Lorentz symmetry is a fundamental space-time symmetry underlying the Standard Model of particle physics and gravity. However, unified theories, such as string theory, allow for violation of this symmetry. Thus, the discovery of Lorentz symmetry violation could be the first hint of these theories. Here, we use high-energy atmospheric neutrinos observed at the IceCube Neutrino Observatory to search for anomalous neutrino oscillations as signals of Lorentz violation. The large range of neutrino energies and propagation baselines, together with high statistics, let us perform the most precise test of space-time symmetry in the neutrino sector to date. We find no evidence for Lorentz violation. This allows us to constrain the size of the dimension-four operator in the Standard-Model Extension for Lorentz violation to the $10^{-28}$ level and to set limits on higher dimensional operators of that theory. These are among the most stringent limits on Lorentz violation across all fields of physics.
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