Space-like singularities in the c=1 matrix model are artifacts of the double scaling limit; beyond it, Fermi surface folds proliferate and the coarse-grained phase space density relaxes to equilibrium via a universal power-law independent of initial state details.
Worldsheet Duals to One-Matrix Models
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abstract
We derive a concrete closed string dual to any interacting Hermitian one-matrix model, away from the double-scaling limit. Matrix and string correlators manifestly agree, to all orders in the genus expansion and all orders in the 't Hooft coupling(s). The worldsheet theory consists of a supersymmetric B-twisted Landau-Ginzburg model coupled to 2d topological gravity. We provide a precise dictionary between traces of the matrix and vertex operators on the worldsheet. Matrix model correlators are explicitly mapped to computable integrals over the moduli space of Riemann surfaces. We perform several direct cross-checks on both sides of the duality. This work furnishes a detailed instantiation of gauge/string duality, in the standard 't Hooft regime, and hopefully a useful worldsheet toy model for the AdS/CFT correspondence, away from the free field limit.
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2026 1verdicts
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Fate of "Space-like singularities" in $c=1$ Matrix Model
Space-like singularities in the c=1 matrix model are artifacts of the double scaling limit; beyond it, Fermi surface folds proliferate and the coarse-grained phase space density relaxes to equilibrium via a universal power-law independent of initial state details.