Bootstrapping $\mathcal{N}=4$ super-Yang-Mills on the conformal manifold

Abstract

We combine supersymmetric localization results with numerical bootstrap techniques to compute upper bounds on the low-lying CFT data of $\mathcal{N}=4$ super-Yang-Mills theory as a function of the complexified gauge coupling $\tau$. In particular, from the stress tensor multiplet four-point function, we extract the scaling dimension of the lowest-lying unprotected scalar operator and its OPE coefficient. While our method can be applied in principle to any gauge group $G$, we focus on $G=SU(2)$ and $SU(3)$ for simplicity. At weak coupling, the upper bounds we find are very close to the corresponding four-loop results. We also give preliminary evidence that these upper bounds become small islands under reasonable assumptions.

31 pages plus appendices, 13 figures, v3 expanded discussion of integration region

Cited by in corpus (1)

• Harnessing S-Duality in $\mathcal{N}=4$ SYM & Supergravity as $SL(2,\mathbb{Z})$-Averaged Strings