Graphs, lattices and deconstruction hierarchies

TL;DR

This paper develops the mathematical framework connecting deconstruction lattices and locality diagrams in conformal models, focusing on classification and structural characterization of these graphs.

Contribution

It introduces key concepts like equilocality classes, deflation map, and stem graphs to characterize locality diagrams in conformal models.

Findings

Characterization of graphs that can serve as locality diagrams.

Introduction of new concepts for classifying deconstruction lattices.

Framework for understanding the structure of conformal model diagrams.

Abstract

The mathematics underlying the connection between deconstruction lattices and locality diagrams of conformal models is developed from scratch, with special emphasis on classification issues. In particular, the notions of equilocality classes, deflation map, essential vertices and stem graphs are introduced in order to characterize those graphs that may arise as locality diagrams.