A collective field theory approach to the large N spectrum of two matrices
Date
2008-03-07T12:27:47Z
Authors
Cook, Martin
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Abstract
Abstract
The collective field theory technique provides a method of tackling problems with two N × N
matrices in the large N limit. The collective field background from one matrix is first found,
then the second matrix is introduced into this background as an impurity. Within the context
of the AdS/CFT correspondence, this technique can be used to describe gauge theory states in
the BMN limit.
This dissertation starts by developing the collective field theory technique, firstly in general
variables, then for one matrix, and subsequently for two matrices. It goes on to introduce a
Yang-Mills interaction term, where two variable identifications are considered. The first is the
more traditional angular momentum eigenstate model. The second is a model that directly uses
two of the Higgs scalars. This model has been mentioned in the literature, but has not been
considered in great depth. The exact two impurity spectrum is found, and the multi-impurity
spectrum is found to first order. The resulting energy values match a spectrum that has been
found for giant magnons.
Description
Keywords
String theory, conformal field theory, eigenvalues, eigenfunctions, supergravity, space-time configurations