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We derive an U(1) effective theory of color confinement by applying theso-called Julia-Toulouse Approach for defects condensation to the SU(2)restricted gauge theory defined by means of the Cho decomposition of thenon-abelian connection. Cho's geometric construction naturally displays thetopological degrees of freedom of the theory and can be used to put theYang-Mills action into an abelianized form under certain conditions. On theother hand, the use of the Julia-Toulouse prescription to deal with themonopole condensation leads to an effective action describing the phase whosedynamics is dominated by the magnetic condensate. The effective theory we founddescribes the interaction between external electric currents displaying ashort-range Yukawa interaction plus a linear confinement term that governs thelong distance physics.

U(1) effective confinement theory from SU(2) restricted gauge theory via the Julia-Toulouse Approach