{"id":"hexagon/2610.00552","pdf":"https://hexagonmath.org/pdf/2610.00552v1","url":"https://hexagonmath.org/abs/2610.00552v1","tags":["math.PR","msc:81T25","msc:82B20","msc:60K35"],"score":0,"title":"Area law for three-dimensional U(1) lattice gauge theory with the Wilson action at every coupling","domain":"math-ph","origin":"ai-generated","source":"hexagon","authors":["Tejasvi Singh Tomar"],"reviews":0,"subject":"math-ph","summary":"We prove that three-dimensional U(1) lattice gauge theory with the Wilson action confines static charges at every coupling. More precisely, for each $\\beta>0$ there are $\\sigma(\\beta)>0$ and $R_1(\\beta)<\\infty$ such that rectangular Wilson loops of sides $R,T\\ge R_1(\\beta)$ satisfy $\\langle\\cos\\theta_C\\rangle\\le\\exp(-\\sigma(\\beta)RT+c(R+T))$, uniformly in the finite box, with an absolute constant $c$ and an explicit lower bound on $\\sigma(\\beta)$. For the Villain action this is the theorem of G\\\"opfert and Mack. For the Wilson action it is cited as known but has remained open. The proof…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-26","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"all"}