Extremal surfaces in glue-on AdS/$$ T\overline{T} $$ holography

The recently introduced concept of timelike entanglement entropy has sparked a lot of interest. Unlike the traditional spacelike entanglement entropy, timelike entanglement entropy involves tracing over a timelike subsystem. In this work, we propose an extension of timelike entanglement entropy to Euclidean space (“temporal entanglement entropy”), and relate it to the renormalization group (RG) flow. Specifically, we show that tracing over a period of Euclidean time corresponds to coarse-graining the system and can be connected to momentum space entanglement. We employ Holography, a framework naturally embedding RG flow, to illustrate our proposal. Within cutoff holography, we establish a direct link between the UV cutoff and the smallest resolvable time interval within the effective theory through the irrelevant $$T\overline{T }$$ deformation. Increasing the UV cutoff results in an enhanced capability to resolve finer time intervals, while reducing it has the opposite effect. Moreover, we show that tracing over a larger Euclidean time interval is formally equivalent to integrating out more UV degrees of freedom (or lowering the temperature). As an application, we point out that the temporal entanglement entropy can detect the critical Lifshitz exponent z in non-relativistic theories which is not accessible from spatial entanglement at zero temperature and density.

Temporal entanglement entropy as a probe of renormalization group flow

Grieninger,

Ikeda,

Kharzeev

2024

One-loop partition functions in $$T\overline{T }$$-deformed AdS3

2024

We study the geometry of $$T\overline{T }$$-deformed BTZ black hole and find it can be regarded as a quotient of hyperbolic space. We then consider the massive scalar field propagating in the $$T\overline{T }$$-deformed BTZ black hole background. The one-loop partition function of scalar field is calculated using the heat kernel method and the Wilson spool proposal. These two methods give consistent result which implies the Wilson spool proposal still holds under $$T\overline{T }$$ deformation. Moreover, we also calculate the one-loop partition function of graviton in $$T\overline{T }$$-deformed BTZ black hole. We find the deformed one-loop partition functions are modified in a simple way, which corresponds to a replacement of the modular parameter. The result precisely matches the large c expansion of $$T\overline{T }$$-deformed CFT partition function. These results provide a further check about the correspondence between $$T\overline{T }$$-deformed CFT2 and AdS3 with mixed boundary condition.

A multiverse model in T2 dS wedge holography

Aguilar-Gutierrez,

Landgren

2024

We construct a multiverse model where empty AdSd+1 space is cut off by a pair of accelerated dSd space universes, at a finite AdS boundary cutoff which we treat as a T2 deformation in the holographic dual, and one in the AdS interior, the IR brane; and denote the construction as T2 dS wedge holography. We glue together several copies of this configuration along the UV cutoff and the IR branes in a periodic matter. To provide the model with dynamics similar to those of near Nariai black holes used in other multiverse toy models, we specialize to d = 2 and add dS JT gravity as an intrinsic gravity theory on the IR branes. We then study the entanglement entropy with respect to a finite cutoff observer, who finds a Page curve transition due to an entanglement island connecting the UV cutoff and IR brane. This process involves the coarse-graining of information outside the causally accessible region to the observer. Our model provides an explicit realization of entanglement between IR and UV degrees of freedom encoded in the multiverse.