The S-matrix bootstrap. Part I: QFT in AdS

• Main Authors: Miguel F. Paulos, Joao Penedones, Jonathan Toledo, Balt C. van Rees, Pedro Vieira
• Format: Article
• Language: English
• Published: SpringerOpen 2017-11-01
• Series: Journal of High Energy Physics
• Subjects: AdS-CFT Correspondence; Boundary Quantum Field Theory; Conformal Field Theory; Scattering Amplitudes
• Online Access: http://link.springer.com/article/10.1007/JHEP11(2017)133

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.