Matrix Models and One Dimensional Open String Theory (Revised)

Details Matrix Models and One Dimensional Open String Theory (Revised) Matrix Models and One Dimensional Open String Theory (Revised)

1992-04-06

arxiv.org/abs/hep-th/9204013v2

Int. J. Mod. Phys. A8 (1993) 3599-3614

Physics

High Energy Physics

High Energy Physics - Theory

17 pages

Scientific paper

10.1142/S0217751X93001466

We propose a random matrix model as a representation for $D=1$ open strings. We show that the model is equivalent to $N$ fermions with spin in a central potential that also includes a long-range ferromagnetic interaction between the fermions that falls off as $1/(r_{ij})^2$. We find two interesting scaling limits and calculate the free energy for both situations. One limit corresponds to Dirichlet boundary conditions for the dual graphs and the other corresponds to Neumann conditions. We compute the boundary cosmological constant and show that it is of order $1/\log(\beta)$. We also briefly discuss a possible analog of the Das-Jevicki field for the open string tachyon. (n.b. This is a revised version of paper previously submitted to xxx@lanl.gov. The original version misidentified the Dirichlet and Neumann cases. This version also includes references to work by Yang that was missing in the original.)

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