Large N Free Energy of 3d N=4 SCFTs and AdS/CFT

Abstract

We provide a non-trivial check of the AdS_4/CFT_3 correspondence recently proposed in arXiv:1106.4253 by verifying the GKPW relation in the large N limit. The CFT free energy is obtained from the previous works (arXiv:1105.2551, arXiv:1105.4390) on the S^3 partition function for 3-dimensional N=4 SCFT T[SU(N)]. This is matched with the computation of the type IIB action on the corresponding gravity background. We unexpectedly find that the leading behavior of the free energy at large N is 1/2 N^2 ln N. We also extend our results to richer theories and argue that 1/2 N^2 ln N is the maximal free energy at large N in this class of gauge theories.

arXiv comment20 pages, 3 figures

References in corpus (27)

• Gauge Theory Correlators from Non-Critical String Theory
• A Stress Tensor for Anti-de Sitter Gravity
• Hierarchies from Fluxes in String Compactifications
• The Holographic Weyl anomaly
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• N=2 dualities
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Mirror Symmetry in Three Dimensional Gauge Theories
• Surface Terms as Counterterms in the AdS/CFT Correspondence
• Towards the F-Theorem: N=2 Field Theories on the Three-Sphere
• The Exact Superconformal R-Symmetry Extremizes Z
• From weak to strong coupling in ABJM 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
• Mirrors of 3d Sicilian theories
• The Virtue of Defects in 4D Gauge Theories and 2D CFTs
• SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
• Holographic Duals of D=3 N=4 Superconformal Field Theories
• Spin-2 spectrum of defect theories
• Near-horizon solutions for D3-branes ending on 5-branes
• From Necklace Quivers to the F-theorem, Operator Counting, and T(U(N))
• 3d Partition Function as Overlap of Wavefunctions
• 3D-partition functions on the sphere: exact evaluation and mirror symmetry
• AGT on the S-duality Wall
• Semiclassical Analysis of the 3d/3d Relation
• Chern-Simons Theory and S-duality

Cited by in corpus (28)

• Islands and Page curves in 4d from Type IIB
• On Holographic Defect Entropy
• T^σ_ρ(G) Theories and Their Hilbert Series
• Three-dimensional N=4 Linear Quivers and non-Abelian T-duals
• Holographic duals of 3d S-fold CFTs
• IIB Duals of D=3 N=4 Circular Quivers
• Massive Anti-de Sitter Gravity from String Theory
• Quantum Gates to other Universes
• Aspects of Defects in 3d-3d Correspondence
• The F-Theorem and F-Maximization
• Holographic and Localization Calculations of Boundary F for $\mathcal{N}=4$ SUSY Yang-Mills Theory
• The Spectrum of Boundary States in Symmetric Orbifolds
• Quantum Phase Transitions in Mass-Deformed ABJM Matrix Model
• Mapping out the internal space in AdS/BCFT with Wilson loops
• New 3d $\mathcal{N}=2$ SCFT's with $N^{3/2}$ scaling
• Matrix Models and Holography: Mass Deformations of Long Quiver Theories in 5d and 3d
• Topologically twisted index of $T[SU(N)]$ at large $N$
• Taming Supersymmetric Defects in 3d-3d Correspondence
• Linear Quivers at Large-$N$
• Janus interface entropy and Calabi's diastasis in four-dimensional $\mathcal{N}=2$ superconformal field theories
• Resolved gravity duals of $\mathcal{N}=4$ quiver field theories in 2+1 dimensions
• Wilson loops and free energies in $3d$ $\mathcal{N}=4$ SYM: exact results, exponential asymptotics and duality
• S-folds and $Ad{S}_3$ flows from the D3-brane
• Holographic Duality for three-dimensional Super-conformal Field Theories
• On the planar limit of 3d $T_{\rho }^{\sigma }[SU(N)]$
• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview
• Double holography in string theory
• Near Horizon Geometry of Strings Ending on Intersecting D8/D4-branes