Geometric formulation of nonperturbative 2D quantum gravity

Details Geometric formulation of nonperturbative 2D quantum gravity Geometric formulation of nonperturbative 2D quantum gravity

Nov 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990phrvl..65.2483s&link_type=abstract

Physical Review Letters, Volume 65, Issue 20, November 12, 1990, pp.2483-2486

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Phase Transitions: General Studies

Scientific paper

It is shown in the context of multicritical Hermitian multimatrix models that certain salient features of nonperturbative 2D quantum gravity have a geometric interpretation in terms of algebraic curves and knots associated to the matrix models via their relation to the generalized Korteweg-de Vries hierarchy. I show that the question of unitarity in these models is linked to the singularity structure of the corresponding algebraic curves as well as to the degree of symmetry of the associated torus knots. Other characteristics of the matrix models have a geometric interpretation as well.

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