Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-07-15
Phys.Lett. B339 (1994) 49-58
Physics
High Energy Physics
High Energy Physics - Theory
12 pages + 2 figures available upon request. LaTeX File
Scientific paper
10.1016/0370-2693(94)91131-2
We consider a model of 2D gravity with the coefficient of the Einstein-Hilbert action having an imaginary part $\pi/2$. This is equivalent to introduce a $\Theta$-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 \`a 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.
Bonelli Giulio
Marchetti P. A.
Matone Marco
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