The Interacting $W_3$ String

Abstract

We present a procedure for computing gauge-invariant scattering amplitudes in the $W_3$ string, and use it to calculate three-point and four-point functions. We show that non-vanishing scattering amplitudes necessarily involve external physical states with excitations of ghosts as well as matter fields. The crossing properties of the four-point functions are studied, and it is shown that the duality of the Virasoro string amplitudes generalises in the $W_3$ string, with different sets of intermediate states being exchanged in different channels. We also exhibit a relation between the scattering amplitudes of the $W_3$ string and the fusion rules of the Ising model.

(Revised version), 26 pages, Plain Tex, CTP TAMU-86/92, KUL-TF-92/43

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Cited by in corpus (16)

• On the Spectrum and Scattering of W_3 Strings
• Critical and non-critical W_{2,4} strings
• The Complete Cohomology of the W3 String
• The covariant scattering and cohomology of $W_3$ strings
• A Review of $W$ Strings
• Lectures on W-Gravity, W-Geometry and \W-Strings
• On the Cohomology of the Noncritical $W$-string
• $W_3$ strings, parafermions and the Ising model
• New Realisations of Minimal Models and the Structure of W-Strings
• Spinor Field Realizations of Non-critical $W_{2,s}$ Strings
• Ghost field realizations of the spinor $W_{2,s}$ strings based on the linear W(1,2,s) algebras
• New Spinor Field Realizations of the Non-Critical $W_3$ String
• On realizing the bosonic string as a noncritical $W_3$-string
• BRST cohomology of the critical $W_4$ string
• Physical States and BRST Operators for Higher-spin $W$ Strings
• Explicit field realizations of W algebras