Large\bf $ w_{1+\infty} $--type constraints in two--matrix and Kontsevich model--different approach

Details Large\bf $ w_{1+\infty} $--type constraints in two--matrix and Kontsevich model--different approach Large\bf $ w_{1+\infty} $--type constraints in two--matrix and Kontsevich model--different approach

1992-11-29

arxiv.org/abs/hep-th/9211131v1

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 8p

Scientific paper

The technique of $Q$-polinomials are used to derive the $w$- constraints in the two-matrix and Kontsevich-like model at finite $N$. These constraints are closed and form Lie algebra. They are associated with the matrices, $\lambda ^n{\partial}_\lambda^m$ with $n,m\geq 0$. In the case of two-matrix model they can be reduced to the $W$-constraints of \cite{8}. For the case of Kontsevich-like model and two-matrix model with the finite polinomial potential, the number of constraints are limited by the power of the finite matrix potential i.e. the spin of $w$-s coincide with that power. This statement is the natural consequence of the form of constraints.

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