Liouville Quantum Field Theory can be seen as a probabilistic theory of 2d
Riemannian metrics eϕ(z)dz2, conjecturally describing scaling limits
of discrete 2d-random surfaces. The law of the random field ϕ in LQFT
depends on weights α∈R that in classical Riemannian geometry
parametrize power law singularities in the metric. A rigorous construction of
LQFT has been carried out in \cite{DKRV} in the case when the weights are below
the so called Seiberg bound: α<Q where Q parametrizes the random
surface model in question. These correspond to conical singularities in the
classical setup. In this paper, we construct LQFT in the case when the Seiberg
bound is saturated which can be seen as the probabilistic version of Riemann
surfaces with cusp singularities. Their construction involves methods from
Gaussian Multiplicative Chaos theory at criticality