Asymptotic Fragility, Near $AdS_2$ Holography and $T\bar{T}$

TL;DR

The paper shows that gravitational dressing of 2D quantum field theories, encapsulated by the dressed $S$-matrix $\hat{S}(\{p_i\})=S(\{p_i\})e^{i \ell^2/4 \sum_{i<j} p_i*p_j}$, is equivalent to the $T\bar{T}$ deformation and emerges as a flat-space limit of near-$AdS_2$ holography. It provides an exact solution for JT gravity coupled to arbitrary matter in flat space, using dynamical coordinates $X^{\pm}$ to construct an exact $(S)$-matrix via $\hat{S}=USU$ with a universal phase, and shows the leading perturbative match to the $T\bar{T}$ operator. Through two holographic routes—a direct boundary-Chern–Simons/LSZ derivation and the Schwarzian boundary correlator limit—the authors reproduce the same dressing and uncover that unitarity in the flat limit requires averaging over the Schwarzian coupling. They also derive a finite-volume spectrum in a prototype $c=24$ CFT case, revealing a localizable, one-loop exact integral, and discuss implications for confining strings and the QCD string, including potential extensions to non-critical strings and bulk gravitational puzzles. Overall, the work unifies gravitational dressing, $T\bar{T}$ deformation, and near-$AdS_2$ holography, offering a tractable, holographically motivated framework for 2D quantum gravity effects on scattering amplitudes with potential impact on string worldsheet theories and finite-volume spectrums.

Abstract

We present the exact solution for the scattering problem in the flat space Jackiw-Teitelboim (JT) gravity coupled to an arbitrary quantum field theory. JT gravity results in a gravitational dressing of field theoretical scattering amplitudes. The exact expression for the dressed $S$-matrix was previously known as a solvable example of a novel UV asymptotic behavior, dubbed asymptotic fragility. This dressing is equivalent to the $T\bar{T}$ deformation of the initial quantum field theory. JT gravity coupled to a single massless boson provides a promising action formulation for an integrable approximation to the worldsheet theory of confining strings in 3D gluodynamics. We also derive the dressed $S$-matrix as a flat space limit of the near $AdS_2$ holography. We show that in order to preserve the flat space unitarity the conventional Schwarzian dressing of boundary correlators needs to be slightly extended. Finally, we propose a new simple expression for flat space amplitudes of massive particles in terms of correlators of holographic CFT's.

Figures (4)

• Figure 1: Particles at the asymptotic boundary of Minkowski space. Arrows correspond to on-shell two-momenta. $\tau$ is the coordinate parametrizing the boundary and ordering is given by the rapidities as described in the text.
• Figure 2: Lines of constant $X^+$ and $X^-$ as seen in the $\sigma$ coordinates.
• Figure 3: (a) Scattering process in the Lorentzian space with LSZ surfaces taken to be hyperbolas, the particles intersect the surfaces at hyperbolic angles determined by their rapidities. (b) The same process but rotated to the Euclidean space. Positions of the particles on the boundary circle are determined by their Euclidean rapidities $\theta_i=\bar{\beta}_i+\pi$. (c) Coupling to JT gravity results into the deformation of the boundary surface. Positions on the boundary are given by $u_i=\bar{\beta}_i+\pi$. The grey bulb on all three figures represents the interaction region ${\cal M}_{int}$.
• Figure 4: The Euclidean $S$-matrix is obtained from the boundary correlators by placing the source corresponding to the $i$-th particle at $\theta_i=\bar{\beta_i}+\pi$.