  Hexagonal boron nitride (hBN) is a wide band gap material with both strong
excitonic light emission in the ultraviolet and strong exciton-phonon coupling.
Luminescence experiments performed on the recently synthesized monolayer form
(m-hBN) present emission spectra that differ from one another, with some
suggesting a coexistence between phonon-assisted and direct emission channels.
Motivated by these results, we investigated the optical response of (m-hBN)
using a new \textit{ab initio} approach that takes into account the effects of
atomic vibrations on the luminescence spectra. We construct the dynamical
exciton-phonon self-energy, then use it to perturbatively correct the optical
response functions and test this approach on bulk hBN as a benchmark. Within
our approach we are able to estimate the renormalisation of the direct peak
induced by phonon-assisted transitions, and this allows us to accurately
describe spectra where both processes are present. We found that the emission
signal of m-hBN is strongly dependent on its interaction with the substrate,
which changes its nature from direct to indirect material and modifies the
screening felt by the electrons. We attribute the m-hBN emission signal to the
bright direct excitons and consider the likelihood of phonon replicas
appearing.
