A String Project in Multicolour QCD

Abstract

Some old and new evidence for the existence of the string (planar random surfaces) representation of multicolour QCD are reviewed. They concern the random surface representation of the strong coupling expansion in lattice multicolour gauge theory in any dimension.Our old idea of modified strong coupling expansion in terms of planar random surfaces, valid for the physical weak coupling phase of the four-dimensional QCD, is explained in detail. Some checks of the validity of this expansion are proposed. (The lectures given in the Trieste Spring School and Workshop-1993 on String Theory)

Large N gauge theory — Expansions and transitions

“…Since tr U n = α n + ᾱ−n after bosonization, we see that we reproduce the picture from the strong coupling expansion if we identify the excitations of the n'th left-moving bosonic mode with nwinding strings, and the n'th right-moving mode with −n-winding strings. The leading O(N 0 ) part of the Hamiltonian (35) preserves string number and gives a string energy proportional to the absolute value of its winding number, while the O(1/N ) piece is a three-string interaction.…”

“…(See [31]; the large N case was discussed in detail by V. Kazakov and I. Kostov at the 1993 Trieste Spring School [35,37].) * Supported in part by DOE grant DE-FG05-90ER40559, NSF PHY-9157016 and the A. J. Sloan Foundation.…”

“…A good starting point for discussing 'QCD string' is the strong coupling expansion, which I will review very briefly. (See [31]; the large N case was discussed in detail by V. Kazakov and I. Kostov at the 1993 Trieste Spring School [35,37]. )…”

Loop equations as generalized Virasoro constraints

“…The arguments are mostly based on the representation of 1/N expansion combined with the strong (or weak) coupling ones in terms of a sum over random surfaces (for a review, e.g. [2]). Recently the substantial progress has been made in the string description of the two dimensional QCD [3].…”