On the spectrum and structure constants of short operators in N=4 SYM at strong coupling

Abstract

We study short operators in planar mathcal{N} = 4 SYM at strong coupling, for general spin and SO(6) symmetric traceless representations. At strong coupling their dimension grows like Delta sim 2sqrt{delta }{lambda}^{1/4} and their spectrum of degeneracies can be analysed by considering the massive spectrum of type II strings in flat space-time. We furthermore compute their structure constants with two arbitrary chiral primary operators. This is done by considering the four-point correlator of arbitrary chiral primary operators at strong coupling in planar mathcal{N} = 4 SYM, including the supergravity approximation plus the infinite tower of stringy corrections that contributes in the flat space limit. Our results are valid for generic rank n symmetric traceless representations of SO(6) and in particular for n ≫ 1, as long as n ≪ λ1/4.