  In this study, we explore the correlation functions of thin-shell operators,
represented semiclassically by a homogeneous, thin interface of dust particles.
Employing the monodromy method, we successfully compute the contribution from
the Virasoro vacuum block and present the monodromy equation in a closed form
without assuming the probe limit. Although an analytical solution to the
monodromy equation remains difficult, we demonstrate that it is perturbatively
solvable within specific limits, including the probe, the heavy-shell, and the
early-time limits. Moreover, we compare our results with gravitational
calculations and find precise agreement. We strengthen our findings by proving
that the thermal correlation functions in gravity, after an inverse Laplace
transformation, satisfy the field theory's monodromy equation. Additionally, we
identify an infinite series of unphysical solutions to the monodromy equation
and discuss their potential geometrical duals.
