How Many $N=4$ Strings Exist ?

Abstract

Possible ways of constructing extended fermionic strings with $N=4$ world-sheet supersymmetry are reviewed. String theory constraints form, in general, a non-linear quasi(super)conformal algebra, and can have conformal dimensions $\ge 1$. When $N=4$, the most general $N=4$ quasi-superconformal algebra to consider for string theory building is $\hat{D}(1,2;\a)$, whose linearisation is the so-called `large' $N=4$ superconformal algebra. The $\hat{D}(1,2;\a)$ algebra has $\Hat{su(2)}_{k^+}\oplus \Hat{su(2)}_{k^-}\oplus\Hat{u(1)}$ Kač-Moody component, and $\a=k^-/k^+$. We check the Jacobi identities and construct a BRST charge for the $\hat{D}(1,2;\a)$ algebra. The quantum BRST operator can be made nilpotent only when $k^{+}=k^{-}=-2$. The $\hat{D}(1,2;1)$ algebra is actually isomorphic to the $SO(4)$-based Bershadsky-Knizhnik non-linear quasi-superconformal algebra. We argue about the existence of a string theory associated with the latter, and propose the (non-covariant) hamiltonian action for this new $N=4$ string theory. Our results imply the existence of two different $N=4$ fermionic string theories: the old one based on the `small' linear $N=4$ superconformal algebra and having the total ghost central charge $c_{\mathrm{gh}}=+12$, and the new one with non-linearly realised $N=4$ supersymmetry, based on the $SO(4)$ quasi-superconformal algebra and having $c_{\mathrm{gh}}=+6$. Both critical string theories have negative `critical dimensions' and do not admit unitary matter representations.

31 pages, LaTeX, Hannover preprint ITP-UH-13/94, September 1994

References in corpus (5)

• W-symmetry in Conformal Field Theory
• On the Uniqueness of String Theory
• Results of the classification of superconformal algebras in two dimensions
• Exceptional Superconformal Algebras
• Space-Time Supersymmetry of Extended Fermionic Strings in $2+2$ Dimensions

Cited by in corpus (5)

• Seven-Sphere and the Exceptional N=7 and N=8 Superconformal Algebras
• 2D (4,4) Hypermultiplets
• No N=4 Strings on Wolf Spaces
• Superstrings from theories with N>1 world-sheet supersymmetry
• A Canticle on (4,0) Supergravity-Scalar Multiplet Systems for a ``Cognoscente''