Causality and stability for Lorentz-CPT violating electrodynamics with dimension-5 operators

TL;DR

This paper investigates Lorentz-violating electrodynamics with dimension-5 operators, analyzing causality, stability, and analyticity for different background vectors, and finds spacelike backgrounds are consistent while timelike and lightlike ones have issues.

Contribution

It extends the analysis of Lorentz-violating electrodynamics to arbitrary background directions, identifying conditions for consistency and stability in these models.

Findings

Spacelike backgrounds preserve stability and analyticity.

Timelike backgrounds lead to causality violations.

Lightlike backgrounds introduce higher-derivative instabilities.

Abstract

Stringent limits on the Myers-Pospelov timelike parameter for photons $\xi<10^{-15}$ coming from astrophysical tests suggest exploring more general preferred backgrounds, such as spacelike and lightlike. We take some steps in this direction. We allow the external four vector $n$ characterizing the Lorentz symmetry breaking to have arbitrary directions in spacetime. We study the consistency for the effective field theories in each privileged frame by demanding causality, stability and analyticity. When specializing to a timelike background we found runaway solutions leading to causality and unitarity violations. We show that the lightlike theory is a higher-derivative theory with more degrees of freedom and nonanalytic solutions leading to instabilities when interactions are turned on. We demonstrate by explicit calculation that both stability and analyticity are preserved for the purely spacelike case while microcausality is highly suppressed. This new anisotropic model opens the possibility to play a role in the search for Planck-scale effects.