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Minimal Models from W-Constrained Hierarchies via the Kontsevich-Miwa Transform

B. ~Gato-Rivera·A. ~M. ~Semikhatov
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Abstract

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 $l$.

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B. ~Gato-Rivera, A. ~M. ~Semikhatov. 1992-05-19. Minimal Models from W-Constrained Hierarchies via the Kontsevich-Miwa Transform. https://doi.org/10.1016/0370-2693(92)91951-5

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