Brownian from $a$ to $b$ conditioned not to hit the boundary, with the exponent $5/8$ replaced by $1$. Finally let us mention that for a SAW from point $a$ on the boundary to point $b$ in the bulk (radial SLE) the probability becomes $|g'_A(a)|^{5/8} |g'_A(b)|^{5/48}$. In CFT language $h_{1,2}$ (with $h_{1,2}=5/8$ for $\kappa=8/3$) is the dimension of the operator $\Phi_{12}$ creating a curve on the boundary, $2 h_{0,1/2}=5/48$ is the dimension of the bulk operator $\Phi_{0,1/2}$ creating a curve in the bulk. $\Phi_{1,3}$ with $h_{1,3}=2$ creates two curves on the boundary conditioned not to annihilate. When generalized, this implies that the force exerted by $n$ polymers with identical endpoints on a given subdomain $A$ connected to the boundary is proportional to $h_{1,n+1}=n(3 n+ 2)/8$, which explains the ratio $h_{1,3}/h_{1,2}=16/5$ found above, see Eq. (\[18\]), for small $y$ (point close to the boundary)[^1].

The simplest example for an object $A$ connected to the boundary is a vertical segment $z=a+i y$ with $y \in [0,h]$, which is removed by the map $g_A(z) = \sqrt{(z-a)^2+h^2} + {{{\mathrm{sign}}}}(a) \sqrt{a^2+h^2}$. The no-hit probability is ${\cal P} = \big( \frac{a^2}{h^2+a^2}\big) ^{ 5/ {16}}$, and the total force $\vec f=k T \vec \nabla \ln {\cal P}$ is: 