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.

• Received 2 October 2023
• Accepted 18 April 2024

DOI:https://doi.org/10.1103/PhysRevD.109.105018

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Published by the American Physical Society