On realizing the bosonic string as a noncritical $W_3$-string

Details On realizing the bosonic string as a noncritical $W_3$-string On realizing the bosonic string as a noncritical $W_3$-string

1994-09-29

arxiv.org/abs/hep-th/9409186v1

Phys. Lett. B346 (1995) 269-274

Physics

High Energy Physics

High Energy Physics - Theory

12 pages, UG-7/94

Scientific paper

10.1016/0370-2693(94)01694-8

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 $c=0$.

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