Continuum Annulus Amplitude from the Two-Matrix Model

Details Continuum Annulus Amplitude from the Two-Matrix Model Continuum Annulus Amplitude from the Two-Matrix Model

1994-10-05

arxiv.org/abs/hep-th/9410015v2

Phys.Rev. D52 (1995) 6016-6019

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, OU-HET 190, revised version. A part of the conclusions has been corrected. A new result on integral representation of

Scientific paper

10.1103/PhysRevD.52.6016

An explicit expression for continuum annulus amplitudes having boundary lengths $\ell_{1}$ and $\ell_{2}$ is obtained from the two-matrix model for the case of the unitary series; $(p,q) = (m + 1, m)$. In the limit of vanishing cosmological constant, we find an integral representation of these amplitudes which is reproduced, for the cases of the $m = 2~(c=0)$ and the $m \rightarrow \infty~(c=1)$, by a continuum approach consisting of quantum mechanics of loops and a matter system integrated over the modular parameter of the annulus. We comment on a possible relation to the unconventional branch of the Liouville gravity.

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