We propose to deploy limits that arise from different tests of the Pauli Exclusion Principle in order: i) to provide theories of quantum gravity with an experimental guidance; ii) to distinguish among the plethora of possible models the ones that are already ruled out by current data; iii) to direct future attempts to be in accordance with experimental constraints. We firstly review experimental bounds on nuclear processes forbidden by the Pauli Exclusion Principle, which have been derived by several experimental collaborations making use of different detector materials. Distinct features of the experimental devices entail sensitivities on the constraints hitherto achieved that may differ one another by several orders of magnitude. We show that with choices of these limits, renown examples of flat noncommutative space-time instantiations of quantum gravity can be heavily constrained, and eventually ruled out. We devote particular attention to the analysis of the $κ$-Minkowski and $θ$-Minkowski noncommutative spacetimes. These are deeply connected to some scenarios in string theory, loop quantum gravity and noncommutative geometry. We emphasize that the severe constraints on these quantum spacetimes, although cannot rule out theories of top-down quantum gravity to whom are connected in various way, provide a powerful limitations of those models that it will make sense to focus on in the future.
We review the main recent progresses in non-commutative space-time phenomenology in underground experiments. A popular model of non-commutative space-time is $θ$-Poincaré 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 $θ$…
Investigations of possible violations of the Pauli Exclusion Principle represent critical tests of the microscopic space-time structure and properties. Space-time non-commutativity provides a class of universality for several Quantum Gravity models. In this context the VIP-2 Lead experiment sets the strongest bounds, searching for Pauli Exclusion Principle violating atomic-transitions in lead, excluding the $θ$-Poincaré Non Commutative Quantum Gravity models far above the Planck scale for non-vanishing $θ_{μν}$ ``electric-like'' components, and up to $6.9 \cdot 10^{-2}$ Planck scales if $θ_{0i…
A manifestation of the Pauli Exclusion Principle is observed when fermions are trapped in the ground state of a 2D harmonic oscillator trap at very low temperatures. This non-interaction of fermions results in the formation of Pauli crystals. This work introduces a statistical mechanical interpretation of the principles that led to the observation of Pauli crystals by calculating the energy, radius and other parameters of the non-interacting arrangement of ultra-cold fermions. This model approaches the problem from two different directions, namely fermion degeneracy and harmonic oscillator tre…
How large can anomalous dimensions be in conformal field theories? What can we do to attain larger values? One attempt to obtain large anomalous dimensions efficiently is to use the Pauli exclusion principle. Certain operators constructed out of constituent fermions cannot form bound states without introducing non-trivial excitations. To assess the efficiency of this mechanism, we compare them with the numerical conformal bootstrap bound as well as with other interacting field theory examples. In two dimensions, it turns out to be the most efficient: it saturates the bound and is located at th…
Assuming that the degrees of freedom of a black hole are finite in number and of fermionic nature, we naturally obtain, within a second-quantized toy model of the evaporation, that the Bekenstein bound is a consequence of the Pauli exclusion principle for these fundamental degrees of freedom. We show that entanglement, Bekenstein and thermodynamic entropies of the black hole all stem from the same approach, based on the entropy operator whose structure is the one typical of Takahashi and Umezawa's Thermofield Dynamics. We then evaluate the von Neumann black hole--environment entropy and notice…
Pauli Exclusion Principle (PEP) violations induced by space-time non-commutativity, a class of universality for several models of Quantum Gravity, are investigated by the VIP-2 Lead experiment at the Gran Sasso underground National Laboratory of INFN. The VIP-2 Lead experimental bound on the non-commutative space-time scale $Λ$ excludes $θ$-Poincaré far above the Planck scale for non vanishing ``electric-like" components of $θ_{μν}$, and up to $6.9 \cdot 10^{-2}$ Planck scales if they are null. Therefore, this new bound represents the tightest one so far provided by atomic transitions tests. T…
