in [18][19][20][21][22][23][24][25].

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We elaborate on the off-shell superspace construction of curvature-squared invariants in minimal five-dimensional supergravity. This is described by the standard Weyl multiplet of conformal supergravity coupled to two compensators being a vector multiplet and a linear multiplet. In this set-up, we review the definition of the off-shell two-derivative gauged supergravity together with the three independent four-derivative superspace invariants defined in arXiv:1410.8682. We provide the explicit expression for the linear multiplet based on a prepotential given by the logarithm of the vector multiplet primary superfield. We then present for the first time the primary equations of motion for minimal gauged off-shell supergravity deformed by an arbitrary combination of these three four-derivative locally superconformal invariants. We also identify a four-derivative invariant based on the linear multiplet compensator and the kinetic superfield of a vector multiplet which can be used to engineer an alternative supersymmetric completion of the scalar curvature squared.

We define a new dilaton Weyl multiplet of $$ \mathcal{N} $$ N = 2 conformal supergravity in four dimensions. This is constructed by reinterpreting the equations of motion of an on-shell hypermultiplet as constraints that render some of the fields of the standard Weyl multiplet composite. The independent bosonic components include four scalar fields and a triplet of gauge two-forms. The resulting, so-called, hyper-dilaton Weyl multiplet defines a 24 + 24 off-shell representation of the local $$ \mathcal{N} $$ N = 2 superconformal algebra. By coupling the hyper-dilaton Weyl multiplet to an off-shell vector multiplet compensator, we obtain one of the two minimal 32 + 32 off-shell multiplets of $$ \mathcal{N} $$ N = 2 Poincaré supergravity constructed by Müller in 1986. On-shell, this contains the minimal $$ \mathcal{N} $$ N = 2 Poincaré supergravity multiplet together with a hypermultiplet where one of its physical scalars plays the role of a dilaton, while its three other scalars are dualised to a triplet of real gauge two-forms. Interestingly, a BF-coupling induces a scalar potential for the dilaton without a standard gauging.