Quiver Yangian and Supersymmetric Quantum Mechanics

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 it...

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Bibliographic Details
Published inCommunications in mathematical physics Vol. 396; no. 2; pp. 713 - 785
Main Authors Galakhov, Dmitry, Yamazaki, Masahito
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2022
Springer Nature B.V
Subjects
Branes
Classical and Quantum Gravitation
Combinatorial analysis
Complex Systems
Configurations
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum mechanics
Quantum Physics
Relativity Theory
Statistical models
Supersymmetry
Theoretical
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Summary: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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-022-04490-y