Construction of holomorphic local conformal framed nets

TL;DR

This paper constructs holomorphic local conformal framed nets from tensor powers of the Virasoro net using binary codes, providing an operator algebraic approach that parallels known vertex operator algebra results.

Contribution

It offers a new operator algebraic construction of holomorphic local conformal framed nets based on binary codes, differing from previous proofs.

Findings

Successful construction of holomorphic local conformal nets from tensor powers of Virasoro nets.

Application of alpha-induction to identify the representation theory of code local conformal nets.

Establishment of an operator algebraic counterpart to known vertex operator algebra results.

Abstract

We construct holomorphic local conformal framed nets extended from a tensor power of the Virasoro net with c=1/2 with a pair of binary codes (C,D) satisfying the conditions given by Lam and Yamauchi for holomorphic framed vertex operator algebras. Our result is an operator algebraic counterpart of theirs, but our proof is entirely different. We apply the alpha-induction in order to identify the representation theory of "code local conformal net" and this gives rise to the existence of the desired local conformal net.