We study effective field theories (EFT) of nuclear structure based on spontaneously broken global $SU(2)_Ltimes SU(2)_R$ chiral symmetry of QCD with two massless quarks, i.e. $SU(2)chi PT$. For ground-state nuclei, this EFT enables expansion and truncation in inverse powers of $Lambda_{chi SB}simeq 1 GeV$, with analytic operators renormalized to all loop orders. We derive the EFT Lagrangian to order $Lambda^0_{chi SB}$. We show that $SU(2)chi PT$ of protons, neutrons and pions admits a semi-classical Static Chiral Nucleon Liquid (Static$chi$NL) phase and that Pion-less $SU(2)chi PT$ emerges in this liquid: far-infrared pions decouple from Static$chi$NL, vastly simplifying the derivation of saturated nuclear matter (the infinite liquid phase) and of finite microscopic liquid drops (ground-state nuclides). Static$chi$NL are made entirely of nucleons with even parity, total spin zero, and even $Z$ and $N$; local expectation values for spin and momenta vanish. They explain the power of pion-less $SU(2)chi PT$ to capture experimental ground-state properties of certain nuclides, this explanation following directly from the global symmetries of QCD with two massless quarks. Mean-field Static$chi$NL non-topological solitons are true solutions of $SU(2)chi PT$s semi-classical symmetries: they obey all CVC and PCAC conservation laws and they have zero internal and external pressure. The nuclear liquid-drop model and the semi-empirical mass formula emerge -- with correct nuclear density and saturation and asymmetry energies -- in an explicit Thomas-Fermi construction. We relate our work to compatible and complementary work in pionless and in halo/ cluster EFTs, also composed entirely of nucleons and applied to light ($Aleq 6$) nuclei, which might provide important (<12.5%) corrections to Static$chi NL$.
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