2D String Theory as Normal Matrix Model

Details 2D String Theory as Normal Matrix Model 2D String Theory as Normal Matrix Model

2003-02-14

arxiv.org/abs/hep-th/0302106v1

Nucl.Phys. B667 (2003) 90-110

Physics

High Energy Physics

High Energy Physics - Theory

lanlmac, 21 pages

Scientific paper

10.1016/S0550-3213(03)00546-7

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.

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