Demons and Abelian projection QCD: action and crossover

SAPQCD, the Abelian projection QCD (APQCD) action, is evaluated using the demon method. For SU(2), SAPQCD at strong coupling is essentially the compact QED (CQED) action with βCQED = 12βSU(2): extended and higher representation plaquettes are absent. Since CQED deconfines when βCQED>∼ 1, this relation must break down as βSU(2) → 2. Indeed we find SAPQCD mutates: near βSU(2) ∼ 2 it gains additional operators, including an exogenous negative magnetic monopole mass shift. SAPQCD for SU(3) has similar behavior. The Appendix gives a brief explanation of the demon method.