Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the structure of open-closed topological field theory in two
  dimensions   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.

31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex