TY - JOUR

T1 - Universal features of Lifshitz Green’s functions from holography

AU - Keeler, Cynthia

AU - Knodel, Gino

AU - Liu, James T.

AU - Sun, Kai

N1 - Publisher Copyright:
© 2015, The Author(s).

PY - 2015/8/17

Y1 - 2015/8/17

N2 - 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 Gω^$$ \mathcal{G}\left(\widehat{\omega}\right) $$, 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.

AB - 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 Gω^$$ \mathcal{G}\left(\widehat{\omega}\right) $$, 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.

KW - AdS-CFT Correspondence

KW - Holography and condensed matter physics (AdS/CMT)

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U2 - 10.1007/JHEP08(2015)057

DO - 10.1007/JHEP08(2015)057

M3 - Article

AN - SCOPUS:84939133084

SN - 1029-8479

VL - 2015

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 8

M1 - 57

ER -