By leveraging the physics of the Higgs branch, we argue that the conformal central charges $a$ and $c$ of an arbitrary 4D $\mathcal{N}=2$ superconformal field theory (SCFT) are rational numbers. Our proof of the rationality of $c$ is conditioned on a well-supported conjecture about how the Higgs branch of an SCFT is encoded in its protected chiral algebra. To establish the rationality of $a$, we further rely on a widely believed technical assumption on the high-temperature limit of the superconformal index.

中文翻译：

---

四个维度的理性

通过利用希格斯分支的物理原理，我们认为共形中心电荷$A$和$C$任意 4D 的$\mathcal{氮}=2$超共形场论（SCFT）是有理数。我们的合理性证明$C$条件是关于 SCFT 的希格斯分支如何编码在其受保护的手性代数中的一个得到充分支持的猜想。确立合理性$A$，我们进一步依赖于人们广泛相信的关于超共形指数高温极限的技术假设。