XY ferromagnets, the superconductor-insulator transition, and the model for

loop-current order in Cuprates. The spectral function of the quantum-critical

fluctuations for this model in 2D for a range of parameters is determined by

topological defects - instantons and 2D vortices; it is a separable function of

space and time, with a 1/τ dependence at criticality. The marginal fermi-liquid

properties for the fermions follow from coupling to such fluctuations.

These fluctuations are directly measured by inelastic neutron scattering in the

quantum-critical region of the new Fe- based compounds, in a 2D ferromagnet

and in heavy-Fermions, and deduced in cuprates through analysis of ARPES.

ARPES also reveals the coupling function of the fermions to the fluctuations

so as to give nearly angle-independent normal self-energy but d-wave pairing

energy.