Parafermions, W strings and their BRST charges

Abstract

We show how to relate the parafermions that occur in the W 3 string to the standard construction of parafermions. This result is then used to show that one of the screening charges that occurs in parafermionic theories is precisely the non-trivial part of the W 3 string BRST charge. A way of generalizing this pattern for a W N string is explained. This enables us to construct the full BRST charge for a W 2,N string and to prove the relation of such a string to the algebra W N−1 for arbitrary N , We also show how to calculate part of the BRST charge for a W N string, and we explain how our method might be extended to obtain the full BRST charge for such a string.

A W-string realization of the bosonic string

“…By taking repeated operator products of e iφ 1 with itself it can be shown that, in terms of φ 1 and φ 2 , Q 1 takes the simple form [7] …”

“…This can be simplified further by defining a new fieldφ 1 in terms of φ 1 by means of the relations [7] e iφ 1 = i∂φ 1 e −iφ 1…”

“…In reference [7] it was explained how, starting from the bosonic fieldφ and bosonized ghost ρ of the W 2,s string, we can define new fields…”

BRST cohomology of the critical W string

“…Recent progress in constructing BRST charges for higher spin strings (e.g. W 2,N or W N strings) has been made in [29].…”

BRST operators for higher-spin algebras

“…Explicit solutions have been found for all s ≤ 8 [2,3], and general existence arguments for one class of solutions for all values of s were given in Refs. [9,2]. Now we turn to the construction of the non-critical BRST operators for W M 2,s ⊗ W L 2,s ′ .…”