  We study the critical two-dimensional Ising model with a defect line (altered
bond strength along a line) in the continuum limit. By folding the system at
the defect line, the problem is mapped to a special case of the critical
Ashkin-Teller model, the continuum limit of which is the $Z_2$ orbifold of the
free boson, with a boundary. Possible boundary states on the $Z_2$ orbifold
theory are explored, and a special case is applied to the Ising defect problem.
We find the complete spectrum of boundary operators, exact two-point
correlation functions and the universal term in the free energy of the defect
line for arbitrary strength of the defect. We also find a new universality
class of defect lines. It is conjectured that we have found all the possible
universality classes of defect lines in the Ising model. Relative stabilities
among the defect universality classes are discussed.
