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- W2070518778 abstract "We introduce a new 1-matrix model with arbitrary potential and the matrix-valued background field. Its partition function is a $tau$-function of KP-hierarchy, subjected to a kind of ${cal L}_{-1}$-constraint. Moreover, partition function behaves smoothly in the limit of infinitely large matrices. If the potential is equal to $X^{K+1}$, this partition function becomes a $tau$-function of $K$-reduced KP-hierarchy, obeying a set of ${cal W} _K$-algebra constraints identical to those conjectured in cite{FKN91} for double-scaling continuum limit of $(K-1)$-matrix model. In the case of $K=2$ the statement reduces to the early established cite{MMM91b} relation between Kontsevich model and the ordinary $2d$ quantum gravity . Kontsevich model with generic potential may be considered as interpolation between all the models of $2d$ quantum gravity with $c<1$ preserving the property of integrability and the analogue of string equation." @default.
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- W2070518778 date "1992-08-01" @default.
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- W2070518778 title "Towards unified theory of 2d gravity" @default.
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- W2070518778 doi "https://doi.org/10.1016/0550-3213(92)90521-c" @default.
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