U(N) Gauge Theory and Lattice Strings
Abstract
The U(N) gauge theory on a Ddimensional lattice is reformulated as a theory of lattice strings (a statistical model of random surfaces). The Boltzmann weights of the surfaces can have both signs and are tuned so that the longitudinal modes of the string are elliminated. The U(\infty) gauge theory is described by noninteracting planar surfaces and the 1/N corrections are produced by surfaces with higher topology as well as by contact interactions due to microscopic tubes, trousers, handles, etc. We pay special attention to the case D=2 where the sum over surfaces can be performed explicitly, and demonstrate that it reproduces the known exact results for the free energy and Wilson loops in the continuum limit. In D=4 dimensions, our lattice string model reproduces the strong coupling phase of the gauge theory. The weak coupling phase is described by a more complicated string whose world surface may have windows. A possible integration measure in the space of continuous surfaces is suggested.
 Publication:

arXiv eprints
 Pub Date:
 June 1993
 arXiv:
 arXiv:hepth/9306110
 Bibcode:
 1993hep.th....6110K
 Keywords:

 High Energy Physics  Theory
 EPrint:
 37 pages, 11 figures not included