论文标题
$ {\ cal n} = 4 $ super-yang-mills理论的双重性全息图
The holography of duality in ${\cal N}=4$ Super-Yang-Mills theory
论文作者
论文摘要
$ {\ cal n} = 4 $ supersymmetric yang-mills理论的空间表现出复杂的全局一式单体对称性和$ sl（2，\ mathbb {z}）$ duality orbits的结构。在本文中，我们从全息双型IIB字符串理论的角度研究了这种结构。 Witten的概括，我们根据规格代数$ SU（n）$，$ SO（N）$和$ sp（n）$绘制不同的理论，以选择散装量规场上的边界条件。我们展示了全息图中产生的单一形式对称性及其异常以及量规理论的二元性能。在此过程中，我们证明了$ su（n）$理论的差异$ sl（2，\ mathbb {z}）$ duality Orbits的数量由$ n $的平方除数给出。
The space of ${\cal N}=4$ supersymmetric Yang-Mills theories exhibits an intricate structure of global one-form symmetries and $SL(2,\mathbb{Z})$ duality orbits. In this paper we study this structure from the point of view of the holographic dual Type IIB string theory. Generalizing work by Witten, we map the different theories based on the gauge algebras $su(N)$, $so(N)$, and $sp(N)$ to a choice of boundary conditions on bulk gauge fields. We show how the one-form symmetries and their anomalies, as well as the duality properties of the gauge theories, arise in the holographic picture. Along the way we prove that the number of disjoint $SL(2,\mathbb{Z})$ duality orbits for the $su(N)$ theories is given by the number of square divisors of $N$.
