WILSON LOOP OBSERVABLES IN (2 + 1)-DIMENSIONAL CHERN-SIMONS SUPERGRAVITY

(2 + 1)-dimensional gravity and supergravity, without a cosmological constant, can be described as Chern-Simons gauge theories of the Poincaré and super-Poincaré groups respectively. The only gauge invariant observables are Wilson loops.In this paper, we consider N = 2 Poincaré supergravity on R × Σ, where R is "time" and the spatial hypersurface Σ is the plane with an arbitrary number, N, of isolated sources or punctures carrying super-Poincaré charges, and examine Wilson loops enclosing one or more of them. We describe how to compute the Wilson loop observables and give explicit expressions for the cases of one and two sources. We also discuss the Poisson brackets between two Wilson loops and derive a rule by which they might be obtained. © 1990.