标题： 二维弦理论作为正规矩阵模型 显示英文标题

标题： 2D String Theory as Normal Matrix Model

摘要： 我们证明，在有限温度下，$c=1$量子弦理论有两种矩阵模型实现方式，它们通过一种对偶变换相关联。 第一种实现方式是由倒置振荡势中的紧致矩阵量子力学给出的标准实现方式。 第二种实现方式，我们在本文中推导得出，由正常矩阵模型给出。 这两种矩阵模型都表现出Toda可积结构，并与一个具有两个刺痕的球面拓扑复曲线的两个对偶环（一个紧致环和一个非紧致环）相关联。 两种矩阵模型的等价性对于任意的快子扰动以及在弦耦合常数的所有阶次下都成立。 显示英文摘要

摘要： 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.