Holographic study of $$ T\overline{T} $$ like deformed HV QFTs: holographic entanglement entropy

We calculate the $$ T\overline{T} $$ T T ¯ -deformed entanglement entropy for integrable quantum field theories (IQFTs) using the form factor bootstrap approach. We solve the form factor bootstrap axioms for the branch-point twist fields and obtain the deformed form factors. Using these form factors, we compute the deformed von Neuman entropy up to two particle contributions. The solution of the form factor axioms is not unique. We find that for the simplest solution of the bootstrap axioms, the UV limit of the entanglement entropy takes the same form as the undeformed one, but the effective central charge is deformed. For solutions with additional CDD-like factors, we can have different behaviors. The IR corrections, which only depends on the particle spectrum is untouched.

$$ T\overline{T} $$-deformed entanglement entropy for IQFT

He,

Hou,

Jiang

2024

Temporal entanglement entropy as a probe of renormalization group flow

Grieninger,

Ikeda,

Kharzeev

2024

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.

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.