Quiver Yangian and Supersymmetric Quantum Mechanics

2020/08/16 by Dmitry Galakhov, Masahito Yamazaki · 1 voice · 51 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Brane #Equivariant map #Instanton #Mathematical physics #Mathematics #Moduli space #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum #Quantum mechanics #Quantum statistical mechanics #Quiver #Supersymmetric quantum mechanics #Yangian #hep-th #math.AG #math.QA #math.RT

paper · pdf · doi:10.1007/s00220-022-04490-y

published in Communications in Mathematical Physics 396(2), 713-785 (Springer Science+Business Media)

arxiv published 2020/08/16 · arxiv updated 2020/08/22 · openalex publication_date 2022/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

The statistical model of crystal melting represents BPS configurations of D-branes on a toric Calabi-Yau three-fold. Recently it has been noticed that an infinite-dimensional algebra, the quiver Yangian, acts consistently on the crystal-melting configurations. We physically derive the algebra and its action on the BPS states, starting with the effective supersymmetric quiver quantum mechanics on the D-brane worldvolume. This leads to remarkable combinatorial identities involving equivariant integrations on the moduli space of the quantum mechanics, which can be checked by numerical computations.

Citations

• Instanton moduli spaces and \mathscr W-algebras
• Phases Of N=2 Theories In 1+1 Dimensions With Boundary
• Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras
• Algebras, BPS states, and strings
• MODULI OF REPRESENTATIONS OF FINITE DIMENSIONAL ALGEBRAS
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Supersymmetry and Morse theory
• Electric-magnetic duality and the geometric Langlands program
• Wall-Crossing, Free Fermions and Crystal Melting
• N=2 Quantum Field Theories and Their BPS Quivers
• Wall crossing in local Calabi Yau manifolds
• Refined open non-commutative Donaldson-Thomas invariants for small crepant resolutions
• Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds

Cited by

• Quiver BPS Indices from Crystal Profiles

Discussions

• "Quiver Yangian and Supersymmetric Quantum Mechanics" (Dmitry Galakhov, Masahito Yamazaki) https://arxiv.org/abs/2008.07006 [bsky, 0 points, 0 comments]

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