Demons and Abelian projection QCD: action and crossover

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