Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-10-29
Nucl.Phys.B603:497-530,2001
Physics
High Energy Physics
High Energy Physics - Theory
38 pages, 17 figures; v2: typos corrected, references updated. This is essentially the final version published in NPB in 2001
Scientific paper
10.1016/S0550-3213(01)00135-3
I discuss the general formalism of two-dimensional topological field theories defined on open-closed oriented Riemann surfaces, starting from an extension of Segal's geometric axioms. Exploiting the topological sewing constraints allows for the identification of the algebraic structure governing such systems. I give a careful treatment of bulk-boundary and boundary-bulk correspondences, which are responsible for the relation between the closed and open sectors. The fact that these correspondences need not be injective nor surjective has interesting implications for the problem of classifying `boundary conditions'. In particular, I give a clear geometric derivation of the (topological) boundary state formalism and point out some of its limitations. Finally, I formulate the problem of classifying (on-shell) boundary extensions of a given closed topological field theory in purely algebraic terms and discuss their reducibility.
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