Universal features of Lifshitz Green's functions from holography

TL;DR

This paper shows that in Lifshitz-scaling theories, the spectral function of scalar operators universally exhibits exponential suppression near zero frequency, regardless of additional symmetries, confirmed through holography and field theory examples.

Contribution

It demonstrates the universal exponential suppression of the spectral function in Lifshitz theories and shows this behavior is robust against higher derivative corrections and perturbative expansions.

Findings

Spectral function exponentially suppressed near zero frequency.

Universality of suppression across Lifshitz theories without extra symmetries.

Robustness of results against higher derivative corrections.

Abstract

We examine the behavior of the retarded Green's function in theories with Lifshitz scaling symmetry, both through dual gravitational models and a direct field theory approach. In contrast with the case of a relativistic CFT, where the Green's function is fixed (up to normalization) by symmetry, the generic Lifshitz Green's function can a priori depend on an arbitrary function $\mathcal G(\hat\omega)$, where $\hat\omega=\omega/|\vec k|^z$ is the scale-invariant ratio of frequency to wavenumber, with dynamical exponent $z$. Nevertheless, we demonstrate that the imaginary part of the retarded Green's function (i.e. the spectral function) of scalar operators is exponentially suppressed in a window of frequencies near zero. This behavior is universal in all Lifshitz theories without additional constraining symmetries. On the gravity side, this result is robust against higher derivative corrections, while on the field theory side we present two $z=2$ examples where the exponential suppression arises from summing the perturbative expansion to infinite order.