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arXiv · 2301.04532

Modularity of Nahm Sums for the Tadpole Diagram

Antun Milas·Liuquan Wang
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Abstract

We prove Rogers-Ramanujan type identities for the Nahm sums associated with the tadpole Cartan matrix of rank $3$. These identities reveal the modularity of these sums, and thereby we confirm a conjecture of Penn, Calinescu and the first author in this case. We show that these Nahm sums together with some shifted sums can be combined into a vector-valued modular function on the full modular group. We also present some conjectures for a general rank.

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Antun Milas, Liuquan Wang. 2023-01-11. Modularity of Nahm Sums for the Tadpole Diagram. https://arxiv.org/abs/2301.04532

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