Multicritical Symmetry Breaking and Naturalness of Slow Nambu-Goldstone Bosons

TL;DR

This paper explores spontaneous symmetry breaking without Lorentz invariance, focusing on the naturalness and dispersion relations of Nambu-Goldstone modes with multicritical Lifshitz scaling, revealing new natural quadratic dispersion phenomena.

Contribution

It introduces a mechanism for natural quadratic NG modes protected by polynomial shift symmetry, expanding understanding of symmetry breaking in non-Lorentz-invariant systems.

Findings

NG modes with quadratic dispersion are natural and do not break time reversal symmetry

The mechanism is protected by an enhanced polynomial shift symmetry

NG modes can be associated with a single broken generator without pairwise symmetry

Abstract

We investigate spontaneous global symmetry breaking in the absence of Lorentz invariance, and study technical Naturalness of Nambu-Goldstone (NG) modes whose dispersion relation exhibits a hierarchy of multicritical phenomena with Lifshitz scaling and dynamical exponents $z>1$. For example, we find NG modes with a technically natural quadratic dispersion relation which do not break time reversal symmetry and are associated with a single broken symmetry generator, not a pair. The mechanism is protected by an enhanced `polynomial shift' symmetry in the free-field limit.