Novel quantum criticality due to emergent topological conservation law in high-$T_c$ cuprates

We argue that in strongly correlated electron system collective instanton excitations of the phase field (dual to the charge) arise with a great degree of stability, governed by gauge flux changes by an integer multiple of $2\pi$. By unraveling consequences of the non-trivial topology of the charge gauge U(1) group, we found that the pinning of $\mu$ and the zero-temperature divergence of charge compressibility $\kappa \sim \mathrm{\partial }{n}_e\mathrm{/}\mathrm{\partial }\mu$ defines novel “hidden” quantum criticality on verge of the Mott transition governed by the protectorate of stable topological numbers rather than Landau paradigm of the symmetry breaking.