Induced Gravity from Theory Space

TL;DR

This paper explores how the eigenvalues of the Laplacian on a graph structure in a theory space determine the mass spectrum and UV divergences, enabling the construction of divergence-free induced gravity models at one-loop level.

Contribution

It introduces a novel approach linking graph theory with induced gravity, showing how to avoid one-loop divergences using the graph's degree matrix.

Findings

Mass spectrum determined by Laplacian eigenvalues

One-loop UV divergence controlled by graph degree matrix

Constructed models of divergence-free induced gravity

Abstract

The mass spectrum of a model constructed in a theory space is expressed by eigenvalues of the Laplacian on the graph structure of the theory space. The nature of the one-loop UV divergence in the vacuum energy is then controlled only by the degree matrix of the graph. Using these facts, we can construct models of induced gravity which do not suffer from divergences at the one-loop level.