We review and systematize two (analytic) bootstrap techniques in two-dimensional conformal field theories using the S-modular transformation. The first one gives universal results in asymptotic regimes by relating extreme temperatures. Along with the presentation of known results, we use this technique to also derive asymptotic formulae for the Zamolodchikov recursion coefficients which match previous conjectures from numerics and from Regge asymptotic analysis. The second technique focuses on intermediate temperatures. We use it to sketch a methodology to derive a bound on off-diagonal squared OPE coefficients, as well as to improve existing bounds on the spectrum in case of non-negative diagonal OPE coefficients.

中文翻译：

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S 转换引导程序的各个方面

我们使用 S 模变换回顾并系统化二维共形场理论中的两种（分析）引导技术。第一个通过关联极端温度给出渐近状态的普遍结果。随着已知结果的呈现，我们还使用这种技术推导出了 Zamolodchikov 递归系数的渐近公式，该公式与先前从数值和 Regge 渐近分析中得出的猜想相匹配。第二种技术侧重于中间温度。我们用它来勾画一种方法来推导非对角平方 OPE 系数的界限，以及在非负对角 OPE 系数的情况下改进频谱上的现有界限。