Summations over equilaterally triangulated surfaces and the critical string measure
Measures on surfaces have always been defined through triangulations. In this work triangulation is done by equilateral triangles all of the same size. This is combined with a technique which assigns to each equilateral triangulation of a two-dimensional surface a Riemann surface defined over a certain extension of the field of rational numbers, that is, an arithmetic surface. Thus in the author's formulation the sum over randomly triangulated surfaces defines an invariant measure on the moduli space of arithmetic surfaces. In the case of critical string theory it is shown, by explicit computations, that the author's measure approximates correctly the continuum measure.
scientific article; zbMATH DE number 54713
scientific article