2D String Theory as Normal Matrix Model

Abstract

We show that the $c=1$ bosonic string theory at finite temperature has two matrix-model realizations related by a kind of duality transformation. The first realization is the standard one given by the compactified matrix quantum mechanics in the inverted oscillator potential. The second realization, which we derive here, is given by the normal matrix model. Both matrix models exhibit the Toda integrable structure and are associated with two dual cycles (a compact and a non-compact one) of a complex curve with the topology of a sphere with two punctures. The equivalence of the two matrix models holds for an arbitrary tachyon perturbation and in all orders in the string coupling constant.

lanlmac, 21 pages

References in corpus (9)

• Matrix Models, Topological Strings, and Supersymmetric Gauge Theories
• On Geometry and Matrix Models
• A Matrix Model for the Two Dimensional Black Hole
• Viscous fingering and a shape of an electronic droplet in the Quantum Hall regime
• Time-dependent backgrounds of 2D string theory
• On Associativity Equations in Dispersionless Integrable Hierarchies
• Correlators in 2D string theory with vortex condensation
• String Equation for String Theory on a Circle
• Thermodynamics of 2D string theory

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