Conformal field theory, solitons, and elliptic Calogero--Sutherland models

Abstract

We construct a non-chiral conformal field theory (CFT) on the torus that accommodates a second quantization of the elliptic Calogero-Sutherland (eCS) model. We show that the CFT operator that provides this second quantization defines, at the same time, a quantum version of a soliton equation called the non-chiral intermediate long-wave (ncILW) equation. We also show that this CFT operator is a second quantization of a generalized eCS model which can describe arbitrary numbers of four different kinds of particles; we propose that these particles can be identified with solitons of the quantum ncILW equation.

56 pages

References in corpus (7)

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• The classical hydrodynamics of the Calogero-Sutherland model
• On the non-chiral intermediate long wave equation II: periodic case
• The Coleman correspondence at the free fermion point
• The Quantum Hydrodynamics of the Sutherland Model
• Higher order deformed elliptic Ruijsenaars operators
• Elliptic soliton solutions of the spin non-chiral intermediate long-wave equation