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- Title
Improved Spin-Wave Estimate for Wilson Loops in U(1) Lattice Gauge Theory.
- Authors
Garban, Christophe; Sepúlveda, Avelio
- Abstract
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 [ 24 ], we obtain the following estimate for a large loop |$\gamma $| at low temperatures: |$ |\langle W_\gamma \rangle _{\beta }|\leq \exp \Big (-\frac {C_{GFF}} {2\beta }(1+C \beta e^{- 2\pi ^2 \beta })(|\gamma |+o(|\gamma |)) \Big)\,.$| Our result is in line with recent works [ 4 , 9 , 13 , 15 ] which analyze the case where the gauge group is discrete. In the present case where the gauge group is continuous and Abelian, the fluctuations of the gauge field decouple into a Gaussian part, related to the so-called free electromagnetic wave [ 11 , 23 ], and a gas of topological defects. As such, our work gives new quantitative bounds on the fluctuations of the latter which complement the works by Guth and Frölich-Spencer [ 17 , 27 ]. Finally, we improve, also in a non-perturbative way, the correction term from |$e^{-2\pi ^2\beta }$| to |$e^{-\pi ^2\beta }$| in the case of the free-energy of the system. This provides a matching lower-bound with the prediction of Guth [ 27 ] based on renormalization group techniques.
- Subjects
LATTICE theory; RENORMALIZATION group; CONTINUOUS groups; ELECTROMAGNETIC waves; SPIN waves; RENORMALIZATION (Physics); LOW temperatures; GAUGE field theory
- Publication
IMRN: International Mathematics Research Notices, 2023, Vol 2023, Issue 21, p18142
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnac356