标题： 弦场理论在圆柱面上的二维QCD：W-无穷大电流代数的一个实现 显示英文标题

标题： String Field Theory of Two Dimensional QCD on a Cylinder: A Realization of W-infinity Current Algebra

摘要： 我们研究了二维量子色动力学在圆柱上的情况，其中空间是一个长度为$L$的圆。 我们将理论用规范不变的胶子算符和多绕圈介子（开弦）算符来表述。 介子双线性算符满足一个$W_\infty$的流代数。 胶子部分（闭弦）包含了纯粹的量子力学自由度。 用非相对论费米子描述该部分会导致一个$W_\infty$代数。 因此，整个理论的激发谱根据两个不同的代数来组织：介子部分$W_\infty$流代数的一个楔子子代数，以及胶球部分$W_\infty$代数的一个楔子子代数。 在大$N$极限下，理论变得半经典，并且可以得到胶子自由度的有效描述。 我们在小$L$极限下解决了胶子的有效理论。 我们得到了一个与（欧几里得）$c=1$弦理论的“离散态”相一致的胶球能谱。 我们讨论了这些结果对(a)有限温度下的QCD和(b)弦理论的意义。 显示英文摘要

摘要： We consider 2-dimensional QCD on a cylinder, where space is a circle of length $L$. We formulate the theory in terms of gauge-invariant gluon operators and multiple-winding meson (open string) operators. The meson bilocal operators satisfy a $W_\infty$ current algebra. The gluon sector (closed strings) contains purely quantum mechanical degrees of freedom. The description of this sector in terms of non-relativistic fermions leads to a $W_\infty$ algebra. The spectrum of excitations of the full theory is therefore organized according to two different algebras: a wedge subalgebra of $W_\infty$ current algebra in the meson sector and a wedge subalgebra of $W_\infty$ algebra in the glueball sector. In the large $N$ limit the theory becomes semiclassical and an effective description for the gluon degrees of freedom can be obtained. We have solved the effective theory of the gluons in the small $L$ limit. We get a glueball spectrum which coincides with the `discrete states' of the (Euclidean) $c=1$ string theory. We remark on the implications of these results for (a) QCD at finite temperature and (b) string theory.