  We present an analytical expression for the static many-body local field
factor $G_{+}(q)$ of a homogeneous two-dimensional electron gas, which
reproduces Diffusion Monte Carlo data and embodies the exact asymptotic
behaviors at both small and large wave number $q$. This allows us to also
provide a closed-form expression for the exchange and correlation kernel
$K_{xc}(r)$, which represents a key input for density functional studies of
inhomogeneous systems.
