Correlation functions in theories with Lifshitz scaling

TL;DR

This paper explores correlation functions in Lifshitz-scaling theories, revealing their connection to conformal field theories and analyzing quasinormal modes in Lifshitz black holes, with implications for thermalization.

Contribution

It demonstrates that autocorrelation functions in Lifshitz theories can be mapped to two-dimensional conformal field theories and provides analytical results for quasinormal modes in Lifshitz black hole backgrounds.

Findings

Correlation functions relate to 2D conformal field theories.

Analytical quasinormal mode spectra at low momenta.

Distinct high-momentum behavior affecting thermalization.

Abstract

The 2+1 dimensional quantum Lifshitz model can be generalised to a class of higher dimensional free field theories that exhibit Lifshitz scaling. When the dynamical critical exponent equals the number of spatial dimensions, equal time correlation functions of scaling operators in the generalised quantum Lifshitz model are given by a d-dimensional higher-derivative conformal field theory. Autocorrelation functions in the generalised quantum Lifshitz model in any number of dimensions can on the other hand be expressed in terms of autocorrelation functions of a two-dimensional conformal field theory. This also holds for autocorrelation functions in a strongly coupled Lifshitz field theory with a holographic dual of Einstein-Maxwell-dilaton type. The map to a two-dimensional conformal field theory extends to autocorrelation functions in thermal states and out- of-equilbrium states preserving symmetry under spatial translations and rotations in both types of Lifshitz models. Furthermore, the spectrum of quasinormal modes of scalar field perturbations in Lifshitz black hole backgrounds can be obtained analytically at low spatial momenta and exhibits a linear dispersion relation at z = d. At high momentum, the mode spectrum can be obtained in a WKB approximation and displays very different behaviour compared to holographic duals of conformal field theories. This has implications for thermalisation in strongly coupled Lifshitz field theories with z > 1.