We consider a model of 2D gravity with the coefficient of the Euler characteristic 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 spaces of punctured spheres and the 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.
Nonperturbative 2-D gravity, punctured spheres and Theta vacua in string theories / Bonelli, G.; Marchetti, P. A.; Matone, M.. - In: PHYSICS LETTERS. SECTION B. - ISSN 0370-2693. - 339:1-2(1994), pp. 49-58. [10.1016/0370-2693(94)91131-2]
Nonperturbative 2-D gravity, punctured spheres and Theta vacua in string theories
Bonelli, G.;
1994-01-01
Abstract
We consider a model of 2D gravity with the coefficient of the Euler characteristic 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 spaces of punctured spheres and the 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.File | Dimensione | Formato | |
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