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arXiv · 2205.00818

Modular Anomaly Equation for Schur Index of $\mathcal{N}=4$ Super-Yang-Mills

Min-xin Huang
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Abstract

We propose a novel modular anomaly equation for the unflavored Schur index in the $\mathcal{N}=4$ $SU(N)$ super-Yang-Mills theory. The vanishing conditions overdetermine the modular ambiguity ansatz from the equation, thus together they are sufficient to recursively compute the exact Schur indices for all $SU(N)$ gauge groups. Using the representations as MacMahon's generalized sum-of-divisors functions and Jacobi forms, we then prove our proposal as well as elucidate a general formula conjectured by Pan and Peelaers.

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Min-xin Huang. 2022-05-02. Modular Anomaly Equation for Schur Index of $\mathcal{N}=4$ Super-Yang-Mills. https://doi.org/10.1007/jhep08(2022)049

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