# Noncommutative fields and the short-scale structure of spacetime

## TL;DR

This paper explores how quantum gravity effects, modeled through non-commutative fields, can lead to a finite short-distance potential and suggest a dimensional reduction or smoothing of point sources at the Planck scale.

## Contribution

It introduces a non-commutative field framework to analyze UV behavior of potentials, revealing finiteness and possible dimensional reduction due to quantum gravity effects.

## Key findings

- Short-distance potential becomes finite
- Indicates dimensional reduction in UV
- Point sources are effectively smoothed out

## Abstract

There is a growing evidence that due to quantum gravity effects the effective spacetime dimensionality might change in the UV. In this letter we investigate this hypothesis by using quantum fields to derive the UV behaviour of the static, two point sources potential. We mimic quantum gravity effects by using non-commutative fields associated to a Lie group momentum space with a Planck mass curvature scale. We find that the static potential becomes finite in the short-distance limit. This indicates that quantum gravity effects lead to a dimensional reduction in the UV or, alternatively, that point-like sources are effectively smoothed out by the Planck scale features of the non-commutative quantum fields.