BPS Solitons and Killing Spinors in Three Dimensional

In the framework of three dimensional extended supergravity theories, we demonstrate that there exist non-trivial Killing spinors over BPS soliton configurations, even when the space-time is asymptotically conical. We also show that there are no physical fermionic zero modes on these backgrounds. We further generalize these results to the case of semilocal systems. The connection between Bogomol’nyi bounds [1] for the mass of extended solutions in bosonic field theories and the supercharge algebra of the corresponding supersymmetric extensions is by now well understood. The topological charges of the purely bosonic theory coincide with the central extensions of the supersymmetry algebra in the N-extended model [2, 3, 4]. The Bogomol’nyi bound then arises from the positivity of the supercharge algebra. The conditions imposed by the N-extended supersymmetric invariance are exactly those ensuring the existence of a Bogomol’nyi bound in the purely bosonic system. Moreover, the bound is saturated by field configurations that preserve a certain amount of the supersymmetries of the Lagrangian.