Meromorphic CFTs have central charges c = 8$\mathbb{N}$: a proof based on the MLDE approach and Rademacher series

Arpit Das

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arXiv · 2312.02129

Meromorphic CFTs have central charges c = 8$\mathbb{N}$: a proof based on the MLDE approach and Rademacher series

Arpit Das

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Abstract

In this short note, we present a simple and elementary proof that meromorphic conformal field theories (CFTs) have central charges of the form: $c=8N$ with $N\in\mathbb{N}$ (the set of natural numbers) using the modular linear differential equations (MLDEs) approach. We first set up the 1-character MLDE for arbitrary value of the Wronskian index: $\ell$. From this we get the general form of the meromorphic CFT's character. We then study its modular transformations and the asymptotic value of it's Fourier coefficients -- using Rademacher series -- to conclude that odd values of $\ell$ make the character in-admissible implying that the central charge for admissible character has to be a multiple of 8.

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Arpit Das. 2023-12-04. Meromorphic CFTs have central charges c = 8$\mathbb{N}$: a proof based on the MLDE approach and Rademacher series. https://arxiv.org/abs/2312.02129

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