The Complex Structure of 2D Surfaces

Abstract

The complex structure of a surface generated by the two-dimensional dynamical triangulation(DT) is determined by measuring the resistivity of the surface. It is found that surfaces coupled to matter fields have well-defined complex structures for cases when the matter central charges are less than or equal to one, while they become unstable beyond c=1. A natural conjecture that fine planar random network of resistors behave as a continuous sheet of constant resistivity is justified numerically for c<1.

Comments: 4 pages of Latex, 6 Postscript figures(not include Fig.6). Uuencoded and use fleqn.sty, espcrc2.sty and psfig.sty files. Fig.6 available by request from ntsuda@theory.kek.jp, together with a hard copy of the paper. Contribution to Lattice'95