Holography Beyond AdS

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 $AdS_3$ in the infrared and a linear dilaton spacetime $R^{1,1}\times R_\phi$ 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.