  We determine the exact threshold of the extended Seiberg bound for the
existence of correlation functions in the boundary Liouville conformal field
theory in the unit disk. In probabilistic terms, our result is a toolbox
yielding the threshold for the existence of positive moments of Gaussian
multiplicative chaos measure, appliable to the case where singularities of
arbitrary (co-)dimension in the background metric are present. We improve
previous results of this type for 0-dimensional singularities in [DKRV16] and a
sufficient condition for the 1-dimensional singularity in an unpublished
appendix of [HRV18]. In particular, we prove the optimality of the moment bound
threshold for boundary Gaussian multiplicative chaos conjectured in [HRV18],
which is equivalent to the so-called unit volume Seiberg bound of the boundary
Liouville conformal field theory.
