Towards unified theory of 2 d gravity

  title={Towards unified theory of 2 d gravity},
  author={S. Kharchev and Andrey I. Marshakov and Andrei Mironov and Alexei Morozov},
We introduce a new 1-matrix model with arbitrary potential and the matrix-valued background field. Its partition function is a τ-function of KP-hierarchy, subjected to a kind of 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 τ-function of K-reduced KP-hierarchy, obeying a set of W K-algebra constraints identical to those conjectured in [1] for double-scaling… CONTINUE READING
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