1994/10/09 by David J. Gross, Andrei Matytsin · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1016/0550-3213(94)00570-5
published as Nucl.Phys. B437 (1995) 541-584 · 48 pages, preprint PUPT-1503
arxiv created 1994/10/09 · arxiv updated 2009/11/30
Large N two-dimensional QCD on a cylinder and on a vertex manifold (a sphere with three holes) is investigated. The relation between the saddle-point description and the collective field theory of QCD2 is established. Using this relation, it is shown that the Douglas--Kazakov phase transition on a cylinder is associated with the presence of a gap in the eigenvalue distributions for Wilson loops. An exact formula for the phase transition on disc with an arbitrary boundary holonomy is found. The role of instantons in inducing such transitions is discussed. The zero-area limit of the partition function on a vertex manifold is studied. It is found that this partition function vanishes unless the boundary conditions satisfy a certain selection rule which is an analogue of momentum conservation in field theory.