THE BRST CHARGE FOR THE $\hat D (2, 1; \alpha)$ NONLINEAR QUASI-SUPERCONFORMAL ALGEBRA

Abstract

The quantum BRST charge for the most general, two-dimensional, nonlinear, N = 4 quasi-superconformal algebra [Formula: see text], whose linearization is the so-called 'large' N = 4 superconformal algebra, is constructed. The [Formula: see text] algebra has [Formula: see text] Kač–Moody component, and α = k−/k+. As a pre-requisite to our construction, we check the [Formula: see text] Jacobi identities and construct a classical BRST charge. Then, we analyze the quantum BRST charge nilpotency conditions and find the only solution, k+ = k− = −2. The [Formula: see text] algebra is actually isomorphic to the SO(4)-based Bershadsky–Knizhnik nonlinear quasi-superconformal algebra. We argue about the existence of a new string theory with (i) the nonlinearly realized N = 4 worldsheet supersymmetry, (ii) non-unitary matter in a [Formula: see text] representation of k = −2 and c = −6, and (iii) negative 'critical dimension'.