Level repulsion in $$ \mathcal{N} $$ = 4 super-Yang-Mills via integrability, holography, and the bootstrap
Shai M. Chester, Ross Dempsey, Silviu S. Pufu
Abstract
A bstract We combine supersymmetric localization with the numerical conformal bootstrap to bound the scaling dimension and OPE coefficient of the lowest-dimension unprotected operator in $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 SU( N ) super-Yang-Mills theory for a wide range of N and Yang-Mills couplings g YM . We find that our bounds are approximately saturated by weak coupling results at small g YM . Furthermore, at large N our bounds interpolate between integrability results for the Konishi operator at small g YM and strong-coupling results, including the first few stringy corrections, for the lowest-dimension double-trace operator at large g YM . In particular, our scaling dimension bounds describe the level splitting between the single- and double-trace operators at intermediate coupling.