A decay of weakly metastable phase coupled to two-dimensional Liouville
gravity is considered in the semiclassical approximation. The process is
governed by the ``critical swelling'', where the droplet fluctuation favors a
gravitational inflation inside the region of lower energy phase. This
geometrical effect modifies the standard exponential suppression of the decay
rate, substituting it with a power one, with the exponent becoming very large
in the semiclassical regime. This result is compared with the power-like
behavior of the discontinuity in the specific energy of the dynamical lattice
Ising model. The last problem is far from being semiclassical, and the
corresponding exponent was found to be 3/2. This exponent is expected to govern
any gravitational decay into a vacuum without massless excitations. We
conjecture also an exact relation between the exponent in this power-law
suppression and the central charge of the stable phase.Comment: Extended version of a talk presented at XXXIII International
Conference on High Energy Physics, Moscow, July 26 - August 02, 2006. v2: few
typos corrected, a reference and an acknowledgement adde
