Twisting D(2,1; α) Superspace

Abstract

We develop a three‐dimensional N=4 theory of rigid supersymmetry describing the dynamics of a set of hypermultiplets (normalΛIαα′trueα̇′,ϕIαA) on a curved AdS3 worldvolume background, whose supersymmetry is captured by the supergroup normalD2false(2,1;αfalse). 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 normalD2false(2,1;αfalse) 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 α+1, which in our model is related to a sort of gauging in the absence of dynamical gauge fields.