The BRST Charge for the \hat{D}(2,1;\a) Non-Linear Quasi-Superconformal Algebra

The quantum BRST charge for the most general, two-dimensional, non-linear, $N=4$ quasi-superconformal algebra \hat{D}(1,2;\a), whose linearisation is the so-called `large' $N=4$ superconformal algebra, is constructed. The \hat{D}(1,2;\a) algebra has \Hat{su(2)}_{k^+}\oplus \Hat{su(2)}_{k^-}\oplus\Hat{u(1)} Ka\v{c}-Moody component, and \a=k^-/k^+. As a pre-requisite to our construction, we check the \hat{D}(1,2;\a) Jacobi identities and construct a classical BRST charge. Then, we analyse the quantum BRST charge nilpotency conditions and find the only solution, $k^+=k^-=-2$. 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 new string theory with (i) the non-linearly realised $N=4$ world-sheet supersymmetry, (ii) non-unitary matter in a \hat{D}(1,2;\a) representation of $k=-2$ and $c=-6$, and (iii) negative `critical dimension'.Comment: 13 pages, LaTeX, Hannover preprint ITP-UH-12/94, September 199

The OSp(32|1) versus OSp(8|2) supersymmetric M-brane action from self-dual (2,2) strings

Taking the (2,2) strings as a starting point, we discuss the equivalent integrable field theories and analyze their symmetry structure in 2+2 dimensions from the viewpoint of string/membrane unification. Requiring the Lorentz invariance and supersymmetry in the (2,2) string target space leads to an extension of the (2,2) string theory to a theory of 2+2 dimensional supermembranes (M-branes) propagating in a higher dimensional target space. The origin of the hidden target space dimensions of the M-brane is related to the maximally extended supersymmetry implied by the Lorentz covariance and dimensional reasons. The K"ahler-Chern-Simons-type action describing the self-dual gravity in 2+2 dimensions is proposed. Its maximal supersymmetric extension (of the Green-Schwarz-type) naturally leads to the 2+10 (or higher) dimensions for the M-brane target space. The proposed OSp(32|1) supersymmetric action gives the pre-geometrical description of M-branes, which may be useful for a fundamental formulation of F&M theory.Comment: 12 pages, LaTeX, misprints corrected, the final version to appear in the Modern Physics Letters