Probes for String-Inspired Foam, Lorentz, and CPT Violations in Astrophysics

Lorentz invariance is such a basic principle in fundamental physics that it must be constantly tested and that any proposal of its violation and breakdown of CPT symmetry, that might characterize some approaches to quantum gravity, should be treated with care. In this review we examine, among other scenarios, such instances in supercritical~(Liouville) string theory, particularly in some brane models for ``quantum foam''. Using the phenomenological formalism introduced here, we analyze the observational hints of Lorentz violation in time-of-flight lags of cosmic photons and neutrinos which fit excellently stringy space-time foam scenarios. We further demonstrate how stringent constraints from other astrophysical data, including the recent first detections of multi-TeV events in $\gamma$-ray burst 221009A and PeV cosmic photons by the Large High Altitude Air Shower Observatory~(LHAASO), are satisfied in this context. Such models thus provide a unified framework for all currently observed phenomenologies of space-time symmetry breaking at Planckian scales.