Constraining noncommutative field theories with holography

TL;DR

This paper explores the interplay between noncommutative quantum field theories and holography, deriving constraints on their parameters and implications for experimental bounds like muon g-2 and vacuum birefringence.

Contribution

It establishes a relationship between UV/IR cutoffs and noncommutativity scale, revealing limitations on fitting experimental data and the impact of holography on perturbative regimes.

Findings

Constraints from muon g-2 exclude observable vacuum birefringence.

Holography imposes a lower energy limit related to noncommutativity scale.

Effective theories may struggle to simultaneously satisfy all experimental bounds.

Abstract

An important window to quantum gravity phenomena in low energy noncommutative (NC) quantum field theories (QFTs) gets represented by a specific form of UV/IR mixing. Yet another important window to quantum gravity, a holography, manifests itself in effective QFTs as a distinct UV/IR connection. In matching these two principles, a useful relationship connecting the UV cutoff $\Lambda_{\rm UV}$, the IR cutoff $\Lambda_{\rm IR}$ and the scale of noncommutativity $\Lambda_{\rm NC}$, can be obtained. We show that an effective QFT endowed with both principles may not be capable to fit disparate experimental bounds simultaneously, like the muon $g-2$ and the masslessness of the photon. Also, the constraints from the muon $g-2$ preclude any possibility to observe the birefringence of the vacuum coming from objects at cosmological distances. On the other hand, in NC theories without the UV completion, where the perturbative aspect of the theory (obtained by truncating a power series in $ \Lambda_{\rm NC}^{-2}$) becomes important, a heuristic estimate of the region where the perturbative expansion is well-defined $E/ \Lambda_{\rm NC} \lesssim 1$, gets affected when holography is applied by providing the energy of the system $E$ a $\Lambda_{\rm NC}$-dependent lower limit. This may affect models which try to infer the scale $\Lambda_{\rm NC}$ by using data from low-energy experiments.