The seven-vertex matrix model realizes sine-Liouville gravity through a shared classical spectral curve with matrix quantum mechanics but distinct branes, with dilute-dense flow analogous to a gravitational massless sine-Gordon flow.
The partition function of 2d string theory
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abstract
We derive a compact and explicit expression for the generating functional of all correlation functions of tachyon operators in 2D string theory. This expression makes manifest relations of the $c=1$ system to KP flow and $W_{1+\infty}$ constraints. Moreover we derive a Kontsevich-Penner integral representation of this generating functional.
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Sine-Liouville gravity as a Vertex Model on Planar Graphs
The seven-vertex matrix model realizes sine-Liouville gravity through a shared classical spectral curve with matrix quantum mechanics but distinct branes, with dilute-dense flow analogous to a gravitational massless sine-Gordon flow.