Spontaneous Violation of Lorentz and CPT Symmetry

Abstract

The standard model as well as many of its modern day extensions preserves Lorentz and CPT symmetry. In fact, symmetry under the Lorentz group is a fundamental assumption of virtually any fundamental theory used to describe elementary particle physics. Under very mild assumptions, the postulates of a point particle theory that preserves Lorentz invariance imply that CPT is also preserved [1]. In this proceedings, I will discuss the construction of quantum field theories that break Lorentz and CPT symmetry. There are both experimental and theoretical motivations to develop such theories. Many sensitive experimental tests of Lorentz and CPT symmetry have been performed. For example, high precision tests involving atomic systems [2, 3], clock comparisons [4, 5], and neutral meson oscillations [6, 7] provide stringent tests of Lorentz and CPT symmetry. Recently, a pendulum with a net macroscopic spin angular momentum has been constructed and used to investigate spin-dependent Lorentz and CPT violation [8]. In the past, such experiments have placed bounds on phenomenological parameters that lack any clear connection with the microscopic physics of the standard model. One motivation of constructing a theory in the context of the standard model that allows for Lorentz and CPT violation is the desire to have a single theory within the context of conventional quantum field theory that could relate various experiments and be used to motivate future investigations. This begs the question as to how such effects might arise naturally within the current framework of quantum field theory. The main idea is that miniscule lowenergy remnant effects that violate fundamental symmetries may arise in theories underlying the standard model. One example is string theory in which nontrivial structure of the vacuum solutions may induce observable Lorentz and CPT violations [9, 10, 11]. Rather than attempting a construction based directly on a specific underlying model, such as string theory, we proceed using the generic mechanism of spontaneous symmetry violation to implement the breaking. Terms involving standard model fields that violate Lorentz and CPT symmetry are assumed to arise from a