Multiple chordal SLE(κ) and quantum Calogero-Moser system

2025/05/22 by Jiaxin Zhang, Zhang, Jiaxin
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum many-body systems

paper · pdf · doi:10.48550/arxiv.2505.16093

openalex publication_date 2025/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study multiple chordal SLE(κ) systems in a simply connected domain Ω, where z₁, …, z_n ∈ ∂ Ω are boundary starting points and q ∈ ∂ Ω is an additional marked boundary point. As a consequence of the domain Markov property and conformal invariance, we show that the presence of the marked boundary point q gives rise to a natural equivalence relation on partition functions. While these functions are not necessarily conformally covariant, each equivalence class contains a conformally covariant representative. Building on the framework introduced in \citeDub07, we demonstrate that in the ℍ-uniformization with q = ∞, the partition functions satisfy both the null vector equations and a dilatation equation with scaling exponent d. Using techniques from the Coulomb gas formalism in conformal field theory, we construct two distinct families of solutions, each indexed by a topological link pattern of type (n, m) with 2m ≤ n. In the special case Ω= ℍ and q = ∞, we further show that these partition functions correspond to eigenstates of the quantum Calogero-Moser system, thereby extending the known correspondence beyond the standard (2n, n) setting.

Citations

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Related

• Multiple radial SLE(κ) and quantum Calogero-Sutherland system
• Multiple chordal SLE(0) and classical Calogero-Moser system
• Conformal welding of quantum disks and multiple SLE: the non-simple case
• Multiple SLEs for κ∈ (0,8): Coulomb gas integrals and pure partition functions
• SLE and the free field: Partition functions and couplings