AI 中文总结
研究4D \(\mathcal{N}=2\)超对称QCD混合真空中非阿贝尔弦，用盖奥托 - 古科夫 - 塞伯格方法推导其世界面理论的精确扭曲超势，实现二维扭结与四维受限单极子或夸克质量精确匹配，给出夸克/单极子禁闭物理图像。
AI 中文摘要
我们研究了具有规范群\(U(N)\)和\(N_f\)个夸克超多重态（\(N_f\geq N\)）的4D \(\mathcal{N}=2\)超对称QCD（SQCD）的\(r\)真空中的非阿贝尔弦，其中\(r\lt N\)（标量）夸克形成真空期望值。在量子水平上，规范群正交扇区中的\(N - r - 1\)个单极子也形成凝聚态。这导致了携带色电和色磁通量的磁通管（弦）的形成，分别限制夸克和单极子。我们给出了生活在这种非阿贝尔弦世界面上的二维有效理论的统一描述。特别地，我们使用预解式的盖奥托 - 古科夫 - 塞伯格方法，推导了世界面理论的精确扭曲超势，它因4D混合真空中非微扰胶微子凝聚的存在而变形。接下来，我们将世界面理论和4D SQCD（夸克真空已知）的BPS谱的二维 - 四维对应关系外推到混合真空。即，我们的关键结果是二维扭结质量与四维受限单极子或夸克质量之间的精确匹配。此外，我们提供了混合真空中夸克/单极子禁闭的物理图像。
英文摘要
We study non-Abelian strings supported in $r$-vacua of 4D $\mathcal{N}=2$ supersymmetric QCD (SQCD) with gauge group $U(N)$ and $N_f$ quark hypermultiplets ($N_f\ge N$), where $r<N$ (scalar) quarks develop vacuum expectation values. At the quantum level, $N-r-1$ monopoles in the orthogonal sector of the gauge group also form a condensate. This leads to the formation of flux tubes (strings) that carry both color-electric and color-magnetic fluxes and confine quarks and monopoles, respectively. We present a unified description of the 2D effective theory living on the world sheet of this non-Abelian string. In particular, we derive the exact twisted superpotential of the world sheet theory, which is deformed by the presence of non-perturbative gaugino condensate in 4D hybrid vacua, using the Gaiotto-Gukov-Seiberg method of resolvents. Next, we extrapolate the 2D-4D correspondence of BPS spectra of the world sheet theory and 4D SQCD (known for quark vacua) to hybrid vacua. Namely, our key result is the precise matching between the masses of the two-dimensional kinks and the four-dimensional confined monopoles or quarks. In addition, we provide a physical picture of the quark/monopole confinement in hybrid vacua.
Comments35+$\varepsilon$ pages, 8 figures
