Higher Spin Symmetry and N=4 SYM

TL;DR

This paper explores the spectrum of single-trace operators in free N=4 SYM, organizing them into higher spin algebra representations, analyzing their decomposition upon interaction, and deriving partition functions for semishort primaries.

Contribution

It provides a detailed decomposition of YT-pletons into superconformal representations and computes their anomalous dimensions at large N, advancing understanding of operator spectra in N=4 SYM.

Findings

Decomposition of tripletons into superconformal algebra representations.

Calculation of one-loop anomalous dimensions at large N.

Compact expressions for partition functions of semishort primaries.

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.