Non-Perturbative Effects in 2-D String Theory or Beyond the Liouville Wall

Details Non-Perturbative Effects in 2-D String Theory or Beyond the Liouville Wall Non-Perturbative Effects in 2-D String Theory or Beyond the Liouville Wall

1992-09-22

arxiv.org/abs/hep-th/9209081v1

Int.J.Mod.Phys. A12 (1997) 3477-3515

Physics

High Energy Physics

High Energy Physics - Theory

44 pages, 9 figures available as eps files on request

Scientific paper

We discuss continuous and discrete sectors in the collective field theory of $d=1$ matrix models. A canonical Lorentz invariant field theory extension of collective field theory is presented and its classical solutions in Euclidean and Minkowski space are found. We show that the discrete, low density, sector of collective field theory includes single eigenvalue Euclidean instantons which tunnel between different vacua of the extended theory. We further show that these ``stringy" instantons induce non-perturbative effective operators of strength $e^{-{1\over g}}$ in the extended theory. The relationship of the world sheet description of string theory and Liouville theory to the effective space-time theory is explained. We also comment on the role of the discrete, low density, sector of collective field theory in that framework.

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