Kinematics of Horizon and Singularity and IR/UV Mixing in AdS

Abstract: In [arXiv:1512.02232 [hep-th]] it was argued, based on the construction of a holographic c-function, that the curvature singularity of a black brane can be thought of as a trivial IR fixed point. This is dual to the gapped nature of the thermal state in the IR. So one can say that by taking one kind of low energy limit in the thermal CFT we are probing the near-singularity region. But there is another more conventional low energy limit which corresponds to probing the near-horizon region. Now, instead of one, if we think in terms of these two low-energy limits and take into account the fact that in AdS-CFT the only observables are CFT correlators then we can get a completely different interpretation of the curvature singularity. In a nutshell, the very long wavelength degrees of freedom in the thermal CFT carry information of both the near-horizon and the near-singularity regions, but, the field theory observer cannot, in principle, disentangle the information of the near-horizon region from the information of the near-singularity region using the the thermal CFT correlators. This can be interpreted as a very specific form of holographic "non-locality" in a black hole background which relates the "inside and the outside". We argue in the paper that owing to this "non-locality", the space-like curvature singularity along with its problems, which are all local in nature, completely disappear from the theory or get dissolved. But, the same "non-locality" now tells us that some of the "$e^{-S}$-effects" that one finds, for example, in the late time thermal two-point function, can be thought of as carrying complete information about "Planck-scale effects near the singularity". From the local EFT point of view this may be called "UV-IR-mixing" which is caused by the "non-locality". We also comment on its close relation to black hole complementarity.