Simple variables for AdS5 x S5 superspace

We introduce simple variables for describing the AdS(5) x S-5 superspace, i.e. PSU(2,2 vertical bar 4)/SO(4,1)xSO(5). The idea is to embed the coset superspace into a space described by variables which are in linear (ray) representations of the supergroup PSU(2, 2 vertical bar 4) by imposing certain supersymmetric quadratic constraints (up to two overall U(1) factors). The construction can be considered as a supersymmetric generalisation of the elementary realisations of the AdS(5) and the S-5 spaces by the SO(4,2) and SO(6) invariant quadratic constraints on two six-dimensional flat spaces. (C) 2015 The Author. Published by Elsevier B.V.