Strong-coupling scales and the graph structure of multi-gravity theories

TL;DR

This paper investigates how the interaction structure in multi-gravity theories influences their strong-coupling scales, using graph theory to efficiently estimate bounds and relate theories to higher-dimensional models.

Contribution

It introduces a graph-theoretic framework to analyze the strong-coupling scale dependence on interaction structures in multi-gravity theories.

Findings

Graph properties determine bounds on the strong-coupling scale.

Efficient estimation methods for strong-coupling scales using matrices.

Relation between theory graphs and discretized higher-dimensional theories.

Abstract

In this paper we consider how the strong-coupling scale, or perturbative cutoff, in a multi-gravity theory depends upon the presence and structure of interactions between the different fields. This can elegantly be rephrased in terms of the size and structure of the `theory graph' which depicts the interactions in a given theory. We show that the question can be answered in terms of the properties of various graph-theoretical matrices, affording an efficient way to estimate and place bounds on the strong-coupling scale of a given theory. In light of this we also consider the problem of relating a given theory graph to a discretised higher dimensional theory, a la dimensional deconstruction.