QFT as a set of ODEs

TL;DR

This paper derives a universal set of first order ODEs that describe how boundary and bulk operator data in 2D QFTs change under infinitesimal bulk coupling variations, aiding RG flow analysis.

Contribution

It introduces a novel framework of ODEs to track the evolution of QFT data under coupling changes in 2D theories, connecting solvable and strongly coupled phases.

Findings

Derived universal first order ODEs for QFT data variation

Applicable to RG flow from solvable to strongly coupled phases

Potential to connect hyperbolic space QFTs to flat space limits

Abstract

Correlation functions of local operators in Quantum Field Theory (QFT) on hyperbolic space can be fully characterized by the set of QFT data $\lbrace \Delta_i,C_{ijk},b^{\hat{\mathcal{O}}}_j\rbrace$. These are the scaling dimensions of boundary operators $\Delta_i$, the boundary Operator Product Expansion (OPE) coefficients $C_{ijk}$ and the Boundary Operator Expansion (BOE) coefficients $b^{\hat{\mathcal{O}}}_j$ that characterize how each bulk operator $\hat{\mathcal{O}}$ can be expanded in terms of boundary operators $\mathcal{O}_j$.For simplicity, we focus on two dimensional QFTs and derive a universal set of first order Ordinary Differential Equations (ODEs) that encode the variation of the QFT data under an infinitesimal change of a bulk relevant coupling. In principle, our ODEs can be used to follow a Renormalization Group (RG) flow starting from a solvable QFT into a strongly coupled phase and to the flat space limit.