English

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 33. 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