2021/07/08 by Garban, Christophe, Sepúlveda, Avelio · 2 citations
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)
paper · doi:10.48550/arxiv.2107.04021
In this paper, we obtain bounds on the Wilson loop expectations in 4D U(1) lattice gauge theory which quantify the effect of topological defects. In the case of a Villain interaction, by extending the non-perturbative technique introduced in [GS20a], we obtain the following estimate for a large loop γ at low temperatures: |⟨ Wγ⟩β| ≤ exp (-\fracCGFF 2β(1+C βe- 2π2 β )(|γ|+o(|γ|)) ) . Our result is in the line of recent works [Cha20, Cao20, FLV20, For21] which analyze the case where the gauge group is discrete. In the present case where the gauge group is continuous and Abelian, the fluctuations of the gauge field decouple into a Gaussian part, related to the so-called \em free electromagnetic wave [Gro83, Dri87], and a gas of \em topological defects. As such, our work gives new quantitative bounds on the fluctuations of the latter which complement the works by Guth and Fröhlich-Spencer [Gut80, FS82]. Finally, we improve, also in a non-perturbative way, the correction term from e-2π2β to e-π2β in the case of the free-energy of the system. This provides a matching lower-bound with the prediction of Guth [Gut80] based on renormalization group techniques.