Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation

TL;DR

This paper rigorously proves that L operators in Conformal Field Theory satisfy the Yang-Baxter algebra relations, deriving functional relations for key operators and confirming analyticity assumptions crucial for integrability.

Contribution

It provides a rigorous proof of the Yang-Baxter relations for L operators and derives functional relations for ${f T}$ and ${f Q}$ operators in Conformal Field Theory.

Findings

Proof that L operators satisfy Yang-Baxter algebra

Derivation of functional relations for ${f T}$ and ${f Q}$

Validation of analyticity assumptions used in previous work

Abstract

In this paper we fill some gaps in the arguments of our previous papers [hep-th/9412229,hep-th/9604044]. In particular, we give a proof that the L operators of Conformal Field Theory indeed satisfy the defining relations of the Yang-Baxter algebra. Among other results we present a derivation of the functional relations satisfied by ${\bf T}$ and ${\bf Q}$ operators and a proof of the basic analyticity assumptions for these operators used in [hep-th/9412229,hep-th/9604044].