- \frac{1}{\pi} \int_{tt'} h'(t)h'(t') \ln|t-t'| +O(h^3)$. In the case of two objects, (\[expansion\]) yields their interaction, to lowest order, mediated by the polymer. For small objects one finds ${\cal F}_{\mathrm{int}}= - k T {\frac{5}{4 \pi}} \partial_{a}\partial_b {\cal G}(a,b) \int_t h_a(t) \int_{t'} h_b(t')$. The interaction of a small object at $z$ in the bulk with an arbitrary object on the boundary removed by the map $g(z)$ is obtained from the left passage probability $\cal P$, generalizing Schramm’s formula to ${\cal P} = |g'(0)|^{\frac58}\frac12 \big[ 1+ \frac{\Re g(z)}{|g(z)|} \big]$.

The previous calculations can be extended to fluctuation forces for an object impenetrable to the interface described by SLE for any $\kappa$. For illustration, the force in geometry $\cal A$ at $\theta = \pi/2$ reads $$\vec f = 
 - k T \frac{\vec n_\theta} r
\frac{2 \Gamma \left(\frac{4}{\kappa }\right)}{\sqrt{\pi } \Gamma \left(\frac{4}{\kappa
   }-\frac{1}{2}\right)}\ .$$ Extension to Ising at $T_c$ assumes that the object interacts only with the interface induced by changes in boundary conditions, not the bubbles proliferating at criticality, which seems artificial. Physically meaningful is the polymer at the $\Theta$ point [@DuplantierSaleur1987], conjectured to correspond to $\kappa=6$. Further results follow from recent works: (i) from [@hagendorf] one obtains the force exerted by a 