Tree algebras: An algebraic axiomatization of intertwining vertex operators

Abstract

We describe a completely algebraic axiom system for intertwining operators of vertex algebra modules, using algebraic flat connections, thus formulating the concept of a tree algebra. Using the Riemann-Hilbert correspondence, we further prove that a vertex tensor category in the sense of Huang and Lepowsky gives rise to a tree algebra over C. We also show that the chiral WZW model of a simply connected simple compact Lie group gives rise to a tree algebra over Q.

On discrete field theory properties of the dimer and Ising models and their conformal field theory limits

“…, which specifies a canonical element (23) ι q ∈ P f (Ω is the desired regularization. With respect to this regularization, the partition function is one of the two Jacobi theta functions involving odd powers of q 1/2 (depending on the spin of the gluing), times the factor…”

“…An extension of the approach which models a whole conformal field theory, was developed by Huang and Lepowsky [19], but it does involve analysis, although not Hilbert spaces. Efforts to model the entire conformal field theory as a completely algebraic concept are underway [17,23].…”