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arXiv · 2606.13590

Some new modular Nahm sums of ranks 3 and 4

Zhineng Cao·Liuquan Wang
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Abstract

We discover six new families of modular Nahm sums in ranks 3 and 4. Two of them are rank three sums obtained by modifying two of Zagier's rank three examples. Three rank four families are derived by applying the lift-dual operation to the rank three tadpole Nahm sums studied by Milas and Wang, while the other rank four family is found by the constant term method. To prove modularity, we establish Rogers-Ramanujan type identities that express these Nahm sums as infinite products which are modular.

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Zhineng Cao, Liuquan Wang. 2026-06-11. Some new modular Nahm sums of ranks 3 and 4. https://arxiv.org/abs/2606.13590

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