We revisit the consistency of torus partition functions in (1+1)$d$ fermionic conformal field theories, combining traditional ingredients of modular invariance/covariance with a modernized understanding of bosonization/fermionization dualities. Various lessons can be learned by simply examining the oft-ignored Ramond sector. For several extremal/kinky modular functions in the bootstrap literature, we can either rule out or identify the underlying theory. We also revisit the ${\cal N} = 1$ Maloney-Witten partition function by calculating the spectrum in the Ramond sector, and further extending it to include the modular sum of seed Ramond characters. Finally, we perform the full ${\cal N} = 1$ RNS modular bootstrap and obtain new universal results on the existence of relevant deformations preserving different amounts of supersymmetry.

中文翻译：

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拉蒙德部门的经验教训

我们在（1 + 1）$ d $铁离子共形场理论中重新讨论了环面分配函数的一致性，将模块化不变性/协方差的传统成分与对玻化/费米化对偶性的现代化理解相结合。通过简单地检查经常被忽略的拉蒙德部门，可以学到各种教训。对于bootstrap文献中的一些极端/变型模块化函数，我们可以排除或确定基础理论。我们还通过计算Ramond扇区的频谱，并进一步扩展它以包括种子Ramond字符的模和，来重新考虑$ {\ cal N} = 1 $ Maloney-Witten分区函数。最后，我们执行完整的$ {\ cal N} = 1 $ RNS模块化引导程序，并获得有关保留不同量的超对称性的相关变形的新的通用结果。