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

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