标题： 真空凝聚在库仑分支上 显示英文标题

标题： Vacuum Condensates on the Coulomb Branch

摘要： 我们研究平面$\mathcal{N} = 4$超对称杨-米尔斯理论(SYM)的库仑分支上的关联函数，以及它们与可积性、算符乘积展开(OPE)、求和规则、大电荷展开和全息对应的联系。 首先，我们在弱耦合下计算任意标量算符的一点函数，并推导出一种紧凑的自旋链表示。 接下来，我们研究单环图中初态算符的两点函数，并发现位置空间中OPE的收敛半径是无限的。 我们基于这一发现估计了OPE数据的渐进行为。 最后，我们提出一个具体的非微扰公式，将库仑分支上的关联函数与共形点处大电荷插入的关联函数联系起来，并基于AdS中的大D3膜提供了一个全息解释。 该公式将已知的高电荷部分与秩-1理论的库仑分支之间的联系扩展到了大$N$极限。 显示英文摘要

摘要： We study correlation functions on the Coulomb branch of planar $\mathcal{N} = 4$ super-Yang- Mills theory (SYM), and their relationship with integrability, the operator product expansion (OPE), the sum rule, the large charge expansion, and holography. First, we compute one-point functions of arbitrary scalar operators at weak coupling and derive a compact spin-chain representation. We next study the two-point functions of chiral primaries at one loop and find that the radius of convergence of OPE in position space is infinite. We estimate the asymptotic growth of the OPE data based on this finding. Finally, we propose a concrete nonperturbative formula that connects the correlation functions on the Coulomb branch with the correlation functions with large charge insertions at the conformal point and provide a holographic interpretation based on a large D3-brane in AdS. The formula extends the known connection between the large charge sector and the Coulomb branch for rank-1 theories to the large $N$ limit.