The absence of fermion kinetic terms in supersymmetric-BF gauge theories is established. We do this by means of explicit off-shell (superspace) constructions. As part of our study we give the superspace constraints for D=3, N=4 super Yang-Mills along with the D=3, N=4 superconformal algebra. The puzzle we are interested in solving is the fact that the topological cousins, known as super-BF gauge theories, of certain supersymmetric-BF theories have kinetic terms for the twisted fermions. We show that the map which takes the latter to the former includes a Hodge decomposition of the twisted fermions. In conjunction with this result, we argue that it is natural to modify the naive path integral measure of supersymmetric-BF theories to include the Ray-Singer analytic torsion.
The gravitini zero modes riding on top of the extreme Reissner-Nordström black-hole solution of N = 2 supergravity are shown to be normalizable. The gravitini and dilatini zero modes of axion-dilaton extreme black-hole solutions of N = 4 supergravity are also given and found to have finite norms. These norms are duality invariant. The finiteness and positivity of the norms in both cases are found to be correlated with the Witten-Israel-Nester construction; however, we have replaced the Witten condition by the pure-spin-3 2 constraint on the gravitini. We compare our calculation of the norms with the calculations which provide the moduli space metric for extreme black holes.The action of the N = 2 hypermultiplet with an off-shell central charge describes the solitons of N = 2 supergravity. This action, in the Majumdar-Papapetrou multi-black-hole background, is shown to be N = 2 rigidly supersymmetric.
Bounded (compactifying) potentials arising from a conspiracy between plane wave graviton and dilaton condensates are discussed. So are string propagation and supersymmetry in space-times with curvature singularities.
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