标题： 扩展的Toda晶格层次结构、扩展的双矩阵模型和c=1弦理论 显示英文标题

标题： Extended Toda lattice hierarchy, extended two-matrix model and c=1 string theory

摘要： 我们展示了前一篇文章中提出的双矩阵模型和Toda晶格层次结构如何可以被精确求解：我们得到了每一圈纯快子态关联函数的紧凑公式。 然后我们将模型扩展以包含一组离散态，这些离散态组织在有限维的$sl_2$表示中。 我们也解决了这个扩展的模型，并通过使用$W$约束和流方程找到了离散态的关联函数。 我们的结果与文献中已有结果一致，在那些已经明确计算出特定关联函数的情况下。 我们得出结论，扩展的双矩阵模型是$c=1$弦理论离散态的一种实现。 显示英文摘要

摘要： We show how the two--matrix model and Toda lattice hierarchy presented in a previous paper can be solved exactly: we obtain compact formulas for correlators of pure tachyonic states at every genus. We then extend the model to incorporate a set of discrete states organized in finite dimensional $sl_2$ representations. We solve also this extended model and find the correlators of the discrete states by means of the $W$ constraints and the flow equations. Our results coincide with the ones existing in the literature in those cases in which particular correlators have been explicitly calculated. We conclude that the extented two--matrix model is a realization of the discrete states of $c=1$ string theory.