A construction of admissible $A_1^{(1)}$-modules of level $-{4/3}$

TL;DR

This paper explicitly constructs admissible modules for the affine Lie algebra $A_1^{(1)}$ at level -4/3 using generalized vertex algebras, and shows a subalgebra relation with the W(2,5) algebra at central charge -7.

Contribution

It provides a new explicit construction of admissible modules for $A_1^{(1)}$ at a specific fractional level using generalized vertex algebras.

Findings

Explicit admissible modules constructed for $A_1^{(1)}$ at level -4/3.

Demonstrates the W(2,5) algebra as a subalgebra of the affine vertex algebra $L(-4/3 \\Lambda_0)$.

Connects the structure of admissible modules with known W-algebra investigations.

Abstract

By using generalized vertex algebras associated to rational lattices, we construct explicitly the admissible modules for the affine Lie algebra $A_1 ^{(1)}$ of level $-{4/3}$. As an application, we show that the W(2,5) algebra with central charge c=-7 investigated in math.QA/0207155 is a subalgebra of the simple affine vertex operator algebra $L(-{4/3}\Lambda_0)$.