Topological 1-dimensional field theories over a space X are given by vector bundles with connections over X. We obtain a similar characterization for topological 2-dimensional field theories in terms of Frobenius bundles (vector bundles with fibers Frobenius modules) with connections over LX, the free loop space of X.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/249