Holography Beyond AdS
Meseret Asrat, Amit Giveon, Nissan Itzhaki, David Kutasov

TL;DR
This paper explores a holographic model transitioning from AdS_3 to a linear dilaton spacetime, revealing finite convergence of perturbation theory in the IR and non-local effects manifesting as imaginary parts in two-point functions.
Contribution
It demonstrates the finite radius of convergence for conformal perturbation theory in a holographic setup with an irrelevant operator, and analyzes non-locality effects in the spectral density.
Findings
Finite convergence radius in momentum space for IR two-point functions.
Spectral density acquires an imaginary part above a critical spectral parameter.
Non-perturbative effects lead to imaginary contributions in position space.
Abstract
We continue our study of string theory in a background that interpolates between in the infrared and a linear dilaton spacetime in the UV. This background corresponds via holography to a deformed by a certain irrelevant operator of dimension . 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.
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