On the spectrum and scattering of W3 strings

Abstract

We present a detailed investigation of scattering processes in W 3 string theory. We discover further physical states with continuous momentum, which involve excitations of the ghosts as well as the matter, and use them to gain a better understanding of the interacting theory. The scattering amplitudes display factorisation properties, with states from the different sectors of the theory being exchanged in the various intermediate channels. We find strong evidence for the unitarity of the theory, despite the unusual ghost structure of some of the physical states. Finally, we show that by performing a transformation of the quantum fields that involves mixing the ghost fields with one of the matter fields, the structure of the physical states is dramatically simplified. The new formalism provides a concise framework within which to study the W 3 string.

Spinor field realizations of non-critical strings

“…The BRST charge for W 3 string was first constructed in [6], and the detailed studies of it can be found in [6][7][8][9][10][11][12]. A natural generalization of the W 3 string, i.e.…”

BRST cohomology of the critical W string

“…Note that Q V ir is just the usual Virasoro BRST operator for the matter plus spin-(3,4) ghost systems. The BRST operator in this special basis is the generalisation to W 4 of the W 3 BRST operator of [10], which was obtained from the original one [18] by a canonical redefinition of the fields. The spin-four part Q 2 was in fact already given in [13].…”

“…This relation is clarified by going to a new basis of fields introduced in [10]. In this new basis, a special subsector of the W 3 model was seen to correspond to the Ising model [11], see also [12,10,13,14].…”

“…In that case a nilpotent BRST charge is associated to the spin-three constraint [10,20], and its cohomology corresponds to the Ising model.…”

On realizing the bosonic string as a noncritical W3-string

“…Based on the above numerology, it was suggested in [4] that the above noncritical W 3 -string should in some sense contain a critical Virasoro string with 26 free scalars. After the work of [4] it was shown [6] that, by going to a new basis in the Hilbert space, the BRST operator of the W 3 -algebra can be written as the sum of two, mutually anticommuting, nilpotent BRST operators…”