Unified geometry of antisymmetric tensor gauge fields and gravity

Vector gauge fields are known to be related to connections on principal fibre bundles P(M,G) over space-time M. Here we relate abelian antisymmetric tensor gauge fields of rank r to constrained connections on P(Ω_r?1M,U(1)), the U(1) bundles over the space of all (r?1)-dimensional closed submanifolds of M. In particular, the Kalb-Ramond field (r=2) is seen as such a connection on the bundle over the space of all loops in space-time. Moreover, a Kaluza-Jordan construction on P(Ω₁M,U(1)) leads to the bosonic sector of the N = 1 supergravity action in ten dimensions. This result is highly reminiscent of the α′→ 0 limit of the closed string dual model.