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

Abstract

'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 $\frac{1}{N}$ 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.

13 pages, 1 postscript figure included

References in corpus (3)

• London relation and fluxoid quantization for monopole currents in U(1) lattice gauge theory
• Measurement of the penetration depth and coherence length in U(1) and SU(2) dual Abrikosov vortices
• Decoupling of Photon Propagator in Compact QED

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• Fractal Dimension of Gauge-fixing Defects
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