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

Author: 

Chevyrev, I

Journal: 

Communications in Mathematical Physics

Last Updated: 

2019-10-09T12:59:44.723+01:00

abstract: 

We introduce a space of distributional one-forms $\Omega^1_\alpha$ on the torus $\mathbf{T}^2$ for which holonomies along axis paths are well-defined and induce Hölder continuous functions on line segments. We show that there exists an $\Omega^1_\alpha$-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 Lévy (2003). It holds furthermore that $\Omega^1_\alpha$ embeds into the Hölder-Besov space $\mathcal{C}^{\alpha-1}$ for all $\alpha\in(0,1)$, 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.

Symplectic id: 

991804

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Submitted to ORA: 

Submitted

Publication Type: 

Journal Article