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 $\lambda$.

arXiv commentReference 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 (60)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• A Covariant Holographic Entanglement Entropy Proposal
• Entanglement entropy and conformal field theory
• Towards a derivation of holographic entanglement entropy
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• On Renormalization Group Flows in Four Dimensions
• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Locally Localized Gravity
• Holographic c-theorems in arbitrary dimensions
• Holographic Dual of BCFT
• Type IIB Superstrings, BPS Monopoles, And Three-Dimensional Gauge Dynamics
• Towards the F-Theorem: N=2 Field Theories on the Three-Sphere
• On the RG running of the entanglement entropy of a circle
• Seeing a c-theorem with holography
• Aspects of AdS/BCFT
• Supersymmetric Boundary Conditions in N=4 Super Yang-Mills Theory
• The Bootstrap Program for Boundary CFT_d
• Exact half-BPS Type IIB interface solutions I: Local solution and supersymmetric Janus
• Localization techniques in quantum field theories
• Conformal Field Theories Near a Boundary in General Dimensions
• On the Boundary Entropy of One-dimensional Quantum Systems at Low Temperature
• F-Theorem without Supersymmetry
• Exact half-BPS Type IIB interface solutions II: Flux solutions and multi-Janus
• Nonperturbative Tests of Three-Dimensional Dualities
• The Noncommutative Bion Core
• The Virtue of Defects in 4D Gauge Theories and 2D CFTs
• Gluon and Wilson loop TMDs for hadrons of spin $\le$ 1
• Holographic Duals of D=3 N=4 Superconformal Field Theories
• A Constraint on Defect and Boundary Renormalization Group Flows
• Central Charges for BCFTs and Holography
• Seiberg-Witten Theories on Ellipsoids
• The g-theorem and quantum information theory
• Holography, Entanglement Entropy, and Conformal Field Theories with Boundaries or Defects
• Localization of the four-dimensional N=4 SYM to a two-sphere and 1/8 BPS Wilson loops
• Exact Results for 't Hooft Loops in Gauge Theories on S^4
• Towards a $C$-theorem in defect CFT
• Chern-Simons terms and the Three Notions of Charge
• Universal Entanglement and Boundary Geometry in Conformal Field Theory
• On Holographic Defect Entropy
• Near-horizon solutions for D3-branes ending on 5-branes
• Exact Results in Supersymmetric Field Theories on Manifolds with Boundaries
• An Analytic Approach to BCFT${}_d$
• 3d Partition Function as Overlap of Wavefunctions
• 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
• CFT in AdS and boundary RG flows
• Irreversibility in quantum field theories with boundaries
• Holographic RG Flow on the Defect and g-Theorem
• Anomalies, entropy and boundaries
• Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills
• Large N Free Energy of 3d N=4 SCFTs and AdS/CFT
• N=2 gauge theories on the hemisphere $H{S}^4$
• Boundary F-maximization
• Wilson Surface Central Charge from Holographic Entanglement Entropy
• N=2 SUSY gauge theories on S^4
• 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

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