LARGE N LIMIT OF THE O(N) LINEAR SIGMA MODEL VIA STOCHASTIC QUANTIZATION

• 成果类型: Article
• 署名作者: Shen, Hao; Smith, Scott A.; Zhu, Rongchan; Zhu, Xiangchan
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Beijing Institute of Technology
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1531
• 发表日期: 2022
• 页码: 131-202
• 关键词: quantum-field-theory; symmetry-breaking; borel summability; EQUATIONS; propagation; derivation; expansion; DYNAMICS; systems

摘要

This article studies large N limits of a coupled system of N interacting Phi(4) equations posed over T-d for d = 2, known as the O(N) linear sigma model. Uniform in N bounds on the dynamics are established, allowing us to show convergence to a mean-field singular SPDE, also proved to be globally well posed. Moreover, we show tightness of the invariant measures in the large N limit. For large enough mass, they converge to the (massive) Gaussian free field, the unique invariant measure of the mean-field dynamics, at a rate of order 1/root N with respect to the Wasserstein distance. We also consider fluctuations and obtain tightness results for certain O(N) invariant observables, along with an exact description of the limiting correlations.