Multicritical Symmetry Breaking and Naturalness of Slow Nambu-Goldstone Bosons

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.

Figures (1)

• Figure 1: One-loop corrections to $\Gamma_{AB}$ of the NG modes in the broken phase of the superrenormalizable LSM.