Non-integrable Quantum Field Theories as Perturbations of Certain Integrable Models

TL;DR

The authors develop a first-principles perturbative framework for non-integrable 2D QFTs by expanding around exactly solvable integrable models using the intermediate state representation and Form Factors. This yields explicit first-order corrections to particle masses, vacuum energy, and the elastic $S$-matrix, expressible entirely in terms of FFs from the integrable theory. The method is validated on deformations of the minimal model ${ m M}_{(2,7)}$ and on the scaling region of the Ising model near $T_c$, where FF-based predictions agree with numerical truncation results. The work highlights how ultraviolet data from the integrable base theory constrain non-integrable dynamics and reveals consistency relations tied to the stress-energy sector, pointing to broad applicability for near-integrable QFTs.

Abstract

We approach the study of non--integrable models of two--dimensional quantum field theory as perturbations of the integrable ones. By exploiting the knowledge of the exact $S$-matrix and Form Factors of the integrable field theories we obtain the first order corrections to the mass ratios, the vacuum energy density and the $S$-matrix of the non-integrable theories. As interesting applications of the formalism, we study the scaling region of the Ising model in an external magnetic field at $T \sim T_c$ and the scaling region around the minimal model $M_{2,7}$. For these models, a remarkable agreement is observed between the theoretical predictions and the data extracted by a numerical diagonalization of their Hamiltonian.

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