Non-singlet sectors of the c=1 matrix model with connections to two dimensional string theory

The goal of this thesis is to study non-singlet sectors of the c=1 matrix model in order to determine their connection with string theory in two space-time dimensions. It is well understood that the singlet sector of this matrix model is related to the closed string sector of the string theory. The...

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Main Author: Rabideau, Charles
Language:English
Published: University of British Columbia 2012
Online Access:http://hdl.handle.net/2429/43445
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spelling ndltd-LACETR-oai-collectionscanada.gc.ca-BVAU.2429-434452014-03-26T03:39:10Z Non-singlet sectors of the c=1 matrix model with connections to two dimensional string theory Rabideau, Charles The goal of this thesis is to study non-singlet sectors of the c=1 matrix model in order to determine their connection with string theory in two space-time dimensions. It is well understood that the singlet sector of this matrix model is related to the closed string sector of the string theory. The adjoint sector has been connected to long strings stretching from an FZZT brane at infinity. The goal is to find a sector which includes a large number of these long strings which condense to form an FZZT brane in line with a proposal due to Gaiotto. Sectors corresponding to symmetric and antisymmetric tensor products of the fundamental and antifundamental representation of the U(N) symmetry of the matrix model are studied. Partition functions of the matrix model with a harmonic oscillator potential as well as bases for the Hilbert spaces are found for all these sectors. The first two representations are studied using a collective field approach with the inverted oscillator potential applicable to the c=1 model and are found to contain large numbers of long strings which form a free bosonic gas in the large N limit and so do not condense. On the other hand, in the third sector the degrees of freedom are fermionic and a shift in the ground state energy is found in the harmonic oscillator potential, which points to the existence of a Fermi sea and the condensation of the long strings. A collective field that can be used to study this sector is proposed and the technical difficulties presented by the study of this sector are discussed, but its study is left for future work. 2012-10-17T18:10:59Z 2012-10-17T18:10:59Z 2012 2012-10-17 2012-11 Electronic Thesis or Dissertation http://hdl.handle.net/2429/43445 eng University of British Columbia
collection NDLTD
language English
sources NDLTD
description The goal of this thesis is to study non-singlet sectors of the c=1 matrix model in order to determine their connection with string theory in two space-time dimensions. It is well understood that the singlet sector of this matrix model is related to the closed string sector of the string theory. The adjoint sector has been connected to long strings stretching from an FZZT brane at infinity. The goal is to find a sector which includes a large number of these long strings which condense to form an FZZT brane in line with a proposal due to Gaiotto. Sectors corresponding to symmetric and antisymmetric tensor products of the fundamental and antifundamental representation of the U(N) symmetry of the matrix model are studied. Partition functions of the matrix model with a harmonic oscillator potential as well as bases for the Hilbert spaces are found for all these sectors. The first two representations are studied using a collective field approach with the inverted oscillator potential applicable to the c=1 model and are found to contain large numbers of long strings which form a free bosonic gas in the large N limit and so do not condense. On the other hand, in the third sector the degrees of freedom are fermionic and a shift in the ground state energy is found in the harmonic oscillator potential, which points to the existence of a Fermi sea and the condensation of the long strings. A collective field that can be used to study this sector is proposed and the technical difficulties presented by the study of this sector are discussed, but its study is left for future work.
author Rabideau, Charles
spellingShingle Rabideau, Charles
Non-singlet sectors of the c=1 matrix model with connections to two dimensional string theory
author_facet Rabideau, Charles
author_sort Rabideau, Charles
title Non-singlet sectors of the c=1 matrix model with connections to two dimensional string theory
title_short Non-singlet sectors of the c=1 matrix model with connections to two dimensional string theory
title_full Non-singlet sectors of the c=1 matrix model with connections to two dimensional string theory
title_fullStr Non-singlet sectors of the c=1 matrix model with connections to two dimensional string theory
title_full_unstemmed Non-singlet sectors of the c=1 matrix model with connections to two dimensional string theory
title_sort non-singlet sectors of the c=1 matrix model with connections to two dimensional string theory
publisher University of British Columbia
publishDate 2012
url http://hdl.handle.net/2429/43445
work_keys_str_mv AT rabideaucharles nonsingletsectorsofthec1matrixmodelwithconnectionstotwodimensionalstringtheory
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