# Tests of Pauli Exclusion Principle Violations from Non-commutative quantum gravity

## TL;DR

This paper reviews non-commutative space-time phenomenology and demonstrates that the $ heta$-Poincaré model predicts violations of the Pauli Exclusion Principle, which are already ruled out by existing nuclear transition experiments like DAMA/LIBRA.

## Contribution

It provides the first experimental constraints on the $ heta$-Poincaré non-commutative space-time model using underground nuclear transition data.

## Key findings

- The $ heta$-Poincaré model predicts energy-dependent violations of the Pauli Exclusion Principle.
- DAMA/LIBRA experiment data rules out the $ heta$-Poincaré model up to the Planck scale.

## Abstract

We review the main recent progresses in non-commutative space-time phenomenology in underground experiments. A popular model of non-commutative space-time is $\theta$-Poincar\'e model, based on the Groenewold-Moyal plane algebra. This model predicts a violation of the Spin-statistic theorem, in turn implying an energy and angular dependent violation of the Pauli Exclusion principle. Pauli Exclusion Principle Violating transitions in nuclear and atomic systems can be tested with very high accuracy in underground laboratory experiments such as DAMA/LIBRA and VIP(2). In this paper we derive that the $\theta$-Poincar\'e model can be already ruled-out until the Planck scale, from nuclear transitions tests by DAMA/LIBRA experiment.