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Crystal melting, BPS quivers and plethystics

Bao, J. ORCID: 0000-0002-9583-1696, He, Y-H. ORCID: 0000-0002-0787-8380 & Zahabi, A. (2022). Crystal melting, BPS quivers and plethystics. Journal of High Energy Physics (JHEP)(6), 16. doi: 10.1007/JHEP06(2022)016

Abstract

We study the refined and unrefined crystal/BPS partition functions of D6-D2-D0 brane bound states for all toric Calabi-Yau threefolds without compact 4-cycles and some non-toric examples. They can be written as products of (generalized) MacMahon functions. We check our expressions and use them as vacuum characters to study the gluings. We then consider the wall crossings and discuss possible crystal descriptions for different chambers. We also express the partition functions in terms of plethystic exponentials. For ℂ3 and tripled affine quivers, we find their connections to nilpotent Kac polynomials. Similarly, the partition functions of D4-D2-D0 brane bound states can be obtained by replacing the (generalized) MacMahon functions with the inverse of (generalized) Euler functions.

Publication Type: Article
Additional Information: This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Publisher Keywords: Brane Dynamics in Gauge Theories, Differential and Algebraic Geometry, Gauge Symmetry
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Departments: School of Science & Technology > Mathematics
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