Non-Perturbative Solution of Matrix Models Modified by Trace-Squared Terms

Igor R. Klebanov; Akikazu Hashimoto

doi:10.1016/0550-3213(94)00518-J

paper

Non-Perturbative Solution of Matrix Models Modified by Trace-Squared Terms

arXiv:hep-th/9409064 · doi:10.1016/0550-3213(94)00518-J

Abstract

We present a non-perturbative solution of large $N$ matrix models modified by terms of the form $ g(\TrΦ^4)^2$, which add microscopic wormholes to the random surface geometry. For $g < g_{t}$ the sum over surfaces is in the same universality class as the $g = 0$ theory, and the string susceptibility exponent is reproduced by the conventional Liouville interaction $\sim e^{α_{+} ϕ}$ . For $g = g_{t}$ we find a different universality class, and the string susceptibility exponent agrees for any genus with Liouville theory where the interaction term is dressed by the other branch, $e^{α_{-} ϕ}$ . This allows us to define a double-scaling limit of the $g = g_{t}$ theory. We also consider matrix models modified by terms of the form $g O^{2}$ , where $O$ is a scaling operator. A fine-tuning of $g$ produces a change in this operator's gravitational dimension which is, again, in accord with the change in the branch of the Liouville dressing.

26 pages, PUPT-1498

Non-Perturbative Solution of Matrix Models Modified by Trace-Squared Terms

Abstract

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