Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey

Abstract

We combine supersymmetric localization and the conformal bootstrap to study five-dimensional superconformal field theories. To begin, we classify the admissible counter-terms and derive a general relation between the five-sphere partition function and the conformal and flavor central charges. Along the way, we discover a new superconformal anomaly in five dimensions. We then propose a precise triple factorization formula for the five-sphere partition function, that incorporates instantons and is consistent with flavor symmetry enhancement. We numerically evaluate the central charges for the rank-one Seiberg and Morrison-Seiberg theories, and find strong evidence for their saturation of bootstrap bounds, thereby determining the spectra of long multiplets in these theories. Lastly, our results provide new evidence for the $F$-theorem and possibly a $C$-theorem in five-dimensional superconformal theories.

90 pages, 12 figures, 11 tables; v2: references added; v3: minor corrections

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• Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective
• Gluon Scattering in AdS from CFT
• Solving M-theory with the Conformal Bootstrap
• 5d Partition Functions with A Twist
• Exact results for 5d SCFTs of long quiver type
• Precision test of AdS${}_6$/CFT${}_5$ in Type IIB
• The M-theory Archipelago
• Instantons, Symmetries and Anomalies in Five Dimensions
• One-loop Gluon Amplitudes in AdS
• Defect $a$-Theorem and $a$-Maximization
• Searching for gauge theories with the conformal bootstrap
• Romans Supergravity from Five-Dimensional Holograms
• Massive spin 2 excitations in $Ad{S}_6\times S^2$ warped spacetimes
• Black hole microstate counting in Type IIB from 5d SCFTs
• On Mellin Amplitudes in SCFTs with Eight Supercharges
• Wilson loops in 5d $\mathcal{N}=1$ theories and S-duality
• Chern-Simons theory from M5-branes and calibrated M2-branes
• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• The unitary subsector of generalized minimal models
• Evidence for a 5d F-theorem
• Superconformal Blocks for Mixed 1/2-BPS Correlators with $SU(2)$ R-symmetry
• The 5d Superconformal Index at Large $N$ and Black Holes
• Bootstrapping Coulomb and Higgs branch operators
• Matrix Models and Holography: Mass Deformations of Long Quiver Theories in 5d and 3d
• 2d small N=4 Long-multiplet superconformal block
• 3d N=4 Bootstrap and Mirror Symmetry
• The topological line of ABJ(M) theory
• SYM on Quotients of Spheres and Complex Projective Spaces
• Phases of five-dimensional supersymmetric gauge theories
• 3d defects in 5d: RG flows and defect F-maximization
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• Free Energy on the Sphere for Non-Abelian Gauge Theories
• Generalized quotients and holographic duals for 5d S-fold SCFTs
• Bootstrapping (D, D) Conformal Matter
• Anomaly Matching Across Dimensions and Supersymmetric Cardy Formulae
• Compactifying 5d superconformal field theories to 3d
• Seven-dimensional super Yang-Mills at negative coupling
• $c$-functions in Higher-derivative Flows Across Dimensions
• Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows
• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview