Connecting lattice and relativistic models via conformal field theory

TL;DR

This paper explores the connection between lattice models and conformal field theory through quantum group invariants, analyzing correlation functions, form factors, and solutions of qKZ equations to bridge discrete and continuous models.

Contribution

It introduces a novel framework linking the XXZ-model's infrared limit to conformal field theory via qKZ equations and their solutions, providing new insights into matrix elements and correlation functions.

Findings

Correlation functions relate to level -4 qKZ solutions

Matrix elements decompose with respect to CFT states

Framework bridges lattice models and conformal field theory

Abstract

We consider the quantum group invariant XXZ-model. In infrared limit it describes Conformal Field Theory with modified energy-momentum tensor. The correlation functions are related to solutions of level -4 of qKZ equations. We describe these solutions relating them to level 0 solutions. We further consider general matrix elements (form factors) containing local operators and asymptotic states. We explain that the formulae for solutions of qKZ equations suggest a decomposition of these matrix elements with respect to states of corresponding Conformal Field Theory .