Ultrahigh-energy photons up to 1.4 peta-electronvolts have been observed by new cosmic-ray telescope in China -- a hint that Lorentz invariance might break down at the Planck-scale level.
Recently a series of studies on high energy gamma-ray burst~(GRB) photons suggest a light speed variation with linear energy dependence at the Lorentz violation scale of $3.6 times 10^{17}~mathrm{GeV}$, with subluminal propagation of high energy phot
ons in cosmological space. We propose stringy space-time foam as a possible interpretation for this light speed variation. In such a string-inspired scenario, bosonic photon open-string travels textit{in vacuo} at an infraluminal speed with an energy dependence suppressed by a single power of the string mass scale, due to the foamy structure of space-time at small scales, as described by D-brane objects in string theory. We present a derivation of this deformed propagation speed of the photon field in the infrared (IR) regime. We show that the light speed variation, revealed in the previous studies on GRBs time-delay data, can be well described within such a string approach towards space-time foam. We also derive the value of the effective quantum-gravity mass in this framework, and give a qualitative study on the theory-dependent coefficients. We comment that stringent constraints on Lorentz violation in the photon sector from complementary astrophysical observations can also be explained and understood in the space-time foam context.
The Large High Altitude Air Shower Observatory~(LHAASO) is one of the most sensitive gamma-ray detector arrays currently operating at TeV and PeV energies. Recently the LHAASO experiment detected ultra-high-energy~(UHE; $E_{gamma}gtrsim 100~mathrm{Te
V}$) photon emissions up to $1.4~mathrm{PeV}$ from twelve astrophysical gamma-ray sources. We point out that the detection of cosmic photons at such energies can constrain the photon self-decay motivated by superluminal Lorentz symmetry violation~(LV) to a higher level, thus can put strong constraints to certain LV frameworks. Meanwhile, we suggest that the current observation of the PeV-scale photon with LHAASO may provide hints to permit a subluminal type of Lorentz violation in the proximity of the Planckian regime, and may be compatible with the light speed variation at the scale of $3.6times 10^{17}~mathrm{GeV}$ recently suggested from gamma-ray burst~(GRB) time delays. We further propose detecting PeV photons coming from extragalactic sources with future experiments, based on LV-induced threshold anomalies of $e^{+}e^{-}$ pair-production, as a crucial test of subluminal Lorentz violation. We comment that these observations are consistent with a D-brane/string-inspired quantum-gravity framework, the space-time foam model.
We revisit a supersymmetric string model for space-time foam, in which bosonic open-string states, such as photons, can possess quantum-gravity-induced velocity fluctuations in vacuum. We argue that the suggestion of light speed variation with lower
bound from gamma-ray burst photon time delays can serve as a support for this string-inspired framework, through connecting the experimental finding with model predictions. We also derive the value of the effective quantum-gravity mass in this framework, and give a qualitative study on the model-dependent coefficients. Constraints from birefringent effects and/or photon decays, including the novel $gamma$-decay constraint obtained here from the latest Tibet AS$gamma$ near-PeV photon, are also found to be consistent with predictions in such a quantum-gravity scheme. Future observation that can testify further the theory is suggested.
