Lorentz breaking effective field theory models for matter and gravity: Theory and observational constraints

A number of different approaches to quantum gravity are at least partly phenomenologically characterized by their treatment of Lorentz symmetry, in particular whether the symmetry is exact or modified/broken at the smallest scales. For example, string theory generally preserves Lorentz symmetry while analog gravity and Lifshitz models break it at microscopic scales. In models with broken Lorentz symmetry, there are a vast number of constraints on departures from Lorentz invariance that can be established with low-energy experiments by employing the techniques of effective field theory in both the matter and gravitational sectors. We shall review here the low-energy effective field theory approach to Lorentz breaking in these sectors, and present various constraints provided by available observations.