  We study the interplay of superfluidity and glassy ordering of hard core
bosons with random, frustrating interactions. This is motivated by bosonic
systems such as amorphous supersolid, disordered superconductors with preformed
pairs, and helium in porous media. We analyze the fully connected mean field
version of this problem, which exhibits three low-temperature phases, separated
by two continuous phase transitions: an insulating, glassy phase with an
amorphous frozen density pattern, a nonglassy superfluid phase, and an
intermediate phase, in which both types of order coexist. We elucidate the
nature of the phase transitions, highlighting in particular the role of glassy
correlations across the superfluid-insulator transition. The latter suppress
superfluidity down to T=0, due to the depletion of the low-energy density of
states, unlike in the standard BCS scenario. Further, we investigate the
properties of the coexistence (superglass) phase. We find anticorrelations
between the local order parameters and a nonmonotonous superfluid order
parameter as a function of T. The latter arises due to the weakening of the
glassy correlation gap with increasing temperature. Implications of the mean
field phenomenology for finite dimensional bosonic glasses with frustrating
Coulomb interactions are discussed.
