Representations and fusion rules for the orbifold vertex operator algebras $L_{\widehat{{\mathfrak{sl}}_2}}(k,0{)}^{{\mathbb{Z}}_3}$

Abstract

For the cyclic group ${\mathbb{Z}}_3$ and positive integer $k$, we study the representations of the orbifold vertex operator algebra $L_{\widehat{{\mathfrak{sl}}_2}}(k,0{)}^{{\mathbb{Z}}_3}$. All the irreducible modules for $L_{\widehat{{\mathfrak{sl}}_2}}(k,0{)}^{{\mathbb{Z}}_3}$ are classified and constructed explicitly. Quantum dimensions and fusion rules for the orbifold vertex operator algebra $L_{\widehat{{\mathfrak{sl}}_2}}(k,0{)}^{{\mathbb{Z}}_3}$ are completely determined.

arXiv comment27 pages

References in corpus (6)

• Modular invariance of trace functions in orbifold theory
• Simple currents and extensions of vertex operator algebras
• C_2-cofiniteness of cyclic-orbifold models
• Algebraic orbifold conformal field theories
• Fusion rules for ${\mathbb{Z}}_2$-orbifolds of affine and parafermion vertex operator algebras
• Representations of the orbifold VOAS $L_{\widehat{{\mathfrak{sl}}_2}}(k,0{)}^K$ and the commutant VOAS $C_{{L_{\widehat{{\mathfrak{so}}_m}}(1,0)}^{\otimes 3}}(L_{\widehat{{\mathfrak{so}}_m}}(3,0))$