W-infinity andw-infinity gauge theories, and universality in random matrix models.
Item
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Title
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W-infinity andw-infinity gauge theories, and universality in random matrix models.
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Identifier
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AAI9807952
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identifier
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9807952
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Creator
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Kavalov, Andrew Ruben.
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Contributor
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Adviser: B. Sakita
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Date
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1997
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics | Physics, Condensed Matter | Physics, Elementary Particles and High Energy
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Abstract
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We present a general method of constructing {dollar}W\sb{lcub}\infty{rcub}{dollar} and {dollar}w\sb{lcub}\infty{rcub}{dollar} gauge theories in terms of {dollar}d+2{dollar} dimensional local fields. In this formulation the {dollar}W\sb{lcub}\infty{rcub}{dollar} gauge theory Lagrangians involve non-local interactions, but the {dollar}w\sb{lcub}\infty{rcub}{dollar} theories are entirely local. We discuss the so-called classical contraction procedure by which we derive the Lagrangian of {dollar}w\sb{lcub}\infty{rcub}{dollar} gauge theory from that of the corresponding {dollar}W\sb{lcub}\infty{rcub}{dollar} gauge theory. In order to discuss the relationship between quantum {dollar}W\sb{lcub}\infty{rcub}{dollar} and quantum {dollar}w\sb{lcub}\infty{rcub}{dollar} gauge theory we solve {dollar}d=1{dollar} gauge theory models of a scalar field exactly by using the collective field method. Based on this we conclude that the {dollar}W\sb{lcub}\infty{rcub}{dollar} gauge theory can be regarded as the large N limit of the corresponding {dollar}SU(N){dollar} gauge theory once an appropriate coupling constant renormalization is made, while the {dollar}w\sb{lcub}\infty{rcub}{dollar} gauge theory cannot be.;We propose gauge invariant observables for these theories--{dollar}W\sb{lcub}\infty{rcub}{dollar} Wilson loops. We solve {dollar}W\sb{lcub}\infty{rcub}{dollar} two dimensional Yang-Mills theory on the cylinder exactly. After appropriate coupling constant renormalization {dollar}(g\sp2N\equiv g\sbsp{lcub}c{rcub}{lcub}2{rcub}{dollar}-fixed, {dollar}N\to\infty,{dollar} where N is the volume of the color space) solution agree with {dollar}N\to\infty{dollar} limit of {dollar}SU(N){dollar} Yang-Mills. This theory is equivalent to a {dollar}W\sb{lcub}\infty{rcub}{dollar} one-dimensional unitary matrix model.;We discuss universal behavior of two and higher order density-density correlation functions of matrix models. We calculate the smoothed correlators for a large random matrix model with a potential containing products of two traces tr{dollar}W\sb1(M)\cdot {lcub}\rm tr{rcub}W\sb2(M){dollar} in addition to a single trace tr{dollar}V(M).{dollar} The connected correlation function of density eigenvalues receives corrections besides the universal part derived by Brezin and Zee and it is no longer universal in a strong sense.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
