# Complex structure of a DT surface with $T^2$ topology

## TL;DR

This paper introduces a method to define and analyze the complex structure of dynamically triangulated torus surfaces, comparing numerical results with Liouville theory to establish their equivalence.

## Contribution

It proposes a new approach to define moduli for DT surfaces with torus topology and demonstrates their correspondence with Liouville theory.

## Key findings

- Distribution of moduli matches Liouville theory predictions
- Establishes equivalence between DT surfaces and Liouville theory in complex structure
- Numerical measurements support theoretical models

## Abstract

A method of defining the complex structure(moduli) for dynamically triangulated(DT) surfaces with torus topology is proposed. Distribution of the moduli parameter is measured numerically and compared with the Liouville theory for the surface coupled to c = 0, 1 and 2 matter. Equivalence between the dynamical triangulation and the Liouville theory is established in terms of the complex structure.