# Universal features of Lifshitz Green’s functions from holography

Keeler, Cynthia (Niels Bohr International Academy, Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK 2100, Copenhagen, Denmark) ; Knodel, Gino (Michigan Center for Theoretical Physics, Randall Laboratory of Physics, The University of Michigan, Ann Arbor, MI, 48109-1040, U.S.A.) ; Liu, James (Michigan Center for Theoretical Physics, Randall Laboratory of Physics, The University of Michigan, Ann Arbor, MI, 48109-1040, U.S.A.) ; Sun, Kai (Michigan Center for Theoretical Physics, Randall Laboratory of Physics, The University of Michigan, Ann Arbor, MI, 48109-1040, U.S.A.)

15 August 2015

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 G ω ^ $\mathcal{G}\left(\widehat{\omega}\right)$ , where ω ^ = ω / k → z $\widehat{\omega}=\omega /{\left|\overrightarrow{k}\right|}^z$ 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.

Published in: JHEP 1508 (2015) 057