W∞andw∞Gauge Theories and Contraction

✍ Scribed by An Kavalov; B Sakita

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 362 KB
• Volume: 255
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.1996.5646

✦ Synopsis

We present a general method of constructing W and w gauge theories in terms of d+2 dimensional local fields. In this formulation the W gauge theory Lagrangians involve nonlocal interactions, but the w theories are entirely local. We discuss the so-called classical contraction procedure by which we derive the Lagrangian of w gauge theory from that of the corresponding W gauge theory. In order to discuss the relationship between quantum W and quantum w 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 W 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 w gauge theory cannot be.

1997 Academic Press Replacing the Moyal bracket by a Poisson bracket we define the w algebra. It is an algebra of area-preserving diffeomorphism. As an introduction we discuss this issue in section 2 together with the so-called classical contraction procedure by which the W algebra is transformed to the w algebra.