THE COVARIANT SCATTERING AND COHOMOLOGY OF W₃ STRINGS

Abstract

A general formalism for covariant W 3 string scattering is given. It is found necessary to use screening charges that are constructed from the W 3 fields including ghosts. The scattering amplitudes so constructed contain within them Ising model correlation functions and agree with those found previously by the authors. Using the screening charge and a picture changing operator, an infinite number of states in the cohomology of Q are generated from only three states. We conjecture that, apart from discrete states, these are all the states in the cohomology of Q.

On the spectrum and scattering of W3 strings

“…Our formalism for describing W 3 string scattering does not suffer from any of the deficiencies mentioned in [23], and indeed, since the authors of [23] perform all their calculations by using the procedures that we have developed, (or, in the case of amplitudes involving screening charges, a procedure that is directly equivalent to ours), their results necessarily agree with ours.…”

“…The new result of [23] amounts to the observation that there are further amplitudes that can be obtained, using the formalism that we presented in [11] and this paper, by including discrete states that cannot normal order with the external physical states. By this means, one can indeed obtain scattering amplitudes involving more than two L eff = 15 16 external states.…”

“…After this preprint was circulated, a paper by Freeman and West on related topics appeared [23]. They assert that the procedure we introduced in [11] for calculating W 3 string scattering amplitudes is incorrect, and that it gives results that violate unitarity and the assumptions of S-matrix theory.…”

“…The authors of [23] introduce a screening charge S = dz U(z) in order to obtain further scattering amplitudes beyond those that we have computed. It is easy to see that this screening charge is related by a descent equation to our ℓ = 6 discrete state D 0 [ 2 7 Q] given in (6.18).…”

“…In fact, in the new formalism introduced in section 6 of this paper, their screening current U, after removing a total derivative, is simply given by U = β e 7 Q] by making the replacment (2.14). In fact the screening charge S given in [23] is nothing but a special case of our standard replacement of a spin 0 physical state by a spin 1 current that can be integrated over the worldsheet to give BRST-invariant amplitudes. Not surprisingly, therefore, the new amplitudes obtained in [23] by including screening charges are in on-toone correspondence with amplitudes that we can compute by including discrete states.…”