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

Shai M. Chester; Ross Dempsey; Silviu S. Pufu

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arXiv · 2111.07989

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

Shai M. Chester·Ross Dempsey·Silviu S. Pufu

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Abstract

We combine supersymmetric localization results with numerical bootstrap techniques to compute upper bounds on the low-lying CFT data of ${\cal N} = 4$ 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.

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Shai M. Chester, Ross Dempsey, Silviu S. Pufu. 2021-11-15. Bootstrapping $\mathcal{N}=4$ super-Yang-Mills on the conformal manifold. https://arxiv.org/abs/2111.07989

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