Speaker
Description
Harmonic ${\cal N}=2$ superspace was discovered in 1984 as the powerful unique tool of the geometric superfield off-shell description of ${\cal N}=2, 4D$ supersymmetric field theories with the maximal spins 1, 2, and 1/2 (${\cal N}=2$ Yang-Mills theories, supergravity and matter hypermultiplets). Later on, harmonic superspace methods were successfully applied to set up the previously unknown off-shell formulations of the gauge ${\cal N}=2$ higher-spin theories in terms of the unconstrained analytic ${\cal N}=2$ superfields, in both conformal and non-conformal cases. Based on a recent work with Nikita Zaigraev, I show how to deduce ${\cal N}=2$ higher-spin theories on AdS$_4$ superbackground, proceeding from the harmonic superspace realizations of ${\cal N}=2$ superconformal symmetry $SU(2,2|2)$.The basic idea is to introduce a constant isotriplet $c^{ik}$ that breaks $SU(2,2|2)$ down to AdS$_4$ supersymmetry $OSp(2|4;R)$. The superfield Weyl transformation relating ordinary ${\cal N}=2$ harmonic superspace to its AdS$_4$ deformation is defined and $OSp(2|4;R)$-invariant action of massive hypermultiplet is derived, employing this transform.
