On realizing the bosonic string as a noncritical W3-string

Abstract

We discuss a realization of the bosonic string as a noncritical W 3 -string. The relevant noncritical W 3 -string is characterized by a Liouville sector which is restricted to a (non-unitary) (3, 2) W 3 minimal model with central charge contribution c l = −2. Furthermore, the matter sector of this W 3 -string contains 26 free scalars which realize a critical bosonic string. The BRST operator for this W 3 -string can be written as the sum of two, mutually anticommuting, nilpotent BRST operators: Q = Q 0 + Q 1 in such a way that the scalars which realize the bosonic string appear only in Q 0 while the central charge contribution of the fields present in Q 1 equals zero. We argue that, in the simplest case that the Liouville sector is given by the identity operator only, the Q 1 -cohomology is given by a particular (non-unitary) (3, 2) Virasoro minimal model at c = 0.

Physical states and BRST operators for higher-spin W strings

“…The string coordinates are called 'matter' fields while the non-decoupled gravitational fields are represented by a set of so-called 'Liouville' fields. In [9,41], the BRST operators for the Liouville system were obtained. Especially, in [37,42] The physical states in string theory can most elegantly be described by using the BRST formalism.…”

“…The string coordinates are called 'matter' fields while the non-decoupled gravitational fields are represented by a set of so-called 'Liouville' fields. In [9,41], the BRST operators for the Liouville system were obtained. Especially, in [37,42], the BRST operators of W M 2,s ⊗W L 2,s ′ were constructed at the classical level, and much valuable results were given.…”

Embedding of the bosonic string into the W3 string

“…If one were to bosonise the (r, s) fields in that case, the BRST operator would become the same as the one given in Ref. [6], except that in this paper we use Eqn. (7) rather than a two-scalar realisation for the c = −2 Liouville sector, and use T X + T ξη for the c = 26 effective energy-momentum tensor.…”

Non-linear realizations of superconformal and W-algebras as embeddings of strings

“…Later it was found that this is a general phenomenon: a (super)string with N extended world-sheet supersymmetry can be embedded into a superstring with N +1 extended supersymmetry as a particular vacuum state of the latter. Analogous embeddings were constructed for strings associated with nonlinear W type algebras and their linearizing algebras [8]- [11]. It was suggested that all the known strings and superstrings present different vacua of some hypothetical universal string theory.…”

“…An essential peculiarity of this case originating from the nonlinear nature of W and the subalgebra {T m , J m , G + m } become different after passing to the quantum case, but also the structure relations of the latter algebra are modified. Namely, its quantum OPEs are as follows 11) and they differ from the classical ones in that the current G + m acquires an anomalous conformal dimension 3 2 + 9 9−c . Actually, this is none other than the algebra W lin 3 which linearizes another kind of nonlinear algebra, Zamolodchikov's W 3 algebra [20].…”