Solving N $$ \mathcal{N} $$ = 4 SYM BCFT matrix models at large N - Dongming He; Christoph F. Uhlemann (Journal of High Energy Physics)
Abstract Many observables in 4d N $$ \mathcal{N} $$ = 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 AdS4×S2×S2×Σ geometry and provide precision tests of the dualities.