Free, publicly-accessible full text available June 16, 2023
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Abstract We define a natural state space and Markov process associated to the stochastic Yang–Mills heat flow in two dimensions. To accomplish this we first introduce a space of distributional connections for which holonomies along sufficiently regular curves (Wilson loop observables) and the action of an associated group of gauge transformations are both well-defined and satisfy good continuity properties. The desired state space is obtained as the corresponding space of orbits under this group action and is shown to be a Polish space when equipped with a natural Hausdorff metric. To construct the Markov process we show that the stochasticmore »Free, publicly-accessible full text available June 7, 2023
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Free, publicly-accessible full text available May 6, 2023
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Free, publicly-accessible full text available January 1, 2023
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Abstract In this paper we introduce the stochastic Ricci flow (SRF) in two spatial dimensions. The flow is symmetric with respect to a measure induced by Liouville conformal field theory. Using the theory of Dirichlet forms, we construct a weak solution to the associated equation of the area measure on a flat torus, in the full “$L^1$ regime” $\sigma < \sigma _{L^1}=2 \sqrt \pi $ where $\sigma $ is the noise strength. We also describe the main necessary modifications needed for the SRF on general compact surfaces and list some open questions.
