Embedding of the Bosonic String into the $W_3$ String

Abstract

We investigate new realisations of the $W_3$ algebra with arbitrary central charge, making use of the fact that this algebra can be linearised by the inclusion of a spin-1 current. We use the new realisations with $c=102$ and $c=100$ to build non-critical and critical $W_3$ BRST operators. Both of these can be converted by local canonical transformations into a BRST operator for the Virasoro string with $c=28-2$, together with a Kugo-Ojima topological term. Consequently, these new realisations provide embeddings of the Virasoro string into non-critical and critical $W_3$ strings.

11 pages. (Some referencing changes)

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Cited by in corpus (7)

• Ghost field realizations of the spinor $W_{2,s}$ strings based on the linear W(1,2,s) algebras
• MORE ON THE LINEARIZATION OF $W$-ALGEBRAS
• New Spinor Field Realizations of the Non-Critical $W_3$ String
• Higher-spin Realisations of the Bosonic String
• Spinor field realizations of the non-critical $W_{2,4}$ string based on the linear $W_{1,2,4}$ algebra
• Physical States and BRST Operators for Higher-spin $W$ Strings
• Explicit field realizations of W algebras