Twisting D(2,1; \alpha) Superspace

TL;DR

This paper constructs a 3D $ abla=4$ supersymmetric theory on curved AdS$_3$ space, revealing novel features through two twists that relate to Chern-Simons terms and massive Dirac particles, extending previous models.

Contribution

It introduces a new 3D $ abla=4$ supersymmetric model with twists that connect to Chern-Simons theory and massive particles, generalizing the Alvarez-Valenzuela-Zanelli model.

Findings

Lagrangian includes a Chern-Simons term with an odd one-form field.

Second twist interprets the setup as describing massive Dirac particles.

Provides a generalization of the Alvarez-Valenzuela-Zanelli model.

Abstract

We develop a three-dimensional $\mathcal{N}=4$ theory of rigid supersymmetry describing the dynamics of a set of hypermultiplets $(\Lambda^{\alpha\alpha'\dot{\alpha}'}_I,\,\phi^{\alpha A}_I)$ on a curved AdS$_3$ worldvolume background, whose supersymmetry is captured by the supergroup ${\rm D}^2(2,1;\, \boldsymbol{\alpha})$. 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 ${\rm D}^2(2,1;\, \boldsymbol{\alpha})$ 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.