Solving $\mathcal{N}=4$ SYM BCFT matrix models at large $N$

Abstract

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 $\mathrm{Ad}{\mathrm{S}}_4\times {\mathrm{S}}^2\times {\mathrm{S}}^2\times \mathrm{\Sigma }$ geometry and provide precision tests of the dualities.

19 pages, 6 figures; v2: published version

References in corpus (30)

• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Locally Localized Gravity
• Open and Closed String Interpretation of SUSY CFT's on Branes with Boundaries
• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Exact half-BPS Type IIB interface solutions I: Local solution and supersymmetric Janus
• Exact half-BPS Type IIB interface solutions II: Flux solutions and multi-Janus
• Nonperturbative Tests of Three-Dimensional Dualities
• Holographic Duals of D=3 N=4 Superconformal Field Theories
• Islands and Page curves in 4d from Type IIB
• On Holographic Defect Entropy
• Near-horizon solutions for D3-branes ending on 5-branes
• 3D-partition functions on the sphere: exact evaluation and mirror symmetry
• Non-perturbative Defect One-Point Functions in Planar $\mathcal{N}=4$ Super-Yang-Mills
• Exact results for 5d SCFTs of long quiver type
• IIB Duals of D=3 N=4 Circular Quivers
• Precision test of AdS${}_6$/CFT${}_5$ in Type IIB
• Spectral curves, emergent geometry, and bubbling solutions for Wilson loops
• Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills
• Holographic and Localization Calculations of Boundary F for $\mathcal{N}=4$ SUSY Yang-Mills Theory
• N=2 gauge theories on the hemisphere $H{S}^4$
• Wilson loops in 5d long quiver gauge theories
• Electrostatic description of 3d $\mathcal{N}=4$ linear quivers
• Mapping out the internal space in AdS/BCFT with Wilson loops
• Matrix Models and Holography: Mass Deformations of Long Quiver Theories in 5d and 3d
• Duality and Transport for Supersymmetric Graphene from the Hemisphere Partition Function
• Topologically twisted index of $T[SU(N)]$ at large $N$
• Wilson loops for 5d and 3d conformal linear quivers
• Splitting interfaces in 4d $\mathcal{N}=4$ SYM
• Binary AdS black holes coupled to a bath in Type IIB

Cited by in corpus (1)

• One-point functions for doubly-holographic BCFTs and backreacting defects