  There is increasing interest in the study of nonperturbative aspects of
three-dimensional quantum field theories (QFT). They appear as holographic dual
to theories of (strongly coupled) gravity. For instance, in Holographic
Cosmology, the two-point function of the Energy-Momentum Tensor (EMT) of a
particular class of three-dimensional QFTs can be mapped into the power
spectrum of the Cosmic Microwave Background in the gravitational theory.
However, the presence of divergent contact terms poses challenges in extracting
a renormalised EMT two-point function on the lattice. Using a $\phi^4$ theory
of adjoint scalars valued in the $\mathfrak{su}(N)$ Lie Algebra as a
proof-of-concept motivated by Holographic Cosmology, we apply a novel method
for filtering out such contact terms by making use of infinitely differentiable
"bump" functions which enforce a smooth window that excludes contributions at
zero spatial separation. The process effectively removes the local contact
terms and allows us to extract the continuum limit behaviour of the
renormalised EMT two-point function.
