Multicritical Symmetry Breaking and Naturalness of Slow Nambu-Goldstone Bosons

We investigate spontaneous global symmetry breaking in the absence of Lorentz invariance and study technical naturalness of Nambu-Goldstone modes for which the dispersion relation exhibits a hierarchy of multicritical phenomena with Lifshitz scaling and dynamical exponents z > 1. For example, we find Nambu-Goldstone 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.