Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-09-03
Mod.Phys.Lett. A10 (1995) 79-90
Physics
High Energy Physics
High Energy Physics - Theory
13 pages, LaTeX, Hannover preprint ITP-UH-12/94, September 1994
Scientific paper
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'.
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