Towards unified theory of 2d gravity

S. Kharchev, A. Marshakov, A. Mironov, A. Morozov, A. Zabrodin

Research output: Contribution to journalArticlepeer-review

128 Citations (Scopus)


We introduce a new one-matrix model with arbitrary potential and matrix-valued background field. Its partition function is a τ-function of KP hierarchy, subjected to a kind of L-1 constraint. Moreover, the partition function behaves smoothly in the limit of infinitely large matrices. If the potential is equal to XK + 1, this partition function becomes a τ-function of K-reduced KP hierarchy, obeying a set of WK algebra constraints identical to those conjectured for the double-scaling continuum limit of the (K - 1) matrix model. In the case of K = 2 the statement reduces to an earlier established relation between the Kontsevich model and ordinary 2d quantum gravity. The Kontsevich model with generic potential may be considered as an interpolation between all the models of 2d quantum gravity, with c < 1 preserving the property of integrability and the analogue of the string equation.

Original languageEnglish
Pages (from-to)181-240
Number of pages60
JournalNuclear Physics B
Issue number1-2
Publication statusPublished - 3 Aug 1992
Externally publishedYes


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