Constraining noncommutative field theories with holography

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 ΛUV, the IR cutoff ΛIR and the scale of noncommutativity 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 Λ −2 NC ) 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.PACS numbers: 11.10.-z, 11.15.-q, 11.10.Nx, 04.60.-m Quantum field theories (QFTs) constructed on noncommutative (NC) spacetime:have received a great deal of interest lately mainly because of the possible appearance of such spacetimes in string theory [1][2][3][4][5]. In these QFTs noncommutativity is characterized by a real antisymmetric matrix θ µν of dimension of length squared, which in the context of string theory reflects the properties of the background. At tree level a QFT formulated with (1) should switch to its commutative relative whenever the momenta of the field quanta are lowered below θ −1/2 . In contrast, at loop level the inherent nonlocality of the full theory shows up in the UV/IR mixing phenomenon [6], meaning that switching to ordinary theories may occur at much lower momenta, depending on the ultimate UV cutoff in the theory. Figuratively speaking, the effect describes the linear growth of the size of a particle with its momentum, showing thus unambiguously its quantum-gravity origin [7].The phenomenon of UV/IR mixing [6] is best understood by examining the behavior of the (nonplanar) loop graphs with the ordinary product of fields replaced by the Moyal star(⋆)-product (see e.g., [3,4]). This results in phase factors depending on the virtual momenta of internal loops [8]. In a theory without UV completion (Λ UV → ∞) these phase factors, although efficient in damping out the high-energy part of the graphs, becomes together inefficient to control the vanishing momenta, i.e., the original UV divergences reappear as IR divergences. On the other hand, in presence of a finite Λ UV no one sort of divergence will appear since the said phase factors effectively transform the highest energy scale (Λ UV ) into the lowest one (Λ IR ). The theory ...

Inferring type and scale of noncommutativity from the PTOLEMY experiment

“…If the space-like noncommutativity is to be realized in nature, one obtains Λ max NC of order of 10 9 TeV, for the reheating temperature high enough. This value is consistent with the number of constraints on Λ NC obtained from particle physic phenomenology [33,[45][46][47][48][49][50][51][52][53][54][55][56], but still several orders below the (theoretically appealing) string or the Planck scale. Under the same circumstances but with light-like noncommutativity, the value Λ max NC will strongly depend on the reheating temperature.…”

Spacetime noncommutativity and ultrahigh energy cosmic ray experiments

“…By comparison of our Feynman rule (14) with those from [19,21], it is clear that our model would also produce the UV/IR mixing in computing quantum corrections; thus, our model is not perturbatively renormalizable, and it is not clear how to interpret the quantum corrections and to relate them to the observations [42]. In return, we obtain the well-behaved deep inelastic cross section at ultrahigh energies.…”

Nonassociative Snyder ϕ4 quantum field theory

“…Moreover, any possible nonperturbative effect like the celebrated UV/IR mixing in [14,40,41] is also lost. Among other features, UV/IR mixing connects the noncommutative field theories with holography via UV and IR cutoffs in a model independent way [42,43]. Holography and UV/IR mixing are known in the literature as possible windows to quantum gravity [10,42].…”