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A unitary vertex operator algebra arising from the 3C-algebra

Xiangyu Jiao, Wen Zheng

Abstract

We give an algebraic proof of the unitarity of the vertex operator algebra $L(21/22, 0)\oplus L(21/22, 8)$ and of all its irreducible ordinary modules, using a coset realization arising from the $3C$-algebra. Motivated by the structure of the resulting module decomposition, we establish a general result on fusion rules for commutant vertex operator subalgebras within the framework of modular tensor categories. As an application of this general result, we explicitly determine the fusion rules of all irreducible $L(21/22, 0)\oplus L(21/22, 8)$-modules.

A unitary vertex operator algebra arising from the 3C-algebra

Abstract

We give an algebraic proof of the unitarity of the vertex operator algebra and of all its irreducible ordinary modules, using a coset realization arising from the -algebra. Motivated by the structure of the resulting module decomposition, we establish a general result on fusion rules for commutant vertex operator subalgebras within the framework of modular tensor categories. As an application of this general result, we explicitly determine the fusion rules of all irreducible -modules.
Paper Structure (4 sections, 16 theorems, 36 equations)

This paper contains 4 sections, 16 theorems, 36 equations.

Table of Contents

  1. Introduction
  2. Constructions of the $3C$-algebra and its irreducible modules
  3. Unitarity of the VOA $L(21/22, 0)\oplus L(21/22, 8)$ and its modules
  4. Fusion rules

Key Result

Theorem 2.1

There are exactly five irreducible $U$-modules $U(2k), 0 \le k \le 4$. In fact, $U(0)=U$ and as $L(1/2, 0)\otimes L(21/22,0)$-modules,

Theorems & Definitions (30)

  • Theorem 2.1
  • Definition 3.1
  • Definition 3.2
  • Definition 3.3
  • Proposition 3.4
  • Theorem 3.5
  • proof
  • Lemma 3.6
  • proof
  • Theorem 3.7
  • ...and 20 more