标题： 求解大$N$时的$\mathcal N=4$对称边界共形场论矩阵模型 显示英文标题

标题： Solving $\mathcal N=4$ SYM BCFT matrix models at large $N$

摘要： 许多在4d$\mathcal N=4$SYM中具有Gaiotto-Witten边界条件的可观测量可以通过超对称局域化精确地用矩阵模型描述。 边界通常通过边界上的规范对称性降低或作为显式的边界自由度引入新的自由度，从而导致非平凡的矩阵模型。 我们推导出在大$N$时主导这些矩阵模型的鞍点，这些鞍点用广义Lambert W函数表示。 在弦理论中，BCFTs由终止在D5和NS5膜上的D3膜实现。 我们独立地从具有$\rm AdS_4\times S^2\times S^2\times\Sigma$几何结构的全息对偶中推导出这些鞍点，并提供了对偶性的精确测试。 显示英文摘要

摘要： Many observables in 4d $\mathcal N=4$ SYM with Gaiotto-Witten boundary conditions can be described exactly by matrix models via supersymmetric localization. The boundaries typically introduce new degrees of freedom, through a reduction of the gauge symmetry on the boundary or as explicit boundary degrees of freedom, leading to non-trivial matrix models. We derive the saddle points dominating these matrix models at large $N$, expressed in terms of generalized Lambert W-functions. In string theory the BCFTs are realized by D3-branes ending on D5 and NS5 branes. We independently derive the saddle points from the holographic duals with $\rm AdS_4\times S^2\times S^2\times\Sigma$ geometry and provide precision tests of the dualities.