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

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arxiv 2205.00818 v2 pith:GCCBQ75J submitted 2022-05-02 hep-th

classification hep-th
keywords equationmodularschuranomalyindexmathcalsuper-yang-millsambiguity
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Interior zeros of supersymmetric indices

    hep-th 2026-07 accept novelty 7.0 of 10

    Interior zeros of a supersymmetric index exist iff its arithmetic coefficients δ(ν) grow exponentially at rate set by the nearest zero, detectable from finitely many q-series terms.

  2. A landscape of 4d N=1 SCFTs with a=c

    hep-th 2024-12 conditional novelty 6.0 of 10

    Starting from an SU(3) gauging of three D2(SU(3)) Argyres-Douglas theories with an adjoint chiral multiplet, the authors map the tree of relevant deformations that preserve a=c and find 21 fixed points, including flow...

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