论文标题
量子几何形状和$θ$ - 角五维超级阳米尔斯
Quantum Geometry and $θ$-Angle in Five-Dimensional Super Yang-Mills
论文作者
论文摘要
五维$ sp（n）$ supersymmetric yang-mills承认$ \ mathbb {z} _2 $版本的theta angle $θ$。在本说明中，我们将$ \ MATHCAL {n} = 1 $ $ sp（1）$ gauge理论$θ=π$的seiberg-witten几何形状进行了双重量化，在歧管$ s^1 \ times \ times \ times \ mathbb {r}^4 $上。至关重要的是，$ \ mathbb {r}^4 $放置在$ω$ - background上，这提供了两个参数来量化几何形状。从物理上讲，我们正在计算1/2-bps基本的威尔逊循环的情况下，它们都包装了$ s^1 $。从数学上讲，这相当于证明$ qq $ - 字符的规律性，用于量子Aggine代数$ u_q（\ widehat {a_1}）$的spin-1/2表示，由于$θ$ - 角，有一定的转折。我们从两个不同的字符串理论图片中激发了这些结果。首先，在类型IIB中的$（P，Q）$ - Web设置中，该循环以D3 Brane为特征。其次，在类型的I'字符串设置中，该循环的特征是D4 Brane受到方向投影的约束。我们在$ n> 1 $时对更高排名$ sp（n）$的概括以及Chern-Simons级别的$ su（n）$理论评论，当$ n> 2 $时。
Five-dimensional $Sp(N)$ supersymmetric Yang-Mills admits a $\mathbb{Z}_2$ version of a theta angle $θ$. In this note, we derive a double quantization of the Seiberg-Witten geometry of $\mathcal{N}=1$ $Sp(1)$ gauge theory at $θ=π$, on the manifold $S^1\times\mathbb{R}^4$. Crucially, $\mathbb{R}^4$ is placed on the $Ω$-background, which provides the two parameters to quantize the geometry. Physically, we are counting instantons in the presence of a 1/2-BPS fundamental Wilson loop, both of which are wrapping $S^1$. Mathematically, this amounts to proving the regularity of a $qq$-character for the spin-1/2 representation of the quantum affine algebra $U_q(\widehat{A_1})$, with a certain twist due to the $θ$-angle. We motivate these results from two distinct string theory pictures. First, in a $(p,q)$-web setup in type IIB, where the loop is characterized by a D3 brane. Second, in a type I' string setup, where the loop is characterized by a D4 brane subject to an orientifold projection. We comment on the generalizations to the higher rank case $Sp(N)$ when $N>1$, and the $SU(N)$ theory at Chern-Simons level $κ$ when $N>2$.
