W{1+ \infty} algebra, W_3 algebra, and Friedan-Martinec-Shenker bosonization

Abstract

We show that the vertex algebra W{1+ \infty} with central charge -1 is isomorphic to a tensor product of the simple W_3 algebra with central charge -2 and a Heisenberg vertex algebra generated by a free bosonic field. We construct a family of irreducible modules of the W_3 algebra with central charge -2 in terms of free fields and calculate the full character formulas of these modules with respect to the full Cartan subalgebra of the W_3 algebra.

Latex, 23 pages

References in corpus (5)

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• Orbifolds and cosets of minimal $\mathcal{W}$-algebras
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• Universal two-parameter ${\mathcal{W}}_{\infty }$-algebra and vertex algebras of type $\mathcal{W}(2,3,\dots ,N)$
• Invariant theory and the Heisenberg vertex algebra
• Bosonic ghostbusting -- The bosonic ghost vertex algebra admits a logarithmic module category with rigid fusion
• The structure of the Kac-Wang-Yan algebra
• Fusion rules and complete reducibility of certain modules for affine Lie algebras
• Invariant chiral differential operators and the W_3 algebra
• A Hilbert theorem for vertex algebras
• Singular support of a vertex algebra and the arc space of its associated scheme
• The second bosonization of the CKP hierarchy
• A construction of admissible $A_1^{(1)}$-modules of level $-4/3$
• Cosets of free field algebras via arc spaces
• Multilocal bosonization
• A note on Cauchy's formula
• Tau functions of the charged free bosons
• Simple weak modules for some subalgebras of the Heisenberg vertex algebra and Whittaker vectors
• Correlation functions of charged free boson and fermion systems
• Bosonizations of ${\widehat{\mathfrak{sl}}}_2$ and Integrable Hierarchies
• Classification of irreducible modules of certain subalgebras of free boson vertex algebra
• A note on the affine vertex algebra associated to $\mathfrak{gl}(1|1)$ at the critical level and its generalizations
• A commutant realization of Odake's algebra
• Representations of the vertex algebra $W_{1+\infty }$ with a negative integer central charge
• On some vertex algebras related to $V_{-1}(\mathfrak{sl}(n))$ and their characters
• Indecomposable Representations in Z_n Symmetric b,c Ghost Systems via Deformations of the Virasoro Field
• Lie subalgebras of differential operators on the super circle
• Free Field realization of the ${\hat{\mathcal{D}}}_q$ Algebra for the $\eta$-$\xi$ system, Integrals of Motion and Characters