Abstract
We give a new derivation of the finite N master loop equation for lattice Yang-Mills theory with structure group , or . The case was initially proved by Chatterjee in [6], and 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.
Acknowledgments
H.S. gratefully acknowledges financial support from NSF grants DMS-1954091 and CAREER DMS-2044415, and helpful discussions with Ilya Chevyrev. S.S. and R.Z. are grateful to the financial supports by National Key R&D Program of China (No. 2022YFA1006300). R.Z. is grateful to the financial supports of the NSFC (No. 12271030), and BIT Science and Technology Innovation Program Project 2022CX01001 and the financial supports by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project-ID 317210226–SFB 1283, and helpful discussions with Xin Chen. S. A. Smith is grateful for financial support from the Chinese Academy of Sciences. We also would like to thank Todd Kemp for discussion on relevant references, and an anonymous referee who drew our attention to very interesting and relevant papers [17, 15, 1] and [16, 18, 19].
Citation
Hao Shen. Scott A. Smith. Rongchan Zhu. "A new derivation of the finite N master loop equation for lattice Yang-Mills." Electron. J. Probab. 29 1 - 18, 2024. https://doi.org/10.1214/24-EJP1090
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