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arXiv · 2407.21725

Proofs of Mizuno's Conjectures on Rank Three Nahm Sums of Index $(1,2,2)$

Boxue Wang·Liuquan Wang
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Abstract

Mizuno provided 15 examples of generalized rank three Nahm sums with symmetrizer $\mathrm{diag}(1,2,2)$ which are conjecturally modular. Using the theory of Bailey pairs and some $q$-series techniques, we establish a number of triple sum Rogers--Ramanujan type identities. These identities confirm the modularity of all of Mizuno's examples except that two Nahm sums are sums of modular forms of weights $0$ and $1$. We also prove Mizuno's conjectural modular transformation formulas for two vector-valued functions consisting of Nahm sums with symmetrizers $\mathrm{diag}(1,1,2)$ and $\mathrm{diag}(1,2,2)$.

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BibTeXRIS

Boxue Wang, Liuquan Wang. 2024-07-31. Proofs of Mizuno's Conjectures on Rank Three Nahm Sums of Index $(1,2,2)$. https://arxiv.org/abs/2407.21725

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