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arXiv · 2602.14483

Modular Nahm sums for symmetrizable matrices of indices $({2,\ldots, 2},1)$ and $({1,\ldots, 1},2)$

Julia Q. D. Du·Kathy Q. Ji·Erin Y. Y. Shen·Clara X. Y. Xu
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Abstract

In this paper, we present three families of modular Nahm sums for symmetrizable matrices with arbitrary rank $r\geq 2$ of indices $({2,\ldots, 2},1)$ and $({1,\ldots, 1},2)$. Specifically, the cases corresponding to $r = 2$ and $r = 3$ of these families have been previously demonstrated by Mizuno, Warnaar, and B. Wang-L. Wang. Building upon these three families, we construct two vector-valued automorphic forms, one of which is a vector-valued modular function when $r$ is odd.

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Julia Q. D. Du, Kathy Q. Ji, Erin Y. Y. Shen, Clara X. Y. Xu. 2026-03-07. Modular Nahm sums for symmetrizable matrices of indices $({2,\ldots, 2},1)$ and $({1,\ldots, 1},2)$. https://arxiv.org/abs/2602.14483

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