Bootstrapping $\mathcal{N}=3$ superconformal theories

Abstract

We initiate the bootstrap program for $\mathcal{N}=3$ superconformal field theories (SCFTs) in four dimensions. The problem is considered from two fronts: the protected subsector described by a $2d$ chiral algebra, and crossing symmetry for half-BPS operators whose superconformal primaries parametrize the Coulomb branch of $\mathcal{N}=3$ theories. With the goal of describing a protected subsector of a family of $\mathcal{N}=3$ SCFTs, we propose a new $2d$ chiral algebra with super Virasoro symmetry that depends on an arbitrary parameter, identified with the central charge of the theory. Turning to the crossing equations, we work out the superconformal block expansion and apply standard numerical bootstrap techniques in order to constrain the CFT data. We obtain bounds valid for any theory but also, thanks to input from the chiral algebra results, we are able to exclude solutions with $\mathcal{N}=4$ supersymmetry, allowing us to zoom in on a specific $\mathcal{N}=3$ SCFT.

54 pages (43 plus five appendices), 7 figures; v2: improvements for clarity

References in corpus (10)

• The 4d Superconformal Index from q-deformed 2d Yang-Mills
• Bounds on 4D Conformal and Superconformal Field Theories
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
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• Constraints on Chiral Operators in N=2 SCFTs
• Notes on S-folds and $\mathcal{N}=3$ theories
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• A slow review of the AGT correspondence
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• Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory
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• Inverse Bootstrapping Conformal Field Theories
• New Methods for Conformal Correlation Functions
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• Schur sector of Argyres-Douglas theory and $W$-algebra
• On the chiral algebra of Argyres-Douglas theories and S-duality
• Superconformal Blocks for SCFTs with Eight Supercharges
• An N=1 Lagrangian for an N=3 SCFT
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• The Chiral Algebra of Genus Two Class $\mathcal{S}$ Theory
• Holographic S-fold theories at one loop
• Bootstrapping (D, D) Conformal Matter
• Notes on $n$-point Witten diagrams in AdS${}_2$
• Higher derivative invariants in four dimensional N=3 Poincare supergravity
• Macdonald Indices for Four-dimensional $\mathcal{N}=3$ Theories
• Exceptional moduli spaces for exceptional $\mathcal{N}=3$ theories
• Towards general super Casimir equations for $4D$ $\mathcal{N}=1$ SCFTs
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• Harmonic Analysis in d-dimensional Superconformal Field Theory
• Crossing Symmetry for Long Multiplets in 4D $\mathcal{N}=1$ SCFTs
• Four-dimensional $N=1$ theories, S-fold constraints on T-branes, and behaviors in IR and UV
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