{"title":"A new derivation of the finite N master loop equation for lattice Yang-Mills","authors":"Hao Shen, Scott A. Smith, Rongchan Zhu","doi":"10.1214/24-ejp1090","DOIUrl":null,"url":null,"abstract":". We give a new derivation of the finite N master loop equation for lattice Yang-Mills theory with structure group SO ( N ), U ( N ) or SU ( N ). The SO ( N ) case was initially proved by Chatterjee in [Cha19a], and SU ( N ) was analyzed in a follow-up work by Jafarov [Jaf16]. Our approach is based on the Langevin dynamic, an SDE on the manifold of configurations, and yields a simple proof via Itˆo’s formula.","PeriodicalId":50538,"journal":{"name":"Electronic Journal of Probability","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Probability","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/24-ejp1090","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
. We give a new derivation of the finite N master loop equation for lattice Yang-Mills theory with structure group SO ( N ), U ( N ) or SU ( N ). The SO ( N ) case was initially proved by Chatterjee in [Cha19a], and SU ( N ) was analyzed in a follow-up work by Jafarov [Jaf16]. Our approach is based on the Langevin dynamic, an SDE on the manifold of configurations, and yields a simple proof via Itˆo’s formula.
.我们给出了结构群为 SO ( N ) 、U ( N ) 或 SU ( N ) 的晶格杨-米尔斯理论的非 N 主环方程的新推导。SO ( N ) 的情况最初由查特吉在[Cha19a]中证明，而 SU ( N ) 则由贾法洛夫在后续工作[Jaf16]中分析。我们的方法基于朗之文动态，即构型流形上的 SDE，并通过伊特奥公式得到了简单的证明。
期刊介绍：
The Electronic Journal of Probability publishes full-size research articles in probability theory. The Electronic Communications in Probability (ECP), a sister journal of EJP, publishes short notes and research announcements in probability theory.
Both ECP and EJP are official journals of the Institute of Mathematical Statistics
and the Bernoulli society.
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