Correlation functions in the $${\text{TsT}}/T\overline{T }$$ correspondence

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.

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

2024

Negative single-trace $$ T\overline{T} $$ holography holography versus de Sitter

Giveon

2024

In single-trace $$ T\overline{T} $$ T T ¯ holography, for the negative sign of the deformation, the geometries dual to high energy states consist of a singular UV wall that separates black strings in the IR from an asymptotically linear dilaton spacetime. In the hologram, the black strings amount to states in a symmetric product of $$ T\overline{T} $$ T T ¯ deformed CFT2, whose energy and momentum are split equally among the different blocks. The properties of this holographic duality have intriguing similarities with the proposed principles of de Sitter holography. In this note, the analogy between the two is presented. In particular, as the horizon location approaches the UV wall, one obtains a state of maximum finite entropy and infinite temperature. On the other hand, the bulk temperature of the geometry obtained in the limit is small. These properties are identical to those proposed in empty de Sitter holography.

Spectral flow and the conformal block expansion for strings in AdS3

Iguri,

Kovensky,

Toro

2024

We present a detailed study of spectrally flowed four-point functions in the SL(2,ℝ) WZW model, focusing on their conformal block decomposition. Dei and Eberhardt conjectured a general formula relating these observables to their unflowed counterparts. Although the latter are not known in closed form, their conformal block expansion has been formally established. By combining this information with the integral transform that encodes the effect of spectral flow, we show how to describe a considerable number of s-channel exchanges, including cases with both flowed and unflowed intermediate states. For all such processes, we compute the normalization of the corresponding conformal blocks in terms of products of the recently derived flowed three-point functions with arbitrary spectral flow charges. Our results constitute a highly non-trivial consistency check, thus strongly supporting the aforementioned conjecture, and establishing its computational power.