Circular Wilson loops in defect Conformal Field Theory

We study a D3-D5 system dual to a conformal field theory with a codimension-one defect that separates regions where the ranks of the gauge groups differ by $k$. With the help of this additional parameter, as observed by Nagasaki, Tanida and Yamaguchi, one can define a double scaling limit in which the quantum corrections are organized in powers of $\lambda \mathrm{/}{k}^2$, which should allow to extrapolate results between weak and strong coupling regimes. In particular we consider a radius $R$ circular Wilson loop placed at a distance $L$, whose internal space orientation is given by an angle $\chi$. We compute its vacuum expectation value and show that, in the double scaling limit and for small $\chi$ and small $L\mathrm{/}R$, weak coupling results can be extrapolated to the strong coupling limit.