Fermionic Quantum Gravity

Paniak, L. D. ; Szabo, R. J.

arXiv, 0005128 / Harvested from arXiv

Résumé

We study the statistical mechanics of random surfaces generated by NxN one-matrix integrals over anti-commuting variables. These Grassmann-valued matrix models are shown to be equivalent to NxN unitary versions of generalized Penner matrix models. We explicitly solve for the combinatorics of 't Hooft diagrams of the matrix integral and develop an orthogonal polynomial formulation of the statistical theory. An examination of the large N and double scaling limits of the theory shows that the genus expansion is a Borel summable alternating series which otherwise coincides with two-dimensional quantum gravity in the continuum limit. We demonstrate that the partition functions of these matrix models belong to the relativistic Toda chain integrable hierarchy. The corresponding string equations and Virasoro constraints are derived and used to analyse the generalized KdV flow structure of the continuum limit.

Détail

Publié le : 2000-05-14
Classification:  High Energy Physics - Theory,  Condensed Matter - Statistical Mechanics,  Mathematical Physics,  Nonlinear Sciences - Exactly Solvable and Integrable Systems