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arXiv · hep-th/9407026

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

Avinash Dhar·Porus Lakdawala·Gautam Mandal·Spenta R. Wadia
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Abstract

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.

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Avinash Dhar, Porus Lakdawala, Gautam Mandal, Spenta R. Wadia. 1994-07-05. String Field Theory of Two Dimensional QCD on a Cylinder: A Realization of W-infinity Current Algebra. https://doi.org/10.1142/s0217751x95001066

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