Holographic spacetime as an RG flow
Renormalization group (RG) flows describe how to interpolate between theories which are "effective" at particular scales. In the space of theories, RG flows are often said to "start" at some high-energy scale-invariant fixed point (an ultraviolet CFT) and "flow" to some low-energy scale-invariant fixed point (an infrared CFT). They are thus thought of as curves parameterized by some energy cutoff scale.
In the context of AdS/CFT, bulk classical gravitational dynamics with matter present can be viewed as "driving" a "holographic RG flow" with the boundary theory as the UV CFT. Indeed, this is the older way to address the question of how the bulk spacetime "emerges" from the boundary theory. I am interested in applying this view of AdS/CFT to modern approaches involving quantum information.
Within the holographic RG language, there is a natural way to encode the interior of a backreacting AdS black hole; one may analytically continue an RG flow to imaginary energy scales beyond the IR fixed point. The resulting analytic continuation is called a trans-IR flow. Such flows provide a cohesive language with which to conceptualize bulk quantities characterizing the interior physics of black holes. Furthermore, results about the near-singularity geometry of a backreacting black hole may be recontextualized in the language of these RG flows.
We extend our previous work Trans-IR flows to black hole singularities to a class of RG flows in which Lorentz symmetry is spontaneously broken. Our goal is to demonstrate the existence of monotonic functions in trans-IR flows with reduced symmetry. We construct a monotonic function, demonstrating the robustness of the trans-IR picture in less symmetrical flows. We also use a concrete example to show that our monotonic function can reflect nontrivial fluctuations in the dynamics of the black hole interior.
Using thermal states within holography, we construct a monotonic function which counts the degrees of freedom along both an RG flow and its trans-IR analytic continuation which coincides with known monotonic functions from the literature. We numerically examine its behavior for thermal states along RG flows triggered by "minimal" scalar deformations, which amounts to analyzing the behavior of AdS black holes backreacting against Klein-Gordon scalar fields. We also discuss how various quantum information quantities encode aspects of the trans-IR flow, with a particular emphasis on statistical correlations and holographic complexity from action.
E. Caceres, SS, H.-Y. Sun, Imprints of phase transitions on Kasner singularities. arXiv:2305.11177, May 2023.
We examine how near-boundary physics imprints upon the interior dynamics of black holes. Guided by the renormalization-group-flow view of AdS/CFT, this amounts to examining how UV physics leaves imprints upon a trans-IR analytic continuation of an RG flow. We focus on phase transitions of geometric structures in round black holes and whose boundary duals are known---specifically codimension-2 surfaces encoding entanglement entropy and geodesics encoding heavy thermal correlation functions. These transitions are universal in that their occurrence does not stem from the specifics of the bulk matter sector, in contrast with the model-dependent AdS/CMT phase transitions (some of which have been connected to black-hole-interior dynamics in the literature).