c=5/2 Free Fermion Model of WB_{2} Algebra

TL;DR

This paper constructs the $WB_{2}$ algebra explicitly for all central charges, focusing on the $c=5/2$ free fermion realization as a limit of minimal models, confirming the algebra's structure via Casimir operators.

Contribution

It provides an explicit construction of the $WB_{2}$ algebra for all central charges and demonstrates a $c=5/2$ free fermion realization as a limit of minimal models.

Findings

Explicit $WB_{2}$ algebra construction for all $c$

Realization of $c=5/2$ free fermion model as a limit of minimal series

Bosonic currents identified as Casimir operators of $_{2}$

Abstract

We investigate the explicit construction of the $WB_{2}$ algebra, which is closed and associative for all values of the central charge $c$, using the Jacobi identity and show the agreement with the results studied previously. Then we illustrate a realization of $c=\frac{5}{2}$ free fermion model, which is $m \rightarrow \infty$ limit of unitary minimal series, $c ( WB_{2} )=\frac{5}{2} (1-\frac{12}{ (m+3)(m+4) })$ based on the cosets $( \hat{B_{2}} \oplus \hat{B_{2}}, \hat{B_{2} })$ at level $(1,m).$ We confirm by explicit computations that the bosonic currents in the $ WB_{2}$ algebra are indeed given by the Casimir operators of $\hat{B_{2}}$ .