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arXiv 1608.05331hep-thmath-phmath.MP
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杨-米尔斯理论的超弦极限

Superstring limit of Yang-Mills theories

Olaf Lechtenfeld, Alexander D. Popov

备注：
1+11 pages, v2: minor corrections
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摘要：

Shifman和Yung指出，$X^{10}={\mathbb R}^4\times Y^6$上的临界超弦（其中$Y^6$是可分解的锥状结构）是一个有效的理论，可以用来描述定义在$Σ_2\times{\mathbb R}^2$上的具有四个基本Higgs标量的U（2）Yang-Mills-Higgs系统，其中$Σ_2$是一个二维洛伦兹流形.他们的Yang-Mills模型支持具有模空间$X^{10}$的${\mathbb R}^2\subsetΣ_2\times{\mathbb R}^2$上的半局部涡。当缓慢运动薄涡的模量依赖于$Σ_2$坐标时，涡弦可以用临界基本弦来识别。我们证明了在$Σ_2\times T^2_p$上的纯Yang-Mills理论的低能极限下也可以得到类似的结果，其中$T^2_p$是一个带有一个穿刺$p$的二维环面.然后，Shifman和Yung的孤立子涡旋被平坦连接所取代。各种十维超弦目标空间可以作为$T^2_p$上平坦联络的模空间得到，这取决于规范群的选择。完整的格林-施瓦兹西格玛模型需要将规范群扩展到一个超群，并用拓扑项增加作用量。

英文摘要：

It was pointed out by Shifman and Yung that the critical superstring on $X^{10}={\mathbb R}^4\times Y^6$, where $Y^6$ is the resolved conifold, appears as an effective theory for a U(2) Yang-Mills-Higgs system with four fundamental Higgs scalars defined on $Σ_2\times{\mathbb R}^2$, where $Σ_2$ is a two-dimensional Lorentzian manifold. Their Yang-Mills model supports semilocal vortices on ${\mathbb R}^2\subsetΣ_2\times{\mathbb R}^2$ with a moduli space $X^{10}$. When the moduli of slowly moving thin vortices depend on the coordinates of $Σ_2$, the vortex strings can be identified with critical fundamental strings. We show that similar results can be obtained for the low-energy limit of pure Yang-Mills theory on $Σ_2\times T^2_p$, where $T^2_p$ is a two-dimensional torus with a puncture $p$. The solitonic vortices of Shifman and Yung then get replaced by flat connections. Various ten-dimensional superstring target spaces can be obtained as moduli spaces of flat connections on $T^2_p$, depending on the choice of the gauge group. The full Green-Schwarz sigma model requires extending the gauge group to a supergroup and augmenting the action with a topological term.

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