Abstract
We show that two natural approaches to quantum gravity coincide. This identity is nontrivial and relies on the equivalence of each approach to KdV equations. We also investigate related mathematical problems.
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[AvM] Adler, M., van Moerbeke, P.: TheW p-gravity version of the Witten-Kontsevich model. Commun. Math. Phys. (to appear)
[BIZ] Bessis, D., Itzykson, C., Zuber, J.-B.: Qunatum field theory techniques in graphical enumeration. Adv. Appl. Math.1, 109–157 (1980)
[BK] Brézin, E., Kazakov, V.: LettB236, 144 (1990)
[DS] Douglas, M., Shenker, S.: Nucl. Phys.B335, 635 (1990)
[GM] Gross, D., Migdal, A.: Phys. Rev. Lett.64, 127 (1990)
[H] Harer, J.: The cohomology of the moduli space of curves. Lecture Notes of mathematics, vol. 1337. Berlin, Heidelberg, New York: Springer, pp. 138–221
[HZ] Harer, J., Zagier, D.: The Euler characteristic of the moduli space of curves. Inv. Math.85, 457–485 (1986)
[HC] Harish-Chandra: Differential operators on a semisimple Lie algebra. Am. J. Math.79, 87–120 (1957)
[IZ1] Itzykson, C., Zuber, J.-B.: J. Math. Phys.21, 411–421 (1980)
[IZ2] Itzykson, C., Zuber, J.-B.: Commun. Math. Phys.134, 197–207 (1990)
[KS] Kac, V., Schwarz, A.: LettB257, 329 (1991)
[KMMMZ] Kharchev, S., Marshakov, A., Mironov, A., Morozov, A., Zabrodin, A.: Unification of all string models withc<1, FIAN/TD-9/91 and ITEP-M-8/91
[K1] Kontsevich, M.: Intersection theory on the moduli space of curves. Funct. Anal. and Appl.25 (2), 123–128 (1991)
[K2] Kontsevich, M. Intersection theory on the moduli space of curves and the matrix Airy function. 30. Arbeitstagung Bonn. Preprint MPI/91-47
[KM] Kontsevich, M., Mulase, M.: In preparation
[Mh] Mehta, M. L.: Random matrices in nuclear physics and number theory. Contemporary Math.50, 295–309 (1986)
[M] Mumford, D.: Towards an enumerative geometry of the moduli space of curves. In: Arithmetic and geometry, vol. II. Boston: Birkhäuser 1983
[P1] Penner, R. C.: The decorated Teichmüller space of punctured surfaces. Commun. Math. Phys.113, 299–339 (1987)
[P2] Penner, R. C.: Perturbative series and the moduli space of Riemann surfaces. J. Diff. Geom.27, 35–53 (1988)
[P3] Penner, R. C.: The Poincaré dual of the Weil-Petersson Kähler two-form. Preprint, October 1991
[SW] Segal, G. B., Wilson, G.: Loop groops and equations of KdV type. Publ. Math. I.H.E.S.61, 5–65 (1985)
[S] Strebel, K.: Quadratic differentials. Berlin, Heidelberg, New York: Springer 1984
[W1] Witten, E.: Two dimensional gravity and intersection theory on moduli space. Surveys in Diff. Geom.1, 243–310 (1991)
[W2] Witten, E.: On the Kontsevich model and other models of two dimensional gravity. IAS preprint HEP-91/24
[W3] Witten, E.: TheN matrix model and gauged WZW models. IAS preprint HEP-91/26
[Z] Zwiebach, B.: How covariant closed string theory solves a minimal area problem. Commun. Math. Phys.136, 83–118
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Communicated by A. Jaffe
Accepted as doctoral dissertation by the Mathematisch-Naturwissenschaftliche Fakultät, University of Bonn, FRG
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Kontsevich, M. Intersection theory on the moduli space of curves and the matrix airy function. Commun.Math. Phys. 147, 1–23 (1992). https://doi.org/10.1007/BF02099526
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DOI: https://doi.org/10.1007/BF02099526