Improved Spin-Wave Estimate for Wilson Loops in <i>U</i>(1) Lattice Gauge Theory

Abstract In this paper, we obtain bounds on the Wilson loop expectations in 4D $U(1)$ lattice gauge theory, which quantify effect of topological defects. case a Villain interaction, by extending non-perturbative technique introduced [24], following estimate for large $\gamma $ at low temperatures: |\langle W_\gamma \rangle _{\beta }|\leq \exp \Big (-\frac {C_{GFF}} {2\beta }(1+C \beta e^{- 2\pi ^2 } )(|\gamma |+o(|\gamma |)) )\,.$ Our result is line with recent works [4, 9, 13, 15] analyze where group discrete. present continuous and Abelian, fluctuations field decouple into Gaussian part, related to so-called free electromagnetic wave [11, 23], gas As such, our work gives new quantitative latter complement Guth Frölich-Spencer [17, 27]. Finally, improve, also way, correction term from $e^{-2\pi ^2\beta }$ $e^{-\pi free-energy system. This provides matching lower-bound prediction [27] based renormalization techniques.