Asymptotic Fragility, Near $AdS_2$ Holography and $T\bar{T}$ (1706.06604v5)

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.

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

This paper presents a compelling paper on the inteconnection among asymptotic fragility, the $T\bar{T}$ deformation, and near-$AdS_2$ holography within the framework of Jackiw–Teitelboim (JT) gravity. The research focuses on providing an exact solution to the scattering problem within this domain, leading to consequential insights on a novel ultraviolet (UV) asymptotic behavior.

Overview of Key Concepts

1. Asymptotic Fragility:
   • Asymptotic fragility characterizes a distinct UV behavior exhibited by JT gravity when coupled with quantum field theories (QFTs). The gravitational dressing of scattering amplitudes leads to such UV behaviors that deviate from traditional UV asymptotics, avoiding typical fixed-point behavior characteristic of QFTs.
2. $T\bar{T}$ Deformation:
   • The paper establishes the equivalence of gravitational dressing via JT gravity with the $T\bar{T}$ deformation. This deformation is particularly notable for maintaining exact solvability of quantum field theories, impacting key elements such as finite-volume spectra and S-matrices, deviating from typical UV stabilization mechanisms.
3. Near-$AdS_2$ Holography:
   • The investigation deepens into near-$AdS_2$ holography, where typical $AdS_2$ isometries are gauged in JT gravity, necessitating a transformation in conventional understanding, especially concerning boundary physics. The holographic boundary dynamics significantly impact scattering descriptions in the flat space limit.

Technical Contributions

• Gravitational Dressing and Exact Scattering Solution:
  • The gravitational dressing in the JT model is explored as a $T\bar{T}$-like deformation, providing an exact solution to scattering in this modified landscape. By analyzing boundary conditions and correlators, the derivations establish a profound connection between gravitational interactions and known properties of $T\bar{T}$ deformed theories.
• S-matrix formulation:
  • The gravitationally dressed S-matrix is formulated using boundary correlator techniques and an alternative path integral formulation. This offers an intricate, theoretically sound method to compute scattering amplitudes that obey modified symmetry transformations.
• Critical Comparisons:
  • Comparisons with known results in $NAdS_2$ holography allow the paper to map the implications of holographic descriptions onto observable scattering phenomena. The paper utilizes insights from the Schwarzian framework to extend these results to massive particle scenarios in flat space.

Implications and Future Directions

• Theoretical Implications:
  • The equivalence between gravitational dressing and $T\bar{T}$ transformation, and their unified explanation through JT gravity, provides a cohesive landscape in understanding UV aspects of QFTs. The work suggests novel interpretations of quantum gravity effects, notably those lacking sharp local observables and featuring gravitational-like behavior.
• Practical Relevance:
  • The findings are applicable to models where QFTs couple to gravitational fields without engaging traditional UV completions, expanding applicable scenarios for string theories and possibly QCD strings.
• Prospects in AI and Computational Physics:
  • While primarily theoretical, the development presents avenues for simulating gravitational interactions within computational frameworks. Future AI algorithms could harness this coupling to simulate more generalized systems with similar deformations in theoretical physics.

In conclusion, this paper intricately ties together three profound elements of modern theoretical physics—asymptotic fragility, $T\bar{T}$ deformation, and near-$AdS_2$ holography—proposing a harmonized view of JT gravity's role across these diverse contexts. The paper illuminates gravitational impacts on QFT boundaries and posits further exploration into quantum gravitational effects across various physical dimensions.