Holographic torus correlators in AdS3 gravity coupled to scalar field

In the AdS3/CFT2 framework, the Euclidean BTZ black hole corresponds to the dominant high-temperature phase of its dual field theory. We initially employ perturbative methods to solve the Einstein equations as boundary value problems, providing correlators for the energy-momentum tensor operator at low points. Utilizing operator equations established in our previous work, we further compute arbitrary high-point correlators for the energy-momentum tensor operator in the high-temperature phase and recursive relations for these high-point functions. Concurrently, we employ the Chern-Simons formalism to derive consistent results. Further, using the cut-off AdS/$$ T\overline{T} $$ T T ¯ -deformed CFT duality, we calculate the energy-momentum tensor correlators, contributing to the comprehensive understanding of the system’s dynamics. Finally, stress tensor correlators enable us to ascertain the corresponding KdV operator correlators at low-temperature.

Note on holographic torus stress tensor correlators in AdS3 gravity

He,

Li,

et al. 2024

Quantum complexity of $$ T\overline{T} $$-deformation and its implications

Astaneh

2024

We employ holography to calculate the quantum complexity of $$ T\overline{T} $$ T T ¯ -deformation, utilizing the complexity equals volume (CV) and the complexity equals action (CA) proposals within the bulk spacetime with a finite radius cutoff. We find that the complexity of the deformed theory differs from the renormalized complexity of the original theory by a geometric functional: the bending (Willmore) energy of the time-constant slice of the base manifold. We use this result to propose an unambiguous scheme for calculating holographic quantum complexity through the CA proposal.

Bulk-local dS3 holography: the matter with $$ T\overline{T} $$ + Λ2

Batra,

De Luca,

Silverstein

et al. 2024

We propose an algorithm which builds a concrete dual for large-radius 3d de Sitter with a timelike York boundary for both gravity and bulk effective fields. This generalizes the solvable $$ T\overline{T} $$ T T ¯ + Λ2 deformation, whose finite real spectrum accounts for the refined Gibbons-Hawking entropy as a microstate count while reproducing the radial static patch geometry. The required generalization to produce approximately local boundary conditions for bulk quantum fields requires a scheme for defining double-trace operators dual to deformed boundary conditions to realize the finite timelike boundary, valid at finite N. By starting with a small stint of a pure $$ T\overline{T} $$ T T ¯ trajectory, the theory becomes finite, enabling well-defined subtractions to define the double-trace deformation so as to match the large-N prescription of Hartman, Kruthoff, Shaghoulian, and Tajdini to good approximation. We incorporate the matter effecting an uplift from negative to positive cosmological constant, and analyze the effect of matter on the energy spectrum of the theory arising from time-dependent bulk excitations. This validates the cosmic horizon dS3 microstate count for large-radius dS3 holography, embedding $$ T\overline{T} $$ T T ¯ + Λ2 concretely into a larger theory consistent with bulk locality for matter fields. We comment briefly on potential upgrades to four dimensions and other future directions.