Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues

Fuente: arXiv
Guardado en:
Detalles Bibliográficos
Autores principales: Bao, Jiakang, Yamazaki, Masahito
Formato: Preprint
Publicado: 2025
Materias:
Acceso en línea:
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
_version_ 1866916713866461184
author Bao, Jiakang
Yamazaki, Masahito
author_facet Bao, Jiakang
Yamazaki, Masahito
contents We construct statistical mechanical models of crystal melting describing the flavoured Witten indices of $\mathcal{N}\ge 2$ supersymmetric quiver gauge theories. Our results can be derived from the Jeffrey-Kirwan (JK) residue formulas, and generalize the previous results for quivers corresponding to toric Calabi-Yau threefolds and fourfolds to a large class of quivers satisfying the no-overlap condition, including those corresponding to some non-toric Calabi-Yau manifolds. We construct new quiver algebras which we call the double quiver Yangians/algebras, as well as their representations in terms of the aforementioned crystals. For theories with four supercharges, we compare the double quiver algebras with the existing quiver Yangians/BPS algebras, which we show can also be constructed from the JK residues. For theories with two supercharges, the double quiver algebras provide an algebraic description of the BPS states, including the information of the fixed points and their relative coefficients in the full partition functions.
format Preprint
id arxiv_https___arxiv_org_abs_2501_03365
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
Bao, Jiakang
Yamazaki, Masahito
High Energy Physics - Theory
Mathematical Physics
Algebraic Geometry
Combinatorics
We construct statistical mechanical models of crystal melting describing the flavoured Witten indices of $\mathcal{N}\ge 2$ supersymmetric quiver gauge theories. Our results can be derived from the Jeffrey-Kirwan (JK) residue formulas, and generalize the previous results for quivers corresponding to toric Calabi-Yau threefolds and fourfolds to a large class of quivers satisfying the no-overlap condition, including those corresponding to some non-toric Calabi-Yau manifolds. We construct new quiver algebras which we call the double quiver Yangians/algebras, as well as their representations in terms of the aforementioned crystals. For theories with four supercharges, we compare the double quiver algebras with the existing quiver Yangians/BPS algebras, which we show can also be constructed from the JK residues. For theories with two supercharges, the double quiver algebras provide an algebraic description of the BPS states, including the information of the fixed points and their relative coefficients in the full partition functions.
title Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
topic High Energy Physics - Theory
Mathematical Physics
Algebraic Geometry
Combinatorics
url https://arxiv.org/abs/2501.03365