Twisting D(2,1; α) Superspace

Abstract

We develop a three-dimensional $\mathcal{N}=4$ theory of rigid supersymmetry describing the dynamics of a set of hypermultiplets $({\Lambda }_I^{\alpha {\alpha }^{\prime }{\dot{\alpha }}^{\prime }},{\varphi }_I^{\alpha A})$ on a curved AdS${}_3$ worldvolume background, whose supersymmetry is captured by the supergroup ${\mathrm{D}}^2(2,1;\mathbf{\alpha })$. To unveil some remarkable features of this model, we perform two twists, involving the SL$(2,\mathbb{R})$ 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 ${\mathrm{D}}^2(2,1;\mathbf{\alpha })$ 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.

27 pages, one appendix

References in corpus (2)

• N=1 and N=2 pure supergravities on a manifold with boundary
• Geometric supergravitty