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A matrix integral solution to two-dimensional $$W_ p$$-gravity. (English) Zbl 0756.35074
Based on E. Witten’s computations [IASSNS-HEP-91/24 (1991), preprint] and on V. Kac and A. Schwarz’s observation [Phys. Lett. B. 257, 329-334 (1991)] the authors of this article explicitly develop a matrix model for arbitrary “$$p$$” and present a complete proof for $$p\leq 3$$. It is also pointed out that the general proof hinges on the observation that a certain partial differential equation applied to the ratio $$\tau_ p^{(N)}(t)=\tilde A_ p^{(N)}(\Theta)/\tilde B_ p^{(N)}(\Theta)$$ produces at once the stress-energy tensor for $$W_ p$$-gravity and this should have an interesting physical interpretation.
Reviewer: C.Dariescu (Iaşi)

##### MSC:
 35Q53 KdV equations (Korteweg-de Vries equations) 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 53D50 Geometric quantization
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