Level repulsion in N $$ \mathcal{N} $$ = 4 super-Yang-Mills via integrability, holography, and the bootstrap

Abstract

Abstract We combine supersymmetric localization with the numerical conformal bootstrap to bound the scaling dimension and OPE coefficient of the lowest-dimension unprotected operator in N $$ \mathcal{N} $$ = 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.

Keywords

• AdS-CFT Correspondence
• Conformal and W Symmetry
• Nonperturbative Effects
• Supersymmetric Gauge Theory