Embedding of the bosonic string into the W3 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 realisations provide embeddings of the Virasoro string into non-critical and critical W 3 strings.

Higher Spin Realizations of the Bosonic String

“…The realisations also close when this term is omitted, under which circumstance the corresponding string theory is equivalent to the one that is based on the Romans' free-scalar realisation [4]. However, when this term is included, the corresponding BRST operator is equivalent to that of the bosonic string, which can be shown by making a local canonical field redefinition [2]. Thus the new realisations provide embeddings of the bosonic string in the W 3 string.…”

“…As in the case of the critical W 3 string discussed in Ref. [2], we expect that this operator can also be converted into a single term γr.…”

“…However it was shown, for the cases of s = 3, 4, that the current W 0 does not have to be zero, and that instead it could be realised by a parafermionic vertex operator [1,9]. One can alternatively realise W 0 in terms of a ghost-like field [2,3]. It was shown in Ref.…”

“…Note that the Liouville sector enters the Q 1 operator only as a quantum correction. The Q 1 operator is analogous to the one for the W 3 string, where Q 1 = γ(r − 1 3 r 3 s 3 + quantum corrections) [2]. It was shown that the Q 1 operator for W 3 can be converted into a single term γr by a local canonical field redefinition.…”

More on the Linearization of W Algebras

“…Up to now the explicit construction has been carried out for some simplest examples of nonlinear (super)algebras ( W 3 and W (2) 3 [3], W B 2 and W 2,4 [4] ). Besides being a useful tool to construct new field realizations of nonlinear algebras [3][4], these linear algebras provide a suitable framework for considering the embeddings of the Virasoro string in the W -type ones [5].…”