近日，美国弗吉尼亚理工大学Pinak Banerjee团队研究了扭曲等变协同伦中M5膜上的规范势。2025年12月22日出版的《高能物理杂志》发表了这项成果。
研究组对Sati-Schreiber方案中关于C-场通量密度的讨论进行了一些拓展。首先，阐释了对场内容进行全局完备化的必要性：包括十一维超引力中单个M5膜世界体上的通量、规范势与规范变换，以及这些内容如何通过通量量子化律的选择进行编码。
假设H成立——即M理论中的4-通量在被称为4-上同伦的非阿贝尔上同调理论中量子化，而M5膜世界体上的三通量在（扭）3-上同伦中量子化——研究组将文献中已知的部分计算推广至包含背景引力的扭曲情形以及M5膜置于轨形上的情况。最终证明，在上同伦荷化通量的情形中，零同痕通过满射给出传统规范势；而在切向上同伦、旋量上同伦及等变旋量上同伦情形中，同痕的零同痕通过满射给出相应的规范变换。研究组针对这些情形显式构造了满射，并验证了其与相应Bianchi恒等式的一致性关系。
由此，研究组揭示了弯曲时空与轨形上M5膜世界体的局部规范势传统公式如何由上同伦理论重新导出，并因此能够在上同伦荷量子化框架中实现全局完备化。
附：英文原文
Title: Gauge potentials on the M5 brane in twisted equivariant cohomotopy
Author: Banerjee, Pinak
Issue&Volume: 2025-12-22
Abstract:
In this article, we work out some variations on the discussion of the C-field flux densities in the Sati-Schreiber program. We start by explaining the need for global completion of the field content: the fluxes, the gauge potentials and the gauge transformations on the worldvolume of a single M5 brane in eleven-dimensional supergravity, and how this is encoded by the choice of flux quantization law.
Assuming Hypothesis H that the 4-flux in M-Theory is flux quantized in a non-abelian cohomology theory called 4-cohomotopy, and the three-flux on the M5 brane worldvolume in (twisted) 3-cohomotopy, we generalize some previous calculations known in the literature to include twisting by background gravity and placing M5 branes on orbifolds. We show that the null concordances of cohomotopically charged fluxes give rise to the traditional gauge potentials and the null concordances of concordances give rise to the corresponding gauge transformations via surjections, in the cases of tangentially twisted cohomotopy, twistorial cohomotopy and equivariant twistorial cohomotopy. We construct the surjections explicitly for these cases and check the consistency relations with the corresponding Bianchi identities.
Thus, we show how the traditional formulas for the local gauge potentials on M5 brane worldvolume on curved spacetimes and orbifolds are indeed reproduced by the homotopy theory and, as such, become amenable to global completion in cohomotopical charge quantization.
DOI: 10.1007/JHEP12(2025)162
Source: https://link.springer.com/article/10.1007/JHEP12(2025)162