Neutrino interferometry for high-precision tests of Lorentz symmetry

Lorentz symmetry is a foundation of both particle physics and gravity. 
However, Planck scale theories, such as string theory, allow to violate Lorentz symmetry. 
Thus, Lorentz violation may be the first signal of Planck scale physics and there is a world-wide effort to look for it 
with various state-of-the-art technologies. 

Neutrino oscillation physics is very successful in the last 20 years. 
Although the field of oscillation parameter measurements within neutrino Standard Model (nuSM) is very active, 
neutrino oscillation itself can be a tool to look for new physics beyond the nuSM,  
because neutrino oscillation is a natural interferometer and sensitive to tiny effects of nature. 
"Neutrino interferometry" is a new technology to look for a small space-time effect, such as Lorentz violation. 
The sensitivity of neutrino interferometry at IceCube Neutrino Observatory is among the best 
compared with other technologies from table top experiments to astrophysical observations.   

In this talk, I will introduce Lorentz violation and Lorentz violating neutrino oscillations. 
Then I examine the limits of new physics from atmospheric neutrino oscillation data with IceCube. 
Finally, I will show the preliminary results of new physics search from astrophysical very-high-energy neutrino favor data.