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arXiv · 2112.11675

RG Flows and Thermofield-Double States in Holography

Suman Das·Arnab Kundu
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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 ${\cal N}=4$ super Yang-Mills theory at strong coupling. This RG-flow is known to have a non-trivial, interacting ${\cal N}=1$ 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. 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. We also discuss how correlations between the two-copies of the TFD-state depend on this explicit RG-flow.

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Suman Das, Arnab Kundu. 2021-12-22. RG Flows and Thermofield-Double States in Holography. https://doi.org/10.1007/jhep04(2022)167

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