The Complete Spectrum of the $W_N$ String

Abstract

We obtain the complete physical spectrum of the $W_N$ string, for arbitrary $N$. The $W_N$ constraints freeze $N-2$ coordinates, while the remaining coordinates appear in the currents only {\it via} their energy-momentum tensor. The spectrum is then effectively described by a set of ordinary Virasoro-like string theories, but with a non-critical value for the central charge and a discrete set of non-standard values for the spin-2 intercepts. In particular, the physical spectrum of the $W_N$ string includes the usual massless states of the Virasoro string. By looking at the norms of low-lying states, we find strong indications that all the $W_N$ strings are unitary.

28 pages

References in corpus (3)

• The $W_3$-string spectrum
• W3 Constructions on Affine Lie Algebras
• Anomaly Freedom and Realisations for Super-$W_3$ Strings

Cited by in corpus (22)

• W-symmetry in Conformal Field Theory
• Toward the construction of N=2 supersymmetric integrable hierarchies
• On the Spectrum and Scattering of W_3 Strings
• Discrete States in the $W_3$ String
• A BRST Analysis of $W$-symmetries
• The Interacting $W_3$ String
• On the BRST Operator of $W$-Strings
• Critical and non-critical W_{2,4} strings
• The Complete Cohomology of the W3 String
• On the generalized Miura transformation
• On the Cohomology of the Noncritical $W$-string
• Spinor Field Realizations of Non-critical $W_{2,s}$ Strings
• New Realisations of Minimal Models and the Structure of W-Strings
• Ghost field realizations of the spinor $W_{2,s}$ strings based on the linear W(1,2,s) algebras
• A Note of W-algebra Realisations
• On Realisations of W Algebras
• New Spinor Field Realizations of the Non-Critical $W_3$ String
• The Higher Spin Rectangle
• Spinor field realizations of the non-critical $W_{2,4}$ string based on the linear $W_{1,2,4}$ algebra
• BRST cohomology of the critical $W_4$ string
• A Note on N=2 Superstrings
• Physical States and BRST Operators for Higher-spin $W$ Strings