Towards Bootstrapping RG flows: Sine-Gordon in AdS

TL;DR

This paper investigates the non-perturbative constraints on boundary correlation functions during sine-Gordon RG flows in AdS$_2$, using numerical conformal bootstrap to analyze the flow from free scalars to integrable theories.

Contribution

It applies the numerical conformal bootstrap to study RG flows in AdS, providing detailed bounds on correlation functions that connect UV and IR regimes for sine-Gordon models.

Findings

Bounds often saturated near UV and flat-space limits

Correlation functions match perturbation theory close to UV

Analysis reveals partial saturation of bootstrap bounds during flow

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.