Properties of the Abelian Projection Fields in $SU(N)$ Lattice Gluodynamics

Details Properties of the Abelian Projection Fields in $SU(N)$ Lattice Gluodynamics Properties of the Abelian Projection Fields in $SU(N)$ Lattice Gluodynamics

1993-06-17

arxiv.org/abs/hep-lat/9306014v1

Phys.Lett. B316 (1993) 333-338

Physics

High Energy Physics

High Energy Physics - Lattice

13 pages, 1 postscript figure included

Scientific paper

10.1016/0370-2693(93)90334-E

't~Hooft's abelian projection of $SU(N)$ gauge theory yields $N$ mutually constrained, compact abelian fields which are permutationally equivalent. We formulate the notion of ``species permutation'' symmetry of the $N$ abelian projection fields and discuss its consequences for cross-species correlators. We show that at large $N$ cross-species interactions are ${1\over N}$ suppressed relative to same-species interactions. Numerical simulations at $N=3$ support our symmetry arguments and reveal the existence of inter-species interactions of size ${\cal O\/}\bigl({1\over N-1}\bigr)$ as analytically predicted.

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