Center symmetry and area laws

الأصل · EN

SU(Nc) gauge theories containing matter fields may be invariant under transformations of some subgroup of the Zₙc center; the maximum such subgroup is Zₚ, with p depending on Nc and the representations of the various matter fields in the theory. Confining SU(Nc) gauge theories in either 3+1 or 2+1 space-time dimensions and with matter fields in any representation have string tensions for representation R given by σᵣ =σf pᵣ (p-pᵣ) g (pᵣ (p-pᵣ))/(p-1) g(p -1) with pᵣ=nᵣ mod(p), where σf is the string tension for the fundamental representation, g is a positive finite function and nᵣ is the n-ality of R. This implies that a necessary condition for a theory in this class to have an area law is invariance of the theory under a nontrivial subgroup of the center. Significantly, these results depend on p regardless of the value of Nc.