$W_3$ strings, parafermions and the Ising model

Details $W_3$ strings, parafermions and the Ising model $W_3$ strings, parafermions and the Ising model

1993-06-25

arxiv.org/abs/hep-th/9306134v1

Phys.Lett. B314 (1993) 320-327

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, KCL-TH-93-10

Scientific paper

10.1016/0370-2693(93)91243-G

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.

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