Twisting D(2,1; α) Superspace

We develop a three-dimensional (Formula presented.) theory of rigid supersymmetry describing the dynamics of a set of hypermultiplets (Formula presented.) on a curved AdS3 worldvolume background, whose supersymmetry is captured by the supergroup (Formula presented.). To unveil some remarkable features of this model, we perform two twists, involving the SL (Formula presented.) 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 (Formula presented.) 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 (Formula presented.), which in our model is related to a sort of gauging in the absence of dynamical gauge fields.