Towards Bootstrapping RG flows: Sine-Gordon in AdS

Abstract

The boundary correlation functions for a Quantum Field Theory (QFT) in an Anti-de Sitter (AdS) background can stay conformally covariant even if the bulk theory undergoes a renormalization group (RG) flow. Studying such correlation functions with the numerical conformal bootstrap leads to non-perturbative constraints that must hold along the entire flow. In this paper we carry out this analysis for the sine-Gordon RG flows in AdS${}_2$, which start with a free (compact) scalar in the UV and end with well-known massive integrable theories that saturate many S-matrix bootstrap bounds. We numerically analyze the correlation functions of both breathers and kinks and provide a detailed comparison with perturbation theory near the UV fixed point. Our bounds are often saturated to one or two orders in perturbation theory, as well as in the flat-space limit, but not necessarily in between.

62 pages, 22 figures, 1 menhir

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• Fermions in AdS and Gross-Neveu BCFT
• Dispersive Sum Rules in AdS${}_2$
• Scattering bound states in AdS
• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• Large $N$ analytical functional bootstrap I: 1D CFTs and total positivity
• From conformal correlators to analytic S-matrices: CFT${}_1$/QFT${}_2$
• Constructing CFTs from AdS flows