Abstract
Based on the conformal higher-spin superalgebras shsc χ(4 ∥ 1) constructed previously by us, superconformal higher-spin theory in four-dimensional space-time is constructed in the cubic order. The theory contains an infinite tower of SU(2,2 ∥ 1)-supermultiplets with all conformal higher-spin fields interacting among themselves and with conformal supergravity.
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