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.
Fateev,Integrable deformations of sine-liouville conformal field theory and duality, Symmetry, Integrability and Geometry: Methods and Applications(2017)
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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.