Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1992-04-24
Phys.Lett. B288 (1992) 38-46
Physics
High Energy Physics
High Energy Physics - Theory
11 pp REVISED (minor changes in the presentation, easier to read)
Scientific paper
10.1016/0370-2693(92)91951-5
A direct relation between the conformal formalism for 2d-quantum gravity and the W-constrained KP hierarchy is found, without the need to invoke intermediate matrix model technology. The Kontsevich-Miwa transform of the KP hierarchy is used to establish an identification between W constraints on the KP tau function and decoupling equations corresponding to Virasoro null vectors. The Kontsevich-Miwa transform maps the $W^{(l)}$-constrained KP hierarchy to the $(p^\prime,p)$ minimal model, with the tau function being given by the correlator of a product of (dressed) $(l,1)$ (or $(1,l)$) operators, provided the Miwa parameter $n_i$ and the free parameter (an abstract $bc$ spin) present in the constraints are expressed through the ratio $p^\prime/p$ and the level $l$.
~Gato-Rivera B.
~Semikhatov ~M. A.
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