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arXiv · 2505.16585

Expanded regimes of area law for lattice Yang-Mills theories

Sky Cao·Ron Nissim·Scott Sheffield
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Abstract

We extend the parameter regimes for which area law is proven for pure $\mathrm{U}(N)$ lattice Yang-Mills theories, in particular when $N$ is large. This improves on a classical result of Osterwalder-Seiler from 1978. To do so, we view the master loop equation as a linear inhomogeneous equation for Wilson string expectations, and then prove an a priori bound for solutions to the equation. The main novelty is in how we deal with the merger term in the master loop equation. This is done by introducing a truncated model for which the merger term is unproblematic, and then showing that the truncated model well approximates the original model.

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Sky Cao, Ron Nissim, Scott Sheffield. 2025-05-22. Expanded regimes of area law for lattice Yang-Mills theories. https://arxiv.org/abs/2505.16585

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