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Demanding a consistent quantum field theory description of spin 1/2 particlesnear a circular Fermi surface in 2d leads to a unique fermionic theory withrelevant quartic interactions which has an emergent Lorentz symmetry andautomatically has an Sp(4) = SO(5) internal symmetry. The free theory hasresistivity linear in temperature. The interacting theory has a low-energyinteracting fixed point and is thus a non-Landau/Fermi liquid.Anti-ferromagnetic (AF) and superconducting (SC) order parameters are bilinearsin the fields and form the 5-dimensional vector representation of SO(5). An AFphase occurs at low doping which terminates in a first order transition. Weincorporate momentum dependent scattering of Cooper pairs near the Fermisurface to 1-loop and derive a new kind of SC gap equation beyond mean fieldwith a d-wave gap solution. Taking into account the renormalization group (RG)scaling properties near the low energy fixed point, we calculate the completephase diagram as a function of doping, which shows some universal geometricfeatures. The d-wave SC dome terminates on the over-doped side at the fixedpoint of the RG,which is a quantum critical point. Optimal doping is estimatedto occur just below 3/2\pi^2. The critical temperature for SC at optimal dopingis set mainly by the universal nodal Fermi velocity and lattice spacing, and isestimated to average around 140K for LSCO. The pseudogap energy scale isidentified as the RG scale of the coupling.

A model of a 2d non-Fermi liquid with SO(5) symmetry, AF order, and a d-wave SC gap