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arXiv · hep-th/0405057

Higher Spin Symmetry and N=4 SYM

Niklas Beisert·Massimo Bianchi·Jose F. Morales·Henning Samtleben
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Abstract

We assemble the spectrum of single-trace operators in free N=4 SU(N) SYM theory into irreducible representations of the Higher Spin symmetry algebra hs(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, YT-pletons decompose into infinite towers of representations of the superconformal algebra PSU(2,2|4) and anomalous dimensions are generated. We work out the decompositions of tripletons with respect to the N=4 superconformal algebra PSU(2,2|4) and compute their one anomalous dimensions at large N. We then focus on operators/states sitting in semishort superconformal multiplets. By passing them through a semishort-sieve that removes superdescendants, we derive compact expressions for the partition function of semishort primaries.

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Niklas Beisert, Massimo Bianchi, Jose F. Morales, Henning Samtleben. 2004-09-10. Higher Spin Symmetry and N=4 SYM. https://doi.org/10.1088/1126-6708%2F2004%2F07%2F058

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