## Abstract

We continue our study of string theory in a background that interpolates between AdS_{3} in the infrared and a linear dilaton spacetime R^{1,1}×R_{ϕ} in the UV. This background corresponds via holography to a CFT_{2} deformed by a certain irrelevant operator of dimension (2,2). We show that for two point functions of local operators in the infrared CFT, conformal perturbation theory in this irrelevant operator has a finite radius of convergence in momentum space, and one can use it to flow up the renormalization group. The spectral density develops an imaginary part above a certain critical value of the spectral parameter; this appears to be related to the non-locality of the theory. In position space, conformal perturbation theory has a vanishing radius of convergence; the leading non-perturbative effect is an imaginary part of the two point function.

Original language | American English |
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Pages (from-to) | 241-253 |

Number of pages | 13 |

Journal | Nuclear Physics B |

Volume | 932 |

DOIs | |

State | Published - Jul 2018 |

### Bibliographical note

Funding Information:We thank O. Aharony, T. Banks, M. Berkooz, T. Dumitrescu, G. Giribet, D. Jafferis, I. Klebanov, J. Maldacena, S. Sethi, K. Skenderis and M. Strassler for discussions. The work of AG and NI is supported in part by the I-CORE Program of the Planning and Budgeting Committee and the Israel Science Foundation (Center No. 1937/12 ), and by a center of excellence supported by the Israel Science Foundation (grant number 1989/14 ). MA and DK are supported in part by DOE grant DE-SC0009924 . DK thanks Tel Aviv University and the Hebrew University for hospitality during part of this work.

Publisher Copyright:

© 2018 The Author(s)