  We study surface operators in 3d Topological Field Theory and their relations
with 2d Rational Conformal Field Theory. We show that a surface operator gives
rise to a consistent gluing of chiral and anti-chiral sectors in the 2d RCFT.
The algebraic properties of the resulting 2d RCFT, such as the classification
of symmetry-preserving boundary conditions, are expressed in terms of
properties of the surface operator. We show that to every surface operator one
may attach a Morita-equivalence class of symmetric Frobenius algebras in the
ribbon category of bulk line operators. This provides a simple interpretation
of the results of Fuchs, Runkel and Schweigert on the construction of 2d RCFTs
from Frobenius algebras. We also show that every topological boundary condition
in a 3d TFT gives rise to a commutative Frobenius algebra in the category of
bulk line operators. We illustrate these general considerations by studying in
detail surface operators in abelian Chern-Simons theory.
