A new derivation of the finite N master loop equation for lattice Yang-Mills

Hao Shen; Scott A. Smith; Rongchan Zhu

doi:10.1214/24-EJP1090

A new derivation of the finite N master loop equation for lattice Yang-Mills

Hao Shen, Scott A. Smith, Rongchan Zhu

School of Mathematics and Statistics

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

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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 [6], and SU(N) was analyzed in a follow-up work by Jafarov [23]. Our approach is based on the Langevin dynamic, an SDE on the manifold of configurations, and yields a simple proof via Itô’s formula.

Original language	English
Article number	29
Journal	Electronic Journal of Probability
Volume	29
DOIs	https://doi.org/10.1214/24-EJP1090
Publication status	Published - 2024

Keywords

Itô formula
Langevin dynamics
lattice Yang-Mills
loop equations

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10.1214/24-EJP1090

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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 [6], and SU(N) was analyzed in a follow-up work by Jafarov [23]. Our approach is based on the Langevin dynamic, an SDE on the manifold of configurations, and yields a simple proof via It{\^o}{\textquoteright}s formula.",

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AB - 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 [6], and SU(N) was analyzed in a follow-up work by Jafarov [23]. Our approach is based on the Langevin dynamic, an SDE on the manifold of configurations, and yields a simple proof via Itô’s formula.

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KW - loop equations

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A new derivation of the finite N master loop equation for lattice Yang-Mills

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Keywords

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