The Zero Curvature Formulation of TB, sTB Hierarchy and Topological Algebras

Details The Zero Curvature Formulation of TB, sTB Hierarchy and Topological Algebras The Zero Curvature Formulation of TB, sTB Hierarchy and Topological Algebras

1995-11-13

arxiv.org/abs/hep-th/9511091v1

Mod.Phys.Lett. A11 (1996) 1317-1330

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, plain Latex, no figures

Scientific paper

A particular dispersive generalization of long water wave equation in $1+1$ dimensions, which is important in the study of matrix models without scaling limit, known as two--Boson (TB) equation, as well as the associated hierarchy has been derived from the zero curvature condition on the gauge group $SL(2,R)\otimes U(1)$. The supersymmetric extension of the two--Boson (sTB) hierarchy has similarly been derived from the zero curvature condition associated with the gauge supergroup $OSp(2|2)$. Topological algebras arise naturally as the second Hamiltonian structure of these classical integrable systems, indicating a close relationship of these models with 2d topological field theories.

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