  The two-dimensional dissipative quantum XY model is applicable to the
quantum-critical properties of diverse experimental systems, ranging from the
superconductor to insulator transitions, ferromagnetic and antiferromagnetic
transitions in metals, to the loop-current order transition in the cuprates. We
solve the re-expression of this model in terms of topological excitations:
vortices and a variety of instantons, by renormalization group methods. The
calculations explain the extraordinary properties of the model discovered in
Monte-Carlo calculations: the separability of the quantum critical fluctuations
(QCF) in space and time, the spatial correlation length proportional to
logarithm of the temporal correlation length near the transition from
disordered to the fully ordered state, and the occurrence of a phase with
spatial order without temporal order. They are intimately related to the flow
of the metric of time in relation to the metric of space, i.e. of the dynamical
critical exponent $z$. These properties appear to be essential in understanding
the strange metallic phase found in a variety of quantum-critical transitions
as well as the accompanying high temperature superconductivity.
