Large N Limit of the O(N) Linear Sigma Model in 3D
Large N Limit of the O(N) Linear Sigma Model in 3D
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DOI：
10.1007/s00220-022-04414-w
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发表时间：
2021-02
影响因子：
2.4
通讯作者：
Hao Shen;Rongchan Zhu;Xiangchan Zhu
中科院分区：
文献类型：
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作者：
Hao Shen;Rongchan Zhu;Xiangchan Zhu
本文研究了三维环面上O（N）不变线性sigma模型的大N极限，该模型是量子场论的向量值推广。我们研究的问题，通过其随机量子化，这产生了一个耦合系统的N相互作用的SPDE。我们证明了不变测度在largeN极限下的紧性。对于足够大的质量或足够小的耦合常数，他们收敛到（大规模的）高斯自由场的速度orderrelation的Wasserstein距离。我们也得到了一定的O（N）不变可观的紧密性结果。这些将Shen等人（Ann Probab 50（1）：131-202，2022）中的一些结果从二维推广到三维。该证明利用了Gubinelli和Hofmanová最近开发的方法（Commun Math Phys 384（1）：1-75，2021），并结合了许多新技术，例如对扰动对象的均匀inN估计以及解决方案。
In this paper we study the largeNlimit of theO(N)-invariant linear sigma model, which is a vector-valued generalization of thequantum field theory, on the three dimensional torus. We study the problem via its stochastic quantization, which yields a coupled system ofNinteracting SPDEs. We prove tightness of the invariant measures in the largeNlimit. For large enough mass or small enough coupling constant, they converge to the (massive) Gaussian free field at a rate of orderwith respect to the Wasserstein distance. We also obtain tightness results for certainO(N) invariant observables. These generalize some of the results in Shen et al. (Ann Probab 50(1):131–202, 2022) from two dimensions to three dimensions. The proof leverages the method recently developed by Gubinelli and Hofmanová (Commun Math Phys 384(1):1–75, 2021) and combines many new techniques such as uniform inNestimates on perturbative objects as well as the solutions.