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On the Random Matrix Model of the Virasoro Minimal String
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abstract
The model of two dimensional quantum gravity defining the "Virasoro Minimal String", presented recently by Collier, Eberhardt, M\"{u}hlmann, and Rodriguez, was also shown to be perturbatively (in topology) equivalent to a random matrix model. An alternative definition is presented here, in terms of double-scaled orthogonal polynomials, thereby allowing direct access to non-perturbative physics. Already at leading order, the defining string equation's properties yield valuable information about the non-perturbative fate of the model, confirming that the case $(c{=}25,{\hat c}{=}1)$ (central charges of spacelike and timelike Liouville sectors) is special, by virtue of sharing certain key features of the ${\cal N}{=}1$ supersymmetric JT gravity string equation. Solutions of the full string equation are constructed using a special limit, and the (Cardy) spectral density is completed to all genus and beyond. The distributions of the underlying discrete spectra are readily accessible too, as is the spectral form factor. Some examples of these are exhibited.
Forward citations
Cited by 4 Pith papers
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Weil-Petersson volumes for extended JT supergravity from ordinary differential equations
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Further aspects of Supersymmetric Virasoro Minimal Strings
The paper defines the 0B supersymmetric Virasoro minimal string as an average of two 0A models and shows its loop correlators beyond the leading disc and cylinder vanish to all orders in perturbation theory.
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A differential equation for a class of correlation kernels
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Sine-dilaton gravity vs double-scaled SYK: exploring one-loop quantum corrections
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