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Title: Area law for Wilson loops in 4D lattice gauge theory at weak coupling
Plain: Quark confinement shows up mathematically as a loop observable that decays with the area enclosed by the loop. This is proven only when the coupling is strong, far from the regime that describes nature.
Precise: For 4D lattice $\mathrm{SU}(2)$ or $\mathrm{SU}(3)$ gauge theory with Wilson action at large $\beta = 2N/g^{2}\ (N = 2\ \mathrm{or}\ 3)$, prove $\langle W(C)\rangle \le \exp(-\sigma(\beta)\operatorname{Area}(C))$ with string tension $\sigma(\beta) > 0$ for all rectangular loops $C$, uniformly in the infinite-volume limit. Answer: a proof, ideally with $\sigma(\beta) \sim \exp(-c \beta)$ as predicted by asymptotic freedom.
Settled by: A proof of a positive string tension for all $\beta$ in four dimensions.
Kind: well-posed
Answer type: proof
References: (empty)
Literature status: open
Status note: The area law is proven only at strong coupling (small $\beta$), going back to Osterwalder and Seiler (1978).
Posed since: (empty)