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arXiv · hep-th/9402030

Moduli Spaces of Curves with Homology Chains and c=1 Matrix Models

A. S. Cattaneo·A. Gamba·M. Martellini
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Abstract

We show that introducing a periodic time coordinate in the models of Penner-Kontsevich type generalizes the corresponding constructions to the case of the moduli space ${\cal S}_{gn}^k$ of curves $C$ with homology chains $γ\in H_1(C,\zet_k)$. We make a minimal extension of the resulting models by adding a kinetic term, and we get a new matrix model which realizes a simple dynamics of $\zet_k$-chains on surfaces. This gives a representation of $c=1$ matter coupled to two-dimensional quantum gravity with the target space being a circle of finite radius, as studied by Gross and Klebanov.

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A. S. Cattaneo, A. Gamba, M. Martellini. 1994-02-20. Moduli Spaces of Curves with Homology Chains and c=1 Matrix Models. https://doi.org/10.1016/0370-2693(94)90721-8

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