Osterwalder-Schrader axioms for unitary full vertex operator algebras

2024/07/25 by Adamo, Maria Stella, Moriwaki, Yuto, Tanimoto, Yoh
#17B69 #81T05 #81T40 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2407.18222

Abstract

Full Vertex Operator Algebras (full VOA) are extensions of two commuting Vertex Operator Algebras, introduced to formulate compact two-dimensional conformal field theory. We define unitarity, polynomial energy bounds and polynomial spectral density for full VOA. Under these conditions and local C₁-cofiniteness of the simple full VOA, we show that the correlation functions of quasi-primary fields define tempered distributions and satisfy a conformal version of the Osterwalder-Schrader axioms, including the linear growth condition. As an example, we show that a family of full extensions of the Heisenberg VOA satisfies all these assumptions.

Cited by

• Representations of conformal nets associated with infinite-dimensional groups

Related

• 2D conformal field theory and vertex operator algebras
• Lectures on Vertex Operator Algebras and Conformal Blocks
• Simple current extensions of vertex operator algebras by unitary modules
• Non-unitary Wightman CFTs and non-unitary vertex algebras
• Every conformal net has an associated unitary VOA