2023/12/04 by Arpit Das, Das, Arpit
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Meromorphic and Entire Functions #Number Theory (math.NT) #Quantum Algebra (math.QA) #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2312.02129
openalex publication_date 2023/12/04 · openalex created_date 2023/12/06 · openalex updated_date 2026/07/28
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∈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: ℓ. 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 ℓ make the character in-admissible implying that the central charge for admissible character has to be a multiple of 8.