Critical phenomena in the two-dimensional Ising model with a defect li
ne are studied using boundary conformal field theory on the c = 1 orbi
fold. Novel features of the boundary states arising from the orbifold
structure, including continuously varying boundary critical exponents,
are elucidated. New features of the Ising defect problem are obtained
including a novel universality class of defect lines and the universa
l boundary to bulk crossover of the spin correlation function.