Chiral chains for lattice quantum chromodynamics at N/sub c/=infinity
We study chiral fields (U/sub i/ in the group U(N)) on a periodic lattice (U/sub i/=U/sub i/+L), with action S1/=(g-italic/sup 2/)..sigma../sup L//sub l/=1Tr(U/sub l/U/sup //sub l/+1+ U/sup //sub l/U/sub l/+1), as prototypes for lattice gauge theories (quantum chromodynamics (QCD)) at N/sub c/=infinity. Indeed, these chiral chains are equivalent to gauge theories on the surface of an L-faced polyhedron (e.g., L=4 is a tetrahedron, L=6 is the cube, and L=infinity is two-dimensional QCD). The one-link Schwinger-Dyson equation of Brower and Nauenberg, which gives the square of the transfer matrix, is solved exactly for all N. From the large-N solution, we solve exactly the finite chains for L=2, 3, 4, and infinity, on the weak-coupling side of the Gross-Witten singularity, which occurs at ..beta..=(g-italic/sup 2/N)/sup -1/=1/4, 1/3, ..pi../8, and 1/2, respectively. We carry out weak and strong perturbation expansions at N/sub c/=infinity to estimate the singular part for all L, and to show confinement (as g/sup 2/N..-->..infinity) and asymptotic freedom (g/sup 2/N..-->..0) in the Migdal ..beta.. function for QCD. The stability of the location of the Gross-Witten singularity for different-size lattices (L) suggests that QCD at N/sub c/=infinity enjoys this singularity in the transition region from strong to weak coupling.
- Research Organization:
- Department of Physics, University of California, Santa Cruz, California 95064
- DOE Contract Number:
- AC02-76ER03069
- OSTI ID:
- 6835430
- Journal Information:
- Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 23:4; ISSN PRVDA
- Country of Publication:
- United States
- Language:
- English
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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
BOUNDARY CONDITIONS
CHIRALITY
DUALITY
FIELD THEORIES
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
LATTICE FIELD THEORY
MATRIX ELEMENTS
MIGDAL THEORY
PARTICLE PROPERTIES
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
RENORMALIZATION
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