ALGEBRAIC STRUCTURE OF LOCAL SYMMETRIES FOR 2-DIMENSIONAL SUPERPARTICLES ON A CURVED EXTERNAL BACKGROUND

In this paper, a systematic analysis of the structure of local symmetr ies for (1,0)- and (1, 1)-superparticles on a curved external backgrou nd is carried out. Proceeding from the requirement of the correct numb er of first- and second-class constraints, the minimum set of restrict ions on the background superfields is written, under which a correct i nclusion of interaction is guaranteed. The most general form of local symmetries is found for models on this background. The resulting trans formations involve contributions with torsion superfields, and the gau ge algebra turns out to be off-shell closed and nontirivially deformed as compared to the planar case. The requirement of invariance of the action relative to the direct generalization of planar local symmetrie s implies the complete set of D = 2 supergravity constraints on the su perfields as restrictions on the background.