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

• Main Author: Rabideau, Charles
• Language: English
• Published: University of British Columbia 2012
• Online Access: http://hdl.handle.net/2429/43445

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.