Spontaneous Breaking of Non-Relativistic Scale Symmetry

Abstract

We analyze the mechanism of spontaneous symmetry breaking of scale invariance in Galilean invariant field theories. We show that the existence of a dynamic gapless dilaton mode depends on whether the $U(1)$ particle number or the Galilean boost symmetry are spontaneously broken. When both scale and particle number symmetries are spontaneously broken there is one propagating gapless Nambu-Goldstone mode. Its dispersion relation is linear if the chemical potential is nonzero and quadratic otherwise. We discuss the reversibility of RG flows in such theories.

arXiv comment25 pages; revised

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• Symmetry Realization via a Dynamical Inverse Higgs Mechanism
• Spontaneous Symmetry Breaking, Conformal Anomaly and Incompressible Fluid Turbulence
• Near-Schrödinger dynamics at large charge
• Operator spectrum of nonrelativistic CFTs at large charge
• Constraints on anisotropic RG flows from holographic entanglement entropy
• Gapped dilatons in scale invariant superfluids