D-branes and K-theory in 2D topological field theory

Abstract

This expository paper describes sewing conditions in two-dimensional open/closed topological field theory. We include a description of the G-equivariant case, where G is a finite group. We determine the category of boundary conditions in the case that the closed string algebra is semisimple. In this case we find that sewing constraints -- the most primitive form of worldsheet locality -- already imply that D-branes are (G-twisted) vector bundles on spacetime. We comment on extensions to cochain-valued theories and various applications. Finally, we give uniform proofs of all relevant sewing theorems using Morse theory.

arXiv comment88pp. harvmac b-mode. arXiv version has separate figures as gif files. For a dvi file with the figures, or eps figures go to http://www.physics.rutgers.edu/~gmoore/

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