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arXiv 2008.01507math-phhep-thmath.MPnucl-th
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无质量规范玻色子情况下的弯曲杨-米尔斯-希格斯规范理论

Curved Yang-Mills-Higgs gauge theories in the case of massless gauge bosons

Simon-Raphael Fischer

备注：
36 pages (including title page and five pages of the appendix)
发表信息：
Journal of Geometry and Physics 162 (2021) 104104
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摘要：

阿列克谢·科托夫（Alexei Kotov）和托马斯·斯特罗布尔（Thomas Strobl）引入了杨-米尔斯-希格斯规范理论的协变公式，其主要动机是用李代数胚取代李代数。这允许在场强中引入附加的2-形式$ζ$之后，在该束上引入可能的非平坦连接$\nabla$。我们将在李代数丛的简化情况下研究这个理论，因此，只有无质量的规范玻色子，我们将提供$ζ$的物理动机。此外，我们分类$\nabla$使用规范不变性，导致$\nabla$需要是一个李导子律覆盖配对$Ξ$，介绍了麦肯齐。还有一个场的重新定义，保持物理不变，但可能改变$ζ$和$\nabla$的曲率。我们将研究这是否可以导致一个经典理论，我们将意识到，这与麦肯齐关于用李代数丛扩展李代数胚的研究有很强的对应性。我们表明，麦肯齐的障碍类也是一个障碍，有非平面连接，这是不相关的平面连接使用字段的重新定义。这一类是相关的$\mathrm{d}^\nabla ζ$，张量，也衡量失败的Bianchi恒等式的场强和不变的领域下重新定义。这个张量还将提供关于$ζ$在字段重定义后是否可以消失的提示。

英文摘要：

Alexei Kotov and Thomas Strobl have introduced a covariantized formulation of Yang-Mills-Higgs gauge theories whose main motivation was to replace the Lie algebra with Lie algebroids. This allows the introduction of a possibly non-flat connection $\nabla$ on this bundle, after also introducing an additional 2-form $ζ$ in the field strength. We will study this theory in the simplified situation of Lie algebra bundles, hence, only massless gauge bosons, and we will provide a physical motivation of $ζ$. Moreover, we classify $\nabla$ using the gauge invariance, resulting into that $\nabla$ needs to be a Lie derivation law covering a pairing $Ξ$, as introduced by Mackenzie. There is also a field redefinition, keeping the physics invariant, but possibly changing $ζ$ and the curvature of $\nabla$. We are going to study whether this can lead to a classical theory, and we will realize that this has a strong correspondence to Mackenzie's study about extending Lie algebroids with Lie algebra bundles. We show that Mackenzie's obstruction class is also an obstruction for having non-flat connections which are not related to a flat connection using the field redefinitions. This class is related to $\mathrm{d}^\nabla ζ$, a tensor which also measures the failure of the Bianchi identity of the field strength and which is invariant under the field redefinition. This tensor will also provide hints about whether $ζ$ can vanish after a field redefinition.

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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