We propose a mechanism where the under-doped regime of cuprate superconductors is governed by an emergent SU(2) pseudo-spin symmetry connecting the $d$-wave superconducting state to a $d$-wave charge order. The specific SU(2) pairing fluctuations between the $d$-wave SC state and the charge sector lead to the formation of a new state of matter, where local patches of excitons are spontaneously generated and are responsible for the creation of Fermi arcs in the pseudo-gap phase of cuprate superconductors. In momentum space, each exciton patch is formed by a superposition of modulation wave vectors coming from the anti-nodal region. A form factor contrives the wave vectors to prefer the x and y axes, producing a typical checkerboard structure recently observed in the under-doped regime. When the amplitude of the new state vanishes, it becomes critical, and in this region a semiclassical Boltzmann calculation leads to a $T/\ln(T)$ scaling of the resistivity in three dimensions, which describes the strange-metal phase with its long-standing linear-$T$ resistivity anomaly.