$\bar L_n$ the left- and right-moving Virasoro generators, respectively. \[Note in particular that ${\cal L}_0$ generates translations in $\sigma$.\] It follows from conditions (\[cnds\]) that if ${|\!|}{\cal B}{\rangle\!\rangle}$ is a conformal boundary state, [*i.e.*]{}if it is annihilated by all ${\cal L}_n$, then ${\cal O}(A^*,Y^*) {|\!|}{\cal B}{\rangle\!\rangle}$ is also conformal. Thus, if the limit (\[limit\]) were smooth, pulling back the RG flow of a bulk defect to [*any*]{} conformal boundary would induce a (possibly trivial) RG flow of the boundary state. Conformal defect lines, in particular, act as solution-generating symmetries, [*i.e.*]{}  they map conformal to conformal boundary states.

In general, taking the limit (\[limit\]) can be tricky, since the presence of the boundary could conceivably modify the RG flow at distances much greater than $\varepsilon$. There exists, however, one special class of defects that commute with the right-moving Virasoro algebra, $$\left[\; {\bar L}_n  \; ,  \; {\cal O}_{\rm chir}(A,Y)\; \right]\; =
0\ ,$$ and for which the limit (\[limit\]) is trivial. We will refer to them as chiral defects (or anti-chiral if they commute with the left-moving algebra). Chiral defects need not be conformal, but they can be regularised and renormalised in a way that preserves their invariance under $\sigma$-translations. They 