The S-matrix Bootstrap I: QFT in AdS (1607.06109v2)

Abstract: We propose a strategy to study massive Quantum Field Theory (QFT) using conformal bootstrap methods. The idea is to consider QFT in hyperbolic space and study correlation functions of its boundary operators. We show that these are solutions of the crossing equations in one lower dimension. By sending the curvature radius of the background hyperbolic space to infinity we expect to recover flat-space physics. We explain that this regime corresponds to large scaling dimensions of the boundary operators, and discuss how to obtain the flat-space scattering amplitudes from the corresponding limit of the boundary correlators. We implement this strategy to obtain universal bounds on the strength of cubic couplings in 2D flat-space QFTs using 1D conformal bootstrap techniques. Our numerical results match precisely the analytic bounds obtained in our companion paper using S-matrix bootstrap techniques.

• The paper introduces a novel framework employing 1D conformal bootstrap techniques in AdS to derive flat-space scattering amplitudes.
• The paper applies numerical methods to establish universal bounds on cubic couplings in two-dimensional QFT, validating S-matrix predictions.
• The paper elucidates the transition from hyperbolic to flat-space limits, bridging boundary correlators with physical scattering processes.

The S-matrix Bootstrap I: Quantum Field Theory in AdS

The paper "The S-matrix Bootstrap I: QFT in AdS" by Miguel F. Paulos et al. explores a novel approach to studying massive Quantum Field Theory (QFT) using conformal bootstrap methods within hyperbolic space, specifically addressing the AdS (Anti-de Sitter) regime. This paper integrates elements of conformal field theories (CFTs) with QFT dynamics, providing insightful implications for understanding flat-space physics through AdS/CFT correspondence.

Abstract Overview

The authors propose a methodological framework for analyzing massive QFT by considering it in hyperbolic space and evaluating correlation functions at the boundary operators. This innovative approach extends the conformal bootstrap techniques to non-conformal QFTs by investigating the crossover from hyperbolic space to flat space physics, where the curvature radius $R$ tends to infinity, approximating flat-space conditions.

Methodology and Numerical Results

The strategy is implemented to establish universal bounds on the cubic couplings in two-dimensional flat-space QFTs utilizing 1D conformal bootstrap techniques. The paper provides numerical results that align with analytical bounds derived through S-matrix bootstrap methods in related works. These findings are crucial for verifying the theoretical predictions about scattering amplitudes from boundary correlators.

Core Contributions

1. Boundary Correlators: The paper discusses how these solutions of crossing equations in lower dimensions can be studied to derive flat-space scattering amplitudes from their adiabatic limits.
2. Numerical Bootstrap: By applying numerical bootstrap techniques, the authors offer robust constraints on QFT observables, enriching the understanding of the QFT's boundary dynamics and theoretical predictions.
3. Flat-Space Limit Transition: The crossover from AdS (hyperbolic space) to flat-space limits is elucidated, detailing how large scaling dimensions with infinite curvature radius reflect physical scattering processes.
4. Collaboration with S-matrix Techniques: The paper highlights the synergy between the conformal bootstrap and analytic S-matrix bootstrap techniques, enhancing the prediction accuracy for scattering amplitudes in massive QFT scenarios.

Implications and Future Directions

The implications are both theoretical and practical, offering potential pathways for advancements in AI models built upon these QFT paradigms. By establishing connections between boundary correlation functions and S-matrix behaviors, the authors lay foundational work for complex QFT studies in higher dimensions. Future developments could lead to more refined and comprehensive modeling of interactions in both hyperbolic and flat spaces, with practical applications in predictive simulations and experimental physics.

In conclusion, this paper brings forward a pivotal perspective on QFT analysis via conformal bootstrap methodologies in AdS settings, paving the way for enhanced understanding and simulation of flat-space dynamics through boundary conformal theories.