$\mathcal{N}=2$ AdS hypermultiplets in harmonic superspace

Abstract

We present the harmonic superspace formulation of $\mathcal{N}=2$ hypermultiplet in AdS${}_4$ background, starting from the proper realization of $4D,\mathcal{N}=2$ superconformal group $SU(2,2|2)$ on the analytic subspace coordinates. The key observation is that $\mathcal{N}=2$ AdS${}_4$ supergroup $OSp(2|4)$ can be embedded as a subgroup in the superconformal group through introducing a constant symmetric matrix $c^{(ij)}$ and identifying the AdS supercharge as $\hat{I}{¨}_{\hat{I}}^i\pm =Q_{\hat{I}}^i\pm +c^{ik}{S}_{k\hat{I}\pm }$, with $Q$ and $S$ being generators of the standard and conformal $4D,\mathcal{N}=2$ supersymmetries. Respectively, the AdS cosmological constant is given by the square of $c^{(ij)}$, $\hat{I}›=-12c^{ij}{c}_{ij}$. We construct the $OSp(2|4)$ invariant hypermultiplet mass term by adding, to the coordinate AdS transformations, a piece realized as an extra $SO(2)$ rotation of the hypermultiplet superfield. It is analogous to the central charge $x^5$ transformation of flat $\mathcal{N}=2$ supersymmetry and turns into the latter in the super Minkowski limit. As another new result, we explicitly construct the superfield Weyl transformation to the $OSp(2|4)$ invariant AdS integration measure over the analytic superspace, which provides, in particular, a basis for unconstrained superfield formulations of the AdS${}_4$-deformed $\mathcal{N}=2$ hyper Kähler sigma models. We find the proper redefinition of $\hat{I}¸$ coordinates ensuring the AdS-covariant form of the analytic superfield component expansions.

0 + 17 pages, typos corrected, references added; extended version of the article published in PLB