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arXiv · hep-th/9407091

Nonperturbative 2D Gravity, Punctured Spheres and $Θ$-Vacua in String Theories

G. Bonelli·P. A. Marchetti·M. Matone
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Abstract

We consider a model of 2D gravity with the coefficient of the Einstein-Hilbert action having an imaginary part $π/2$. This is equivalent to introduce a $Θ$-vacuum structure in the genus expansion whose effect is to convert the expansion into a series of alternating signs, presumably Borel summable. We show that the specific heat of the model has a physical behaviour. It can be represented nonperturbatively as a series in terms of integrals over moduli spaces of punctured spheres and the sum of the series can be rewritten as a unique integral over a suitable moduli space of infinitely punctured spheres. This is an explicit realization à la Friedan-Shenker of 2D quantum gravity. We conjecture that the expansion in terms of punctures and the genus expansion can be derived using the Duistermaat-Heckman theorem. We briefly analyze expansions in terms of punctured spheres also for multicritical models.

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G. Bonelli, P. A. Marchetti, M. Matone. 1994-07-15. Nonperturbative 2D Gravity, Punctured Spheres and $Θ$-Vacua in String Theories. https://doi.org/10.1016/0370-2693(94)91131-2

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