Instanton R-matrix and W-symmetry

A bstract We study the relation between W 1 + ∞ algebra and Arbesfeld-Schiffmann­ Tsymbaliuk Yangian using the Maulik-Okounkov R-matrix. The central object linking these two pictures is the Miura transformation. Using the results of Nazarov and Sklyanin we find an explicit formula for the mixed R-ma...

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Bibliographic Details
Published inThe journal of high energy physics Vol. 2019; no. 12; pp. 1 - 58
Main Author Procházka, Tomáš
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 12.12.2019
Springer Nature B.V
Subjects
Classical and Quantum Gravitation
Elementary Particles
High energy physics
Instantons
Mathematical analysis
Matrix methods
Object linking & embedding
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Integrable Field Theories
Conformal and W Symmetry
Conformal Field Theory
Higher Spin Symmetry
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Summary:A bstract We study the relation between W 1 + ∞ algebra and Arbesfeld-Schiffmann­ Tsymbaliuk Yangian using the Maulik-Okounkov R-matrix. The central object linking these two pictures is the Miura transformation. Using the results of Nazarov and Sklyanin we find an explicit formula for the mixed R-matrix acting on two Fock spaces associated to two different asymptotic directions of the affine Yangian. Using the free field representation we propose an explicit identification of Arbesfeld-Schiffmann-Tsymbaliuk generators with the generators of Maulik-Okounkov Yangian. In the last part we use the Miura transformation to give a conformal field theoretic construction of conserved quantities and ladder operators in the quantum mechanical rational and trigonometric Calogero-Sutherland models on which a vector representation of the Yangian acts.
ISSN:1029-8479
DOI:10.1007/JHEP12(2019)099