Signature-change events in emergent spacetimes with anisotropic scaling

TL;DR

This paper explores how quantum fields in emergent anisotropic spacetimes with signature change can be realized in condensed matter systems, revealing new insights into quantum gravity analogs and emergent Lorentz symmetry.

Contribution

It demonstrates the physical relevance of signature change events in emergent spacetimes within condensed matter systems with anisotropic scaling.

Findings

Signature change events can occur in effective emergent spacetimes.

Anisotropic scaling helps resolve technical issues in quantum field quantization.

Emergent Lorentz symmetry appears at low energies in the studied systems.

Abstract

We investigate the behaviour of quantum fields coupled to a spacetime geometry exhibiting finite regions of Euclidean (Riemannian) signature. Although from a gravity perspective this situation might seem somewhat far fetched, we will demonstrate its direct physical relevance for an explicitly realizable condensed matter system whose linearized perturbations experience an effective emergent spacetime geometry with externally controllable signature. This effective geometry is intrinsically quantum in origin, and its signature is determined by the details of the microscopic structure. At the level of the effective field theory arising from our condensed matter system we encounter explicit anisotropic scaling in time and space. Here Lorentz symmetry is an emergent symmetry in the infrared. This anisotropic scaling of time and space cures some of the technical problems that arise when working within a canonical quantisation scheme obeying strict Lorentz invariance at all scales, and so is helpful in permitting signature change events to take place.