Holographic and Localization Calculations of Boundary F for $\mathcal{N}=4$ SUSY Yang-Mills Theory

Abstract

$\mathcal{N}=4$ 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 $U(N)$ $\mathcal{N}=4$ 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 $\lambda$.

Reference added; minor typos corrected in Section 2.2 and equations (3.13), (3.14), (3.21), (3.23); terms rearranged in equation (4.19)

References in corpus (17)

• Towards a derivation of holographic entanglement entropy
• Holographic c-theorems in arbitrary dimensions
• Seeing a c-theorem with holography
• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• Exact half-BPS Type IIB interface solutions I: Local solution and supersymmetric Janus
• Gluon and Wilson loop TMDs for hadrons of spin $\le$ 1
• The g-theorem and quantum information theory
• Non-perturbative Defect One-Point Functions in Planar $\mathcal{N}=4$ Super-Yang-Mills
• CFT in AdS and boundary RG flows
• Irreversibility in quantum field theories with boundaries
• Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills
• Large N Free Energy of 3d N=4 SCFTs and AdS/CFT
• Boundary F-maximization
• Duality and Transport for Supersymmetric Graphene from the Hemisphere Partition Function
• Holographic Interpolation between $a$ and $F$
• Janus interface entropy and Calabi's diastasis in four-dimensional $\mathcal{N}=2$ superconformal field theories
• Algebras, traces, and boundary correlators in $\mathcal{N}=4$ SYM

Cited by in corpus (22)

• Islands and Page curves in 4d from Type IIB
• BCFT and Islands in Two Dimensions
• Cosmology from confinement?
• AdS/BCFT with Brane-Localized Scalar Field
• Brane Dynamics of Holographic BCFTs
• The Spectrum of Boundary States in Symmetric Orbifolds
• Electrostatic description of 3d $\mathcal{N}=4$ linear quivers
• Mapping out the internal space in AdS/BCFT with Wilson loops
• Finding $Ad{S}^5\times S^5$ in 2+1 dimensional SCFT physics
• Vacuum Transitions in Two-Dimensions and their Holographic Interpretation
• Giant graviton expansions and ETW brane
• Splitting interfaces in 4d $\mathcal{N}=4$ SYM
• Binary AdS black holes coupled to a bath in Type IIB
• Holographic boundary conformal field theory with $T\bar{T}$ deformation
• A new family of $Ad{S}_4$ S-folds in type IIB string theory
• Supersymmetric Graphene on Squashed Hemisphere
• Comparing top-down and bottom-up holographic defects and boundaries
• On the planar limit of 3d $T_{\rho }^{\sigma }[SU(N)]$
• Solving $\mathcal{N}=4$ SYM BCFT matrix models at large $N$
• One-point functions for doubly-holographic BCFTs and backreacting defects
• At the End of the World: Local Dynamical Cobordism
• Double holography in string theory