<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"> <mml:mrow> <mml:mi mathvariant="script">N</mml:mi> <mml:mo linebreak="goodbreak">=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> AdS hypermultiplets in harmonic superspa

We present the harmonic superspace formulation of N = 2 hypermultiplet in AdS 4 background, starting from the proper realization of 4 D , N = 2 superconformal group S U ( 2 , 2 | 2 ) on the analytic subspace coordinates. The key observation is that N = 2 AdS 4 supergroup O S p ( 2 | 4 ) can be embedded as a subgroup in the superconformal group through introducing a constant symmetric matrix c ( i j ) and identifying the AdS supercharge as Ψ α i = Q α i + c i k S k α , with Q and S being generators of the standard and conformal 4 D , N = 2 supersymmetries. Respectively, the AdS cosmological constant is given by the square of c ( i j ) , Λ = − 12 c i j c i j . We construct the O S p ( 2 | 4 ) invariant hypermultiplet mass term by adding, to the coordinate AdS transformations, a piece realized as an extra S O ( 2 ) rotation of the hypermultiplet superfield. It is analogous to the central charge x 5 transformation of flat 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 O S p ( 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 N = 2 hyper Kähler sigma models. We find the proper redefinition of θ coordinates ensuring the AdS-covariant form of the analytic superfield component expansions.