Integrable System Constructed out of Two Interacting Superconformal Fields

Details Integrable System Constructed out of Two Interacting Superconformal Fields Integrable System Constructed out of Two Interacting Superconformal Fields

1997-02-11

arxiv.org/abs/hep-th/9702090v1

J.Phys.A30:7935-7944,1997

Physics

High Energy Physics

High Energy Physics - Theory

15 pages,latex

Scientific paper

10.1088/0305-4470/30/22/027

We describe how it is possible to introduce the interaction between superconformal fields of the same conformal dimensions. In the classical case such construction can be used to the construction of the Hirota - Satsuma equation. We construct supersymmetric Poisson tensor for such fields, which generates a new class of Hamiltonin systems. We found Lax representation for one of equation in this class by supersymmetrization Lax operator responsible for Hirota - Satsuma equation. Interestingly our supersymmetric equation is not reducible to classical Hirota - Satsuma equation. We show that our generalized system is reduced to the one of the supersymmetric KDV equation (a=4) but in this limit integrals of motion are not reduced to integrals of motion of the supersymmetric KdV equation.

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