Twisting D(2,1; α) Superspace

We develop a three-dimensional N=4 theory of rigid supersymmetry describing the dynamics of a set of hypermultiplets (?I alpha alpha 'alpha?',phi I alpha A) on a curved AdS(3) worldvolume background, whose supersymmetry is captured by the supergroup D2(2,1;alpha). To unveil some remarkable features of this model, we perform two twists, involving the SL(2,R) factors of the theory. After the first twist, our spacetime Lagrangian exhibits a Chern-Simons term associated with an odd one-form field, together with a fermionic "gauge-fixing", in the spirit of the Rozansky-Witten model. The second twist allows to interpret the D2(2,1;alpha) setup as a framework capable of describing massive Dirac particles. In particular, this yields a generalisation of the Alvarez-Valenzuela-Zanelli model of "unconventional supersymmetry". We comment on specific values of the combination alpha+1, which in our model is related to a sort of gauging in the absence of dynamical gauge fields.