Constraining noncommutative field theories with holography

Abstract

An important window to quantum gravity phenomena in low energy noncom-mutative (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 ΛUV, the IR cutoff ΛIR and the scale of non-commutativity ΛNC, 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 $$ \Lambda_{\text{NC}}^{ - 2} $$ ) becomes important, a heuristic estimate of the region where the perturbative expansion is well-defined E/ΛNC ≲ 1, gets affected when holography is applied by providing the energy of the system E a ΛNC-dependent lower limit. This may affect models which try to infer the scale ΛNC by using data from low-energy experiments.