Makeenko-Migdal equations for lattice Yang-Mills-Higgs

Hao Shen; Scott Andrew Smith; Rongchan Zhu

doi:10.1515/ans-2023-0226

Makeenko-Migdal equations for lattice Yang-Mills-Higgs

Hao Shen^*
, Scott Andrew Smith
, Rongchan Zhu

^*Corresponding author for this work

School of Mathematics and Statistics

University of Wisconsin-Madison
Chinese Academy of Sciences

Research output: Contribution to journal › Article › peer-review

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 Itô's formula.

Original language	English
Journal	Advanced Nonlinear Studies
DOIs	https://doi.org/10.1515/ans-2023-0226
Publication status	Accepted/In press - 2026

Keywords

Langevin dynamics
lattice Yang-Mills-Higgs
master loop equations

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10.1515/ans-2023-0226

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title = "Makeenko-Migdal equations for lattice Yang-Mills-Higgs",

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.",

keywords = "Langevin dynamics, lattice Yang-Mills-Higgs, master loop equations",

author = "Hao Shen and Smith, \{Scott Andrew\} and Rongchan Zhu",

note = "Publisher Copyright: {\textcopyright} 2026 the author(s), published by De Gruyter, Berlin/Boston.",

year = "2026",

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language = "English",

journal = "Advanced Nonlinear Studies",

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T1 - Makeenko-Migdal equations for lattice Yang-Mills-Higgs

AU - Shen, Hao

AU - Smith, Scott Andrew

AU - Zhu, Rongchan

PY - 2026

Y1 - 2026

N2 - 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 Itô's formula.

AB - 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 Itô's formula.

KW - Langevin dynamics

KW - lattice Yang-Mills-Higgs

KW - master loop equations

UR - https://www.scopus.com/pages/publications/105042086075

U2 - 10.1515/ans-2023-0226

DO - 10.1515/ans-2023-0226

M3 - Article

AN - SCOPUS:105042086075

SN - 1536-1365

JO - Advanced Nonlinear Studies

JF - Advanced Nonlinear Studies

ER -

Makeenko-Migdal equations for lattice Yang-Mills-Higgs

Abstract

Keywords

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