in Region II. There is physics in both regions which we had not come across before. For example, as we will see, the fluctuations in Region I are quite unlike the Gaussian fluctuations discussed in Sec. II C. The symmetry breaking in Region II remains controversial. There have been two valid reasons for skepticism that Region II has a distinct order parameter. One is that it the extensive investigations on the Cuprates with every available tool and some newly invented had not discovered any credible broken symmetry and the second that although the specific heat decreases near below the line demarcating Region I and II, there is no evidence for any singularity in it as in the typical classical phase transition. However, in the last five years, an elusive proposed order [75–77] has indeed been discovered experimentally in four distinct families of Cuprates [78–81]. Moreover the model representing the observed classical phase transition to this order has a non- diverging specific heat at the transition [32], whose quantitative value is consistent with the experiments [82]. I will now summarize the theoretical results briefly. In a two-dimensional Cuprate model with three degrees of freedom per unit-cell, representing the d$_{x}$ $^{2}$− y 2 -orbital of Copper and the p$_{x}$ and the p$_{y}$ -orbitals on the Oxygen atoms on the x-direction and the y-direction respectively of the Copper, together with on-site and nearest neighbor interactions, two phases which are odd under time-reversal due to spontaneously generated orbital loop- currents but preserving the translational symmetry were shown to be locally stable in a mean-field calculation. The phase observed has the symmetry of one of these phases but there are some other details [78–81] which are different and obtainable only in a more complicated model [83]. The observed as well as the predicted phase has a symmetry which can be characterized as the ordering of a polar time-reversal odd vector L . L describes the loop-current pattern shown in Fig.(12) which preserves even-ness only in reflection on one of the four-possible symmetry planes of the square lattice. L has four-possible orientations, corresponding to the four possible domains of the ordered phase. In the quantum-fluctuation regime, the instantaneous pattern of currents is described by vectors L$_{i}$ , which vary in direction among the four-possible orientations. The quantum-fluctuations are described by the correlation function [9, 10] < U + i ( t ) U$_{j}$ ( t $^{′}$) > , where U$_{i}$ is the generator of the rotation among the four-configurations of L$_{i}$ . It turns out that in the fluctuation regime the discreteness of L$_{i}$ can be replaced by a continuous vector so that the fluctuations are related to the fluctuations of a quantum-fluctuations of a 2 − dimensional rotor. In a model including dissipation due to the coupling of the fluctuations of U$_{i}$ to the fluctuations of the 44