Algebraic structure of local symmetries for two-dimensional superparticles on a curved external background

In this paper, a systematic analysis of the structure of local symmetries for (1,0)- and (1,1 )-superparticles on a curved external background is carried out. Proceeding from the requirement of the correct number of first- and second-class constraints, the minimum set of restrictions on the background superfields is written, under which a correct inclusion of interaction is guaranteed. The most general form of local symmetries is found for models on this background. The resulting transformations involve contributions with torsion superfields, and the gauge 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 symmetries implies the complete set of D = 2 supergravity constraints on the superfields as restrictions on the background.