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

Abstract

We investigate the explicit construction of the $W{B}_2$ 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 $m\to \infty$ limit of unitary minimal series, $c(W{B}_2)=\frac{5}{2}(1-\frac{12}{(m+3)(m+4)})$ based on the cosets $(\widehat{B_2}\oplus \widehat{B_2},\widehat{B_2})$ at level $(1,m).$ We confirm by explicit computations that the bosonic currents in the $W{B}_2$ algebra are indeed given by the Casimir operators of $\widehat{B_2}$ .

16 pages

Cited by in corpus (8)

• W-symmetry in Conformal Field Theory
• The Large N 't Hooft Limit of Coset Minimal Models
• How Complete is the Classification of W-Symmetries ?
• The Primary Spin-4 Casimir Operators in the Holographic SO(N) Coset Minimal Models
• Clustering properties, Jack polynomials and unitary conformal field theories
• BPS kinks in the Gross-Neveu model
• The OPEs of Spin-4 Casimir Currents in the Holographic SO(N) Coset Minimal Models
• Explicit Construction of Spin 4 Casimir Operator in the Coset Model $\widehat{SO}(5{)}_1\times \widehat{SO}(5{)}_m/\widehat{SO}(5{)}_{1+m}$