Yang–Mills measure on the two-dimensional torus as a random distribution

Journal article

We introduce a space of distributional one-forms Ω 1 α on the torus T 2 for which holonomies along axis paths are well-defined and induce Hölder continuous functions on line segments. We show that there exists an Ω 1 α-valued random variable A for which Wilson loop observables of axis paths coincide in law with the corresponding observables under the Yang–Mills measure in the sense of [Lév03]. It holds furthermore that Ω 1 α embeds into the Hölder–Besov space C α−1 for all α ∈ (0, 1), so that A has the correct small scale regularity expected from perturbation theory. Our method is based on a Landau-type gauge applied to lattice approximations.

Authors: Chevyrev, I

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: Communications in Mathematical Physics
• Volume: 372
• Pages: 1027-1058
• Publication date: 2019-09-14
• Acceptance date: 2019-07-25
• DOI: 10.1007/s00220-019-03567-5
• EISSN: 1432-0916
• ISSN: 0010-3616
• Language: English