Higher spin symmetry and = 4 SYM

We assemble the spectrum of single-trace operators in free = 4 SU(N) SYM theory into irreducible representations of the Higher Spin symmetry algebra (2,2|4). Higher Spin representations or YT-pletons are associated to Young tableaux (YT) corresponding to representations of the symmetric group compatible with the cyclicity of color traces. After turning on interactions g_YM≠0, YT-pletons decompose into infinite towers of representations of the superconformal algebra (2,2|4) and anomalous dimensions are generated. We work out the decompositions of tripletons with respect to the = 4 superconformal algebra (2,2|4) and compute their anomalous dimensions to lowest non-trivial order in g_YM²Nat large N. We then focus on operators/states sitting in semishort multiplets of (2,2|4). By passing them through a semishort-sieve that removes superdescendants, we derive compact expressions for the partition function of semishort primaries.