# Spectral Dirac graphs

## TL;DR

This paper introduces spectral Dirac graphs, a class of discrete models that naturally lead to relativistic quantum field theories in the continuum limit, revealing how gauge fields and gravity emerge from graph deformations.

## Contribution

It defines spectral Dirac graphs and analyzes how their deformations produce gauge fields and gravity in the continuum limit, linking discrete models to fundamental physics.

## Key findings

- Deformations with regular continuum limit yield gauge fields.
- Macroscopic deformations produce gravity.
- Microscopic deformations contribute to gauge interactions.

## Abstract

We address the problem of identifying families of discrete models naturally flowing in continuum limit to relativistic quantum field theories. We call them Dirac graphs. In this work, we require the graphs to obey spectrality property, which implies that the adjacency matrix can be represented by a continuous function defined on the spectral space. We also consider deformations of such graphs away from the spectrality. We show that deformations with regular continuum limit result in background gauge field and gravity. Interestingly, gauge interactions appear due to contribution microscopic deformations while the standard gravity can only be a result of macroscopic (adiabatic) deformations.