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Unified Maximally Natural Supersymmetry

Maximally Natural Supersymmetry, an unusual weak-scale supersymmetric extension of the Standard Model based upon the inherently higher-dimensional mechanism of Scherk-Schwarz supersymmetry breaking (SSSB), possesses remarkably good fine tuning given present LHC limits. Here we construct a version with precision $SU(2)_{\rm L} \times U(1)_{\rm Y} $ unification: $\sin^2 θ_W(M_Z) \simeq 0.231$ is predicted to $\pm 2\%$ by unifying $SU(2)_{\rm L} \times U(1)_{\rm Y} $ into a 5D $SU(3)_{\rm EW}$ theory at a Kaluza-Klein scale of $1/R_5 \sim 4.4\,{\rm TeV}$, where SSSB is simultaneously realised. Full unification with $SU(3)_{\rm C}$ is accommodated by extending the 5D theory to a $N=4$ supersymmetric $SU(6)$ gauge theory on a 6D rectangular orbifold at $1/R_6 \sim 40 \,{\rm TeV}$. TeV-scale states beyond the SM include exotic charged fermions implied by $SU(3)_{\rm EW}$ with masses lighter than $\sim 1.2\,{\rm TeV}$, and squarks in the mass range $1.4\,{\rm TeV} - 2.3\,{\rm TeV}$, providing distinct signatures and discovery opportunities for LHC run II.