Bootstrapping Mixed Correlators in 4D $\mathcal{N}=1$ SCFTs

Abstract

The numerical conformal bootstrap is used to study mixed correlators in $\mathcal{N}=1$ superconformal field theories (SCFTs) in $d=4$ spacetime dimensions. Systems of four-point functions involving scalar chiral and real operators are analyzed, including the case where the scalar real operator is the zero component of a global conserved current multiplet. New results on superconformal blocks as well as universal constraints on the space of 4D $\mathcal{N}=1$ SCFTs with chiral operators are presented. At the level of precision used, the conditions under which the putative "minimal" 4D $\mathcal{N}=1$ SCFT may be isolated into a disconnected allowed region remain elusive. Nevertheless, new features of the bounds are found that provide further evidence for the presence of a special solution to crossing symmetry corresponding to the "minimal" 4D $\mathcal{N}=1$ SCFT.

arXiv comment33 pages, 12 figures; v2: Some typos fixed

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• Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey
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• Casimir recursion relations for general conformal blocks
• The M-theory Archipelago
• Long Multiplet Bootstrap
• Defect $a$-Theorem and $a$-Maximization
• Scaling the semidefinite program solver SDPB
• Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory
• Mixed Scalar-Current bootstrap in three dimensions
• New Methods for Conformal Correlation Functions
• Bootstrapping traceless symmetric $O(N)$ scalars
• Superconformal Blocks: General Theory
• blocks_3d: Software for general 3d conformal blocks
• Exploring $SU(N)$ adjoint correlators in $3d$
• Superconformal Blocks for Mixed 1/2-BPS Correlators with $SU(2)$ R-symmetry
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• Differential operators for superconformal correlation functions
• An Automated Generation of Bootstrap Equations for Numerical Study of Critical Phenomena
• Critical Wess-Zumino models with four supercharges from the functional renormalization group
• R-current three-point functions in 4d $\mathcal{N}=1$ superconformal theories
• Bounds on Triangle Anomalies in (3+1)d
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• Analytic Studies of Fermions in the Conformal Bootstrap