W_\infty and w_\infty Gauge Theories and Contraction

Details W_\infty and w_\infty Gauge Theories and Contraction W_\infty and w_\infty Gauge Theories and Contraction

1996-03-05

arxiv.org/abs/hep-th/9603024v1

Annals Phys. 255 (1997) 1-18

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, plain TeX

Scientific paper

10.1006/aphy.1996.5646

We present a general method of constructing Winf and winf gauge theories in terms of d+2 dimensional local fields. In this formulation the \Winf gauge theory Lagrangians involve non-local interactions, but the winf theories are entirely local. We discuss the so-called classical contraction procedure by which we derive the Lagrangian of winf gauge theory from that of the corresponding Winf gauge theory. In order to discuss the relationship between quantum Winf and quantum winf gauge theory we solve d=1 gauge theory models of a Higgs field exactly by using the collective field method. Based on this we conclude that the Winf gauge theory can be regarded as the large N limit of the corresponding SU(N) gauge theory once an appropriate coupling constant renormalization is made, while the winf gauge theory cannot be.

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