the original, unperturbed D-brane.

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In the open channel, the operator ${\cal O}(A,Y)$ describes the interactions of a point defect sitting in the interior of the worldsheet. Such defects have been previously discussed in the condensed-matter [@Oshikawa:1996dj; @Saleur:1998hq] and in the string-theory [@Bachas:2001vj; @Quella:2002ct] literature. By folding the worldsheet along their worldline, one may picture bulk defects geometrically as D-branes in the tensor product, ${\cal M}\times {\cal M}$, of two identical target manifolds. The trivial defect, [*i.e.*]{} the identity operator, corresponds to the diagonal brane in ${\cal M}\times {\cal M}$ [@Bachas:2001vj; @Quella:2002ct]. Its geometric and gauge degrees of freedom are precisely given by two one-form fields living on ${\cal M}$. This fits very nicely with the fact that $A_M(x)$ and $Y_M(x)$ account (together with the tachyon field) for the most general renormalisable couplings on a defect worldline.

Conformal defects are obtained at the fixed points $(A^*,Y^*)$ of the RG flow. The corresponding loop operators commute with the generators of conformal transformations that preserve the defect worldline, $$\label{cnds}
\left[\; {\cal L}_n  \; ,  \; {\cal O}(A^*,Y^*)\; \right]\; =  0\ \
\ \ \ \forall \; n \ ,$$ where ${\cal L}_n = L_n - \bar L_{-n}\ $ with $L_n$ and 