arXiv subjects

Elias Nohra

Publications and source records attributed to Elias Nohra.

3 recordsLinked to original sources

arXiv2026

Universality of two-dimensional Markovian holonomy fields

We prove a universality theorem for a broad class of two-dimensional gauge theories on compact surfaces. Each admissible conjugation-invariant Lévy process on a compact connected Lie group determines a universality class of lattice gauge theories whose continuum limit is the associated Markovian holonomy process. Our result can be seen as a gauge-theoretic analogue of invariance principles for random walks and Lévy processes. This framework includes the Yang--Mills holonomy process and the standard heat-kernel (Villain), Wilson, and Manton lattice actions. The proof uses state-sum formulas of independent interest, separating action-dependent spectral coefficients from action-independent topological coefficients determined by the surface and the marked ribbon type of the loop configuration.

math.PR↗

arXiv2026

Semiclassical analysis for Yang--Mills random connections on compact surfaces

We introduce anisotropic Banach spaces of distributional 1-forms on compact surfaces designed to capture the fine regularity properties of Morse gauge-fixed Yang--Mills random connections. Using singular connections supported on unstable curves of a Morse gradient flow, we provide a new description of the moduli space of flat connections and of its canonical Atiyah--Bott--Goldman symplectic form. When the group is the special unitary group, we prove that in the zero-area limit, the Yang--Mills random connection converges, within these anisotropic spaces, to a random distributional 1-form whose law coincides with our Morse-theoretic representative of the Atiyah--Bott--Goldman measure. Our approach extends the works of Witten, Forman, Liu, and Sengupta by establishing the zero-area limit of the Yang--Mills measure at the level of random distributional connections, rather than only at the level of holonomies. This answers a question of Thierry Lévy on the semiclassical limits of Yang--Mills random connections.

math.PR↗

arXiv2026

The Yang--Mills measure on compact surfaces as a universal scaling limit of lattice gauge models

In this article, we study the 2 dimensional Yang--Mills measure on compact surfaces from a unified continuum and discrete perspective. We construct the Yang--Mills measure as a random distributional 1 form on surfaces of arbitrary genus equipped with an arbitrary smooth area form, using the analytic concept of pseudo-coordinates. Our approach yields a canonical noise-flat decomposition of the measure, reflecting the topology of the surface. We prove a universality theorem stating that the continuum Yang--Mills measure arises as the scaling limit of a wide class of lattice gauge theories -- including Wilson, Manton, and Villain actions -- on any compact surface. We study the convergence in natural spaces of distributions with anisotropic regularity. As further consequences, we obtain a new intrinsic construction of the Yang--Mills measure, independent of the previous constructions in the literature, and prove the convergence of correlation functions and Segal amplitudes on all compact surfaces.

math.PR↗