用奇异值分解构建规范不变量，提升纯SU(N)规范场生成效率。
Normalizing flows for SU($N$) gauge theories employing singular value decomposition
- 基于奇异值分解构造规范不变量，设计规范等变变换。
- 在4⁴格点上训练SU(3)威尔逊作用模型，β=1时表现良好。
- 相比威尔逊环谱流，新方法生成效率更高，适合格点规范理论研究。
本文报告了利用归一化流生成纯SU(N)规范理论中规范场配置的进展。我们讨论如何通过奇异值分解构建规范不变量，并以此作为构建SU(N)规范链规范等变变换的基本单元。采用这一新方法，我们在β=1的4⁴格点上构建了代表性的SU(3)威尔逊作用模型，并对模型进行训练与性能分析，凸显了该技术在规范不变变换中的有效性。此外，还比较了所提算法与威尔逊环谱流的生成效率，结果表明新方法更具优势。
原文摘要 · Abstract (English)
We present a progress report on the use of normalizing flows for generating gauge field configurations in pure SU(N) gauge theories. We discuss how the singular value decomposition can be used to construct gauge-invariant quantities, which serve as the building blocks for designing gauge-equivariant transformations of SU(N) gauge links. Using this novel approach, we build representative models for the SU(3) Wilson action on a \( 4^4 \) lattice with \( β= 1 \). We train these models and provide an analysis of their performance, highlighting the effectiveness of the new technique for gauge-invariant transformations. We also provide a comparison between the efficiency of the proposed algorithm and the spectral flow of Wilson loops.
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