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

Abstract

Abstract We study short operators in planar $$ \mathcal{N} $$ N = 4 SYM at strong coupling, for general spin and SO(6) symmetric traceless representations. At strong coupling their dimension grows like $$ \Delta \sim 2\sqrt{\delta }{\lambda}^{1/4} $$ ∆ ~ 2 δ λ 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 $$ \mathcal{N} $$ 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.