We reviewed the recent developments in the study of conformal field theories in generic space time dimensions using the methods of the conformal bootstrap, in its analytic aspect. These techniques are solely based on symmetries, particularly on the analytic structure and in the associativity of the operator product expansion. We focused on two applications of the analytic conformal bootstrap: the study of the $ϵ$ expansion of the Wilson–Fisher model via the introduction of a dispersion relation and the large N expansion of the maximally supersymmetric Super Yang–Mills theory in four dimensions.

中文翻译：

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分析保形 Bootstrap 的两个应用：快速指南

我们回顾了使用共形自举方法在一般时空维度上的共形场论研究的最新进展，在其分析方面。这些技术完全基于对称性，特别是基于解析结构和算子乘积展开的结合性。我们专注于分析保形自举的两个应用：研究$\epsilon$通过在四个维度上引入色散关系和最大超对称超级杨-米尔斯理论的大N扩展来扩展 Wilson-Fisher 模型。