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We study conformal defects in two important examples of string theoryorbifolds. First, we show that topological defects in the language ofLandau-Ginzburg models carry information about the RG flow between thenon-compact orbifolds $\mathbb{C}/\mathbb{Z}_d$. Such defects are shown tocorrectly implement the bulk-induced RG flow on the boundary. Secondly, westudy what the possible conformal defects are between the $c=1$ bosonic 2Dconformal field theories with target space $S^1/\mathbb{Z}_2$. The defectscataloged here are obtained from boundary states corresponding to D-branes inthe $c=2$ free theory with target space $S^1/\mathbb{Z}_2 \timesS^1/\mathbb{Z}_2$. Via the unfolding procedure, such boundary states are latermapped to defects between the circle orbifolds. Furthermore, we compute thealgebra of the topological class of defects at different radii.

Topological defects in string theory orbifolds with target spaces $\mathbb{C}/\mathbb{Z}_N$ and $S^1/\mathbb{Z}_2$