论文标题
$ {\ cal n} = 4 $ susy yang-mills理论的边界F的全息和本地化计算
Holographic and Localization Calculations of Boundary F for ${\cal N} = 4$ SUSY Yang-Mills Theory
论文作者
论文摘要
$ {\ cal n} = 4 $ supersymmetric yang-mills（sym）理论可以在半空间上定义，并具有各种边界条件，可保留尺度不变性，而原始超对称性的一半则可以定义；具有相同对称性的更通用的理论可以通过在边界处耦合到3D SCFT来获得。这些理论中的每一个都以称为“边界$ f $”的数量为特征，该数量猜想在边界重归化组流量下降低。在本文中，我们计算了$ u（n）$ $ {\ cal n} = 4 $ sym理论的边界$ f $，其弦理论结构最为通用的半匹马对称边界条件，其弦理论构造的d3-布兰是D5-branes和/或ns5-branes的收集。我们首先通过使用双型IIB超级实力溶液中的Ryu-takayanagi公式评估在边界上以半球为中心的半球的纠缠熵来进行计算全息。对于仅在D5 Branes上终止的D3-branes或NS5-Branes的边界条件，我们还通过使用超对称定位来评估半球分区函数来计算边界$ f $。超级$ n $的主要术语和本地化结果完全符合t'hooft耦合$λ$的函数。
${\cal N} = 4$ Supersymmetric Yang-Mills (SYM) theory can be defined on a half-space with a variety of boundary conditions preserving scale invariance and half of the original supersymmetry; more general theories with the same symmetry can be obtained by coupling to a 3D SCFT at the boundary. Each of these theories is characterized by a quantity called "boundary $F$", conjectured to decrease under boundary renormalization group flows. In this paper, we calculate boundary $F$ for $U(N)$ ${\cal N} = 4$ SYM theory with the most general half-supersymmetric boundary conditions arising from string theory constructions with D3-branes ending on collections of D5-branes and/or NS5-branes. We first perform the calculation holographically by evaluating the entanglement entropy for a half-ball centered on the boundary using the Ryu-Takayanagi formula in the dual type IIB supergravity solutions. For boundary conditions associated with D3-branes ending on D5 branes only or NS5-branes only, we also calculate boundary $F$ exactly by evaluating the hemisphere partition function using supersymmetric localization. The leading term at large $N$ in the supergravity and localization results agree exactly as a function of the t' Hooft coupling $λ$.
