### 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 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.

Original language | English (US) |
---|---|

Article number | 57 |

Journal | Journal of High Energy Physics |

Volume | 2015 |

Issue number | 8 |

DOIs | |

State | Published - Aug 17 2015 |

Externally published | Yes |

### Fingerprint

### Keywords

- AdS-CFT Correspondence
- Holography and condensed matter physics (AdS/CMT)

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2015*(8), [57]. https://doi.org/10.1007/JHEP08(2015)057

**Universal features of Lifshitz Green’s functions from holography.** / Keeler, Cynthia; Knodel, Gino; Liu, James T.; Sun, Kai.

Research output: Contribution to journal › Article

*Journal of High Energy Physics*, vol. 2015, no. 8, 57. https://doi.org/10.1007/JHEP08(2015)057

}

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

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)

UR - http://www.scopus.com/inward/record.url?scp=84939133084&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84939133084&partnerID=8YFLogxK

U2 - 10.1007/JHEP08(2015)057

DO - 10.1007/JHEP08(2015)057

M3 - Article

AN - SCOPUS:84939133084

VL - 2015

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1029-8479

IS - 8

M1 - 57

ER -