A holographic perspective on phonons and pseudo-phonons

TL;DR

This paper explores how phonons and pseudo-phonons emerge from spontaneous symmetry breaking in a conformal field theory using holographic models inspired by Q-lattices, providing insights into their low-energy behavior.

Contribution

It introduces a holographic model with a complex scalar in a CFT to study phonons from symmetry breaking, bridging holography and quantum field theory techniques.

Findings

Ward identities are consistent in both QFT and holographic models.

Holographic renormalization confirms the Ward identities.

Correlators encode the low-energy spectrum of phonons.

Abstract

We analyze the concomitant spontaneous breaking of translation and conformal symmetries by introducing in a CFT a complex scalar operator that acquires a spatially dependent expectation value. The model, inspired by the holographic Q-lattice, provides a privileged setup to study the emergence of phonons from a spontaneous translational symmetry breaking in a conformal field theory and offers valuable hints for the treatment of phonons in QFT at large. We first analyze the Ward identity structure by means of standard QFT techniques, considering both spontaneous and explicit symmetry breaking. Next, by implementing holographic renormalization, we show that the same set of Ward identities holds in the holographic Q-lattice. Eventually, relying on the holographic and QFT results, we study the correlators realizing the symmetry breaking pattern and how they encode information about the low-energy spectrum.