Holography Beyond AdS

Abstract We continue our study of string theory in a background that interpolates between A d S 3 in the infrared and a linear dilaton spacetime R 1 , 1 × R ϕ in the UV. This background corresponds via holography to a C F T 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.