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We consider 2-dimensional QCD on a cylinder, where space is a circle oflength $L$. We formulate the theory in terms of gauge-invariant gluon operatorsand multiple-winding meson (open string) operators. The meson bilocal operatorssatisfy a $W_\infty$ current algebra. The gluon sector (closed strings)contains purely quantum mechanical degrees of freedom. The description of thissector in terms of non-relativistic fermions leads to a $W_\infty$ algebra. Thespectrum of excitations of the full theory is therefore organized according totwo different algebras: a wedge subalgebra of $W_\infty$ current algebra in themeson sector and a wedge subalgebra of $W_\infty$ algebra in the glueballsector. In the large $N$ limit the theory becomes semiclassical and aneffective description for the gluon degrees of freedom can be obtained. We havesolved the effective theory of the gluons in the small $L$ limit. We get aglueball spectrum which coincides with the `discrete states' of the (Euclidean)$c=1$ string theory. We remark on the implications of these results for (a) QCDat finite temperature and (b) string theory.Comment: 28 pages, TIFR-TH-94/1

STRING FIELD THEORY OF TWO-DIMENSIONAL QCD ON A CYLINDER: A REALIZATION OF W∞ CURRENT ALGEBRA

STRING FIELD THEORY OF TWO-DIMENSIONAL QCD ON A CYLINDER: A REALIZATION OF W_∞ CURRENT ALGEBRA