Temporally, Spatially or Light-like Modulated Vacua in Lorentz Invariant Theories

TL;DR

This paper investigates various modulated vacuum states in Lorentz invariant theories, classifying them into spatial, temporal, and light-like types, analyzing their stability, symmetry breaking, and fluctuation dynamics.

Contribution

It introduces a comprehensive classification of modulated vacua in Lorentz invariant theories and explores their stability and mode dynamics, including generalized Nambu-Goldstone modes.

Findings

Temporal and light-like vacua impose strict model constraints.

Modulated vacua exhibit unique Nambu-Goldstone modes.

Fluctuation analysis shows absence of ghosts in these vacua.

Abstract

We study the vacuum structure of a class of Lorentz invariant field theories where the vacuum expectation values are not constant but are (phase) modulated. The vacua are classified into spatial, temporal, and light-like modulation types according to the patterns of spontaneous breaking of translational symmetry. The conditions for having temporal or light-like modulated vacua imply severe constraints on the models. We utilize the notion of generalized Nambu-Goldstone modes which appear in the modulated vacua. Finally, we examine fluctuation modes around these vacua and discuss their dynamics and the absence of ghosts.