Modular anomaly equation for Schur index of $$ \mathcal{N} $$ = 4 super-Yang-Mills
A bstract We propose a novel modular anomaly equation for the unflavored Schur index in the $$ \mathcal{N} $$ 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 exa...
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| Published in: | The journal of high energy physics Vol. 2022; no. 8 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
01-08-2022
|
| Online Access: | Get full text |
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| Summary: | A
bstract
We propose a novel modular anomaly equation for the unflavored Schur index in the
$$ \mathcal{N} $$
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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| ISSN: | 1029-8479 1029-8479 |
| DOI: | 10.1007/JHEP08(2022)049 |