On the spectrum and structure constants of short operators in N=4 SYM at strong coupling
Luis F. Alday, Tobias Hansen, Joao A. Silva
Abstract
A bstract We study short operators in planar $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 SYM at strong coupling, for general spin and SO(6) symmetric traceless representations. At strong coupling their dimension grows like $$ \Delta \sim 2\sqrt{\delta }{\lambda}^{1/4} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>∆</mml:mtext> <mml:mo>~</mml:mo> <mml:mn>2</mml:mn> <mml:msqrt> <mml:mi>δ</mml:mi> </mml:msqrt> <mml:msup> <mml:mi>λ</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:math> 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 $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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 ≪ λ 1/4 .