Integrable Discrete Linear Systems and One-Matrix Model

Details Integrable Discrete Linear Systems and One-Matrix Model Integrable Discrete Linear Systems and One-Matrix Model

1991-09-27

arxiv.org/abs/hep-th/9109054v1

Nucl.Phys. B375 (1992) 453-477

Physics

High Energy Physics

High Energy Physics - Theory

31pages

Scientific paper

10.1016/0550-3213(92)90040-I

In this paper we analyze one-matrix models by means of the associated discrete linear systems. We see that the consistency conditions of the discrete linear system lead to the Virasoro constraints. The linear system is endowed with gauge invariances. We show that invariance under time-independent gauge transformations entails the integrability of the model, while the double scaling limit is connected with a time-dependent gauge transformation. We derive the continuum version of the discrete linear system, we prove that the partition function is actually the $\tau$-function of the KdV hierarchy and that the linear system completely determines the Virasoro constraints.

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