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arXiv 2408.16554hep-thmath-phmath.MPnlin.SI
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四维Wess-Zumino-Witten模型中的孤子——迈向可积系统的统一——

Solitons in 4d Wess-Zumino-Witten models -- Towards unification of integrable systems --

Masashi Hamanaka, Shan-Chi Huang

备注：
19 pages, 2 figures; typos corrected, references added, version to appear in Proceedings of the OCNMP-2024 Conference: Bad Ems, 23-29 June 2024
发表信息：
Open Communications in Nonlinear Mathematical Physics, Proceedings: OCNMP Conference, Bad Ems (Germany), 23-29 June 2024 (September 27, 2024) ocnmp:14167
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AI总结：

本文在可积系统统一理论框架下构造了4dWZW模型的孤子解，发现其表现为KP型孤子墙，并指出这些解对应开N=2弦理论中的新型物理对象。

摘要：

我们在与4维/6维Chern-Simons理论相关的可积系统统一理论框架下，构造了四维Wess-Zumino-Witten（4dWZW）模型的孤子解。我们计算了解的作用量密度，发现这些孤子解表现为KP型孤子，即单孤子解在四维空间中的一个三维超平面上具有局域化的作用量/能量密度（孤子墙），而n孤子解描述n个具有相移的相交孤子墙。我们注意到Ward猜想在分裂号差(+,+,-,-)下基本成立。此外，4dWZW模型描述了具有分裂号差的四维时空中开N=2弦理论的弦场论作用量，因此我们的孤子解将描述N=2弦理论中一类新型物理对象。我们还讨论了4dWZW模型中的瞬子解。同时讨论了可积系统统一理论的非对易推广和量子化。

英文摘要：

We construct soliton solutions of the four-dimensional Wess-Zumino-Witten (4dWZW) model in the context of a unified theory of integrable systems with relation to the 4d/6d Chern-Simons theory. We calculate the action density of the solutions and find that the soliton solutions behave as the KP-type solitons, that is, the one-soliton solution has a localized action/energy density on a 3d hyperplane in 4-dimensions (soliton wall) and the n-soliton solution describes n intersecting soliton walls with phase shifts. We note that the Ward conjecture holds mostly in the split signature (+,+,-,-). Furthermore, the 4dWZW model describes the string field theory action of the open N=2 string theory in the four-dimensional space-time with the split signature and hence our soliton solutions would describe a new-type of physical objects in the N=2 string theory. We discuss instanton solutions in the 4dWZW model as well. Noncommutative extension and quantization of the unified theory of integrable systems are also discussed.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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