Multiple chordal SLE(0) and classical Calogero-Moser system

2025/05/22 by Zhang, Jiaxin · 2 citations
#Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.2505.17129

Abstract

We develop a general theory of multiple chordal SLE(0) systems of type (n, m) for positive integers n and m with m ≤ \lfloor n/2 \rfloor, extending the construction of~\citeABKM20 beyond the previously studied case n = 2m. By applying integrals of motion associated with the Loewner evolution, we show that, in the ℍ-uniformization with the marked point q = ∞, the traces of type (n, m) multiple chordal SLE(0) systems correspond to the real locus of real rational functions with n real simple critical points, m simple poles, and a pole of order n - 2m + 1 at infinity. Furthermore, we demonstrate that, under a common capacity parametrization, the Loewner dynamics evolve according to the classical Calogero-Moser Hamiltonian.

Citations

• Multiple radial SLE(0) and classical Calogero-Sutherland System
• Conformal welding of quantum disks and multiple SLE: the non-simple case
• Conformal field theory on the Riemann sphere and its boundary version for SLE
• Pole dynamics and an integral of motion for multiple SLE(0)
• Calculus of conformal fields on a compact Riemann surface
• SLE and Virasoro representations: localization
• Imaginary geometry IV: interior rays, whole-plane reversibility, and\n space-filling trees
• Standard Modules, Induction and the Temperley-Lieb Algebra
• Imaginary Geometry I: Interacting SLEs
• Gaussian free field and conformal field theory
• SLE and the free field: Partition functions and couplings
• Contour lines of the two-dimensional discrete Gaussian free field
• Contour lines of the two-dimensional discrete Gaussian free field
• Conformally invariant scaling limits (an overview and a collection of problems)
• The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz
• Rational functions with real critical points and the B. and M. Shapiro conjecture in real enumerative geometry
• Asymptotic solutions to the sl₂ KZ equation and the intersection of Schubert classes
• Rational functions with prescribed critical points
• Critical points of functions, sl₂ representations, and Fuchsian differential equations with only univalued solutions
• Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials

Cited by

• Asymptotic of Coulomb gas integral, Temperley-Lieb type algebras and pure partition functions
• Multiple chordal SLE(κ) and quantum Calogero-Moser system

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