$W_3$ strings, parafermions and the Ising model

Abstract

We show that any covariant scattering amplitude of the $W_3$ string will contain, as part of its integrand, a factor that obeys the differential equations satisfied by an Ising model correlation function. This factor can thus be identified with such a correlation function, in agreement with a previous result of the authors. The $W_3$ string is also shown to contain an $N=2$ parafermion theory, and hence to contain in addition the non-linear infinite-dimensional $W$-algebra corresponding to this parafermion theory. The physical states form a representation of this algebra.

14 pages, KCL-TH-93-10

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Cited by in corpus (7)

• A Review of $W$ Strings
• On the Cohomology of the Noncritical $W$-string
• Twisted Parafermions
• Parafermions, $W$ Strings and their BRST Charges
• $W$ Strings and Cohomology in Parafermionic Theories
• $A_2^{(2)}$ Parafermions: A New Conformal Field Theory
• On realizing the bosonic string as a noncritical $W_3$-string