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arXiv · 2512.00570

Makeenko-Migdal equations for lattice Yang-Mills-Higgs

Hao Shen·Scott Andrew Smith·Rongchan Zhu
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Abstract

We derive a form of master loop equations for the lattice Yang-Mills-Higgs theory with structure group $SO(N)$, $U(N)$ or $SU(N)$. Compared to the pure Yang-Mills setting, several new operations arise. In fact, to obtain a closed recursion we must broaden the class of observables to include open Wilson lines. Our approach is based on the conditional Langevin dynamic and yields a concise proof via It\^o's formula.

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Hao Shen, Scott Andrew Smith, Rongchan Zhu. 2025-11-29. Makeenko-Migdal equations for lattice Yang-Mills-Higgs. https://arxiv.org/abs/2512.00570

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