Modularity of Nahm Sums for the Tadpole Diagram
Number Theory
2023-01-12 v1
Abstract
We prove Rogers-Ramanujan type identities for the Nahm sums associated with the tadpole Cartan matrix of rank . 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.
Keywords
Cite
@article{arxiv.2301.04532,
title = {Modularity of Nahm Sums for the Tadpole Diagram},
author = {Antun Milas and Liuquan Wang},
journal= {arXiv preprint arXiv:2301.04532},
year = {2023}
}
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25 pages