The Lie h-Invariant Conformal Field Theories and the Lie h-Invariant Graphs

TL;DR

This paper explores Lie h-invariant conformal field theories using the Virasoro master equation, revealing a Lie group-theoretic structure in graph classification related to SO(n).

Contribution

It introduces a Lie h-invariant framework for conformal field theories and applies it to classify Lie h-invariant graphs on SO(n), connecting conformal field theory with graph theory.

Findings

Lie h-invariant CFTs form a broad space including rational CFTs

Characterization of Lie h-invariant graphs on SO(n)

Identification of Lie group-theoretic structures in graph classification

Abstract

We use the Virasoro master equation to study the space of Lie h-invariant conformal field theories, which includes the standard rational conformal field theories as a small subspace. In a detailed example, we apply the general theory to characterize and study the Lie h-invariant graphs, which classify the Lie h-invariant conformal field theories of the diagonal ansatz on SO(n). The Lie characterization of these graphs is another aspect of the recently observed Lie group-theoretic structure of graph theory.