Quiver BPS Indices from Crystal Profiles
Abstract
We derive new exact formulae for elliptic genera in two spacetime dimensions with 𝒩≥ 2 supercharges, as well as their one- and zero-dimensional counterparts (for Witten indices and matrix-model partition functions). Our results are written as a discrete sum over geometric/combinatorial structures of crystals introduced previously by the authors. The contribution from each crystal may be expressed in terms of the boundary data of a finite substructure of the crystal called the molecules. Our results provide vast generalisations of the celebrated Nekrasov partition function enumerated by the Young diagrams, and uncover new combinatorics underlying the crystal melting. We also analyse the thermodynamic limit of crystals arising from two-dimensional 𝒩=(0,2) theories associated with toric Calabi-Yau fourfolds, where a projection of the Calabi-Yau geometry emerges in the limit.
Versions
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BibTeX
@misc{bao2026quiver,
title = {{Quiver BPS Indices from Crystal Profiles}},
author = {Jiakang Bao and Masahito Yamazaki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.03617},
eprint = {2607.03617},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.03617},
}
RIS
TY - UNPB
TI - Quiver BPS Indices from Crystal Profiles
AU - Jiakang Bao
AU - Masahito Yamazaki
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2607.03617
UR - https://arxiv.org/abs/2607.03617
AB - We derive new exact formulae for elliptic genera in two spacetime dimensions with 𝒩≥ 2 supercharges, as well as their one- and zero-dimensional counterparts (for Witten indices and matrix-model partition functions). Our results are written as a discrete sum over geometric/combinatorial structures of crystals introduced previously by the authors. The contribution from each crystal may be expressed in terms of the boundary data of a finite substructure of the crystal called the molecules. Our results provide vast generalisations of the celebrated Nekrasov partition function enumerated by the Young diagrams, and uncover new combinatorics underlying the crystal melting. We also analyse the thermodynamic limit of crystals arising from two-dimensional 𝒩=(0,2) theories associated with toric Calabi-Yau fourfolds, where a projection of the Calabi-Yau geometry emerges in the limit.
ER -