Reversing renormalization-group flows with AdS/CFT

Abstract

For scalar fields in AdS with masses slightly above the Breitenlohner-Freedman bound, appropriate non-local boundary conditions can define a unitary theory. Such boundary conditions correspond to non-local deformations of the dual CFT, and generate a non-local renormalization-group flow. Nevertheless, a bulk analysis suggests that certain such flows lead to local CFTs in the infrared. Since the flows are non-local, they can either increase or decrease the central charge of the CFT. In fact, given any local renormalization-group flow within a certain general class which leads from a UV theory (CFT 1 ) to an IR theory (CFT 2 ), we show that one can find such a non-local flow in which the endpoints are interchanged: the non-local theory flows from CFT 2 in the IR to CFT 1 in the UV. We work at large N , but the flows we consider involve quantum field effects in the bulk, corresponding to 1/N corrections in the dual theory.

CFT dual of the AdS Dirichlet problem: fluid/gravity on cut-off surfaces

“…The key feature to note from the above analysis, is that the expression for the boundary source J φ is non-analytic in k and hence non-local when Fourier-transformed back to position space. Hence, we see that in general we have a map between the non-local double trace deformation on the boundary and the Dirichlet data on Σ D (similar non-local double-trace deformations were explored earlier in [29]).…”

“…This unfortunately is not true and as a result the non-relativistic metrics quoted in v1 of this paper and in [13] only solve Einstein's equations to first order in the non-relativistic gradient expansion. The correct form of the general expressions are now collected in Appendix E. 29 Note that the highlighted terms involve Weyl invariant RicciR µν and SchoutenŜ µν curvature tensors which are defined in Appendix D. 30 Note that we have retained certain terms at O(‫א‬ −3 ) which are actually not necessary to solve the equation of motion (3.1) at this order (eg., the velocity cubed term). This is to facilitate ease of comparison of our results when we undertake the near-horizon analysis in §6, with those in the existing literature.…”

“…Since in the scaling limit ‫א‬ 1 one has from (5.7) that the âµ = µ to leading order things simplify considerably. Using the formulae in the last subsection and including the terms from the second order metric 29 (highlighted) it is easy to show that the bulk metric (3.29) becomes 30…”

Supersymmetric mixed boundary conditions in AdS2 and DCFT1 marginal deformations

“…Although this boundary condition is given in terms of derivatives and not integrals it is also deemed non-local in the sense of[34,35].…”

On the stress tensor of Kerr/CFT

“…See[26] for a discussion of anti-de Sitter boundary conditions with similar properties. In that case they correspond explicitly to non-local deformations of the dual field theory.…”