Abstract
In this article, we consider a Renormalization Group flow of the Thermofield-Double state in a UV-complete description of Holography, by introducing a relevant deformation to the \( \mathcal{N} \) = 4 super Yang-Mills theory at strong coupling. This RG-flow is known to have a non-trivial, interacting \( \mathcal{N} \) = 1 fixed point at the IR. Geometrically, an RG-flow of the TFD-state naturally continues radially and inside the black hole event horizon and yields a Kasner-structure near singularity, as has been observed in recent works. We show that for a generic value of the deformation, the putative IR fixed point remains inside the black hole in a certain sense. By fine-tuning this deformation, the “fixed point” can be brought arbitrarily close to the event horizon, while always remaining inside. Physically, this distinguishes between the vanishing temperature limit of the RG-flows with the one at exactly zero temperature. We further discuss its general implications in the context of Holography, including a study of the recently-proposed Holographic a-function, especially in the interior of the black hole. We also discuss how correlations between the two-copies of the TFD-state depend on this explicit RG-flow.
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Das, S., Kundu, A. RG flows and thermofield-double states in holography. J. High Energ. Phys. 2022, 167 (2022). https://doi.org/10.1007/JHEP04(2022)167
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DOI: https://doi.org/10.1007/JHEP04(2022)167