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 -