Two-dimensional Quantum Gravity and String Field Theory

基于二维面的动力学三角剖分，利用c&t；小于等于&gt；1的非临界弦的非微扰形式，建立了c=1/2非临界弦的弦场理论，即伊辛自旋与二维引力的耦合模型。作为弦上伊辛自旋的允许状态，考虑如下构型：(1)除了任意数量的局部自旋翻转外，所有的伊辛自旋都是向上的。(2)伊辛自旋要么全部向上，要么全部向下。此外，在连续体Liouville理论中，还用半经典展开的方法计算了二维引力中的盘振幅。确定了Liouville场的边界条件。将结果推广到2D超引力将是直接的，这将为建立非临界超弦的弦场理论开辟道路。

String field theories for the c=1/2 non-critical string, i.e., the model of Ising spins coupled to 2d gravity, were constructed by using the non-perturbative formulation of the c<less than or equal>1 non-critical strings based on the dynamical triangulation of 2d surfaces. As allowed states of Ising spins on the string the following configurations were considered separ(1) Ising spins are all up except for an arbitrary number of local spin flips.(2) Ising spins are either all up or all down.Furthermore a disk amplitude in 2d gravity was also computed in the continuum Liouville theory by using the method of the semi-classical expansion. The boundary condition for the Liouville field was determined. An extension of the result to the 2d supergravity will be straightforward and this will open the way to construction of a string field theory for the non-critical superstrings.