Random graph gauge theories as toy models for non-perturbative string theories

TL;DR

This paper introduces simple graph-based models that mimic key features of non-perturbative string theories, such as background independence, dimensional variability, dualities, and string-like excitations.

Contribution

It proposes gauge theories on arbitrary graphs as toy models for non-perturbative string theories, exploring their potential continuum limits related to gravity.

Findings

Models lack background or embedding space.

Ground states can have different effective dimensions.

Duality transformations relate strong and weak coupling regimes.

Abstract

We present simple models which exhibit some of the remarkable features expected to hold for the as yet unknown non-perturbative formulation of string theories. Among these are: (a) the absence of a background or embedding space for the full theory; (b) perturbative ground states (local minima of the action) having the characteristics of spaces of different dimension; (c) duality transformations between large- and small-coupling expansions; and (d) perturbative excitations of these ground states which can be interpreted as string worldsheets or p-brane worldvolumes. In this context we formulate gauge theories on arbitrary graphs and speculate concerning actions for graphs which in a continuum and/or thermodynamic limit might be related to the Einstein-Hilbert action.