Complex Structures Defined on Dynamically Triangulated Surfaces

TL;DR

This paper introduces a method to define complex structures on surfaces created by dynamical triangulation, analyzing their stability with different matter fields and observing a transition at a critical central charge.

Contribution

It presents a new approach to defining complex structures on dynamical triangulated surfaces and explores their stability across various matter field configurations.

Findings

Well-defined complex structures for matter central charges ≤ 1

Instability of complex structures beyond c=1

Transition consistent with theoretical expectations

Abstract

A method to define the complex structure and separate the conformal mode is proposed for a surface constructed by two-dimensional dynamical triangulation. Applications are made for surfaces coupled to matter fields such as $n$ scalar fields ($n=0,1$ and $4$) and $m$ Ising spins ($m=1$ and $3$). We observe a well-defined complex structure for cases when the matter central charges are less than and equal to one, while it becomes unstable beyond $c=1$. This can be regarded as the transition expected in analytic theories.