IR side of bounds on Theories with Spontaneously Broken Lorentz Symmetry

TL;DR

This paper explores how IR quantities reflect UV features in theories with spontaneously broken Lorentz symmetry, establishing bounds on excitation speeds based on low-energy kinematics.

Contribution

It provides a new IR-based formulation of analyticity bounds in Lorentz-violating theories, linking gapped and gapless excitation speeds.

Findings

Gapped excitations must be slower than gapless ones at low momenta.

The bounds are expressed purely in terms of low-energy kinematic quantities.

Results suggest a new interpretation of UV/IR connections in complex theories.

Abstract

In nature, some UV features of dynamics are reflected in IR quantities. In fully relativistic theories, this connection can be probed through the analyticity properties of scattering amplitudes, allowing one to understand which IR theories respect the UV assumptions of quantum field theory. The ensuing analyticity bounds can usually be rephrased as the absence of faster-than-light propagation for low-energy excitations. While it is interesting to understand these relations and their IR characterization for theories that have less idealized properties, it is also more difficult to derive analyticity bounds in these cases. For theories that spontaneously break Lorentz symmetry, recent progress was made by considering correlators of conserved currents and their analyticity properties. In this work, we focus on such theories and work to close the gap from the IR side, finding a natural way to express the known analyticity bounds purely in terms of low-energy kinematical quantities. Our analysis shows that the bounds require gapped excitations to have a slower speed than the gapless ones, at least for momenta that are low with respect to the mass gap. These results suggest a way to interpret the UV/IR connection in more complex theories.