Current OPEs in Superconformal Theories

Abstract

It's well known that in conformal theories the two- and three-point functions of a subset of the local operators-the conformal primaries-suffice, via the operator product expansion (OPE), to determine all local correlation functions of operators. It's less well known that, in superconformal theories, the OPE of superdescendants is generally undetermined from those of the superprimaries, and there is no universal notion of superconformal blocks. We recall these and related aspects of 4d (S)CFTs, and then we focus on the super operator product expansion (sOPE) of conserved currents in 4d N=1 SCFTs. The current-current OPE J(x)J(0) has applications to general gauge mediation. We show how superconformal symmetry, when combined with current conservation, determines the OPE coefficients of superconformal descendants in terms of those of the superconformal primaries. We show that only integer-spin real superconformal primary operators of vanishing R-charge, and their descendants, appear in the sOPE. We also discuss superconformal blocks for four-point functions of the conserved currents.

37 pages, 1 figure. Corrected some formulas, added references

References in corpus (8)

• General Gauge Mediation
• Bounds on 4D Conformal and Superconformal Field Theories
• Bounds in 4D Conformal Field Theories with Global Symmetry
• Supercurrents and Brane Currents in Diverse Dimensions
• More Visible Effects of the Hidden Sector
• A hidden solution to the mu/B_mu problem in gauge mediation
• Superconformally Covariant OPE and General Gauge Mediation
• Simple Models of Superconformal Flavor

Cited by in corpus (42)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Projectors, Shadows, and Conformal Blocks
• Spinning Conformal Blocks
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Carving Out the Space of 4D CFTs
• Improved bounds for CFT's with global symmetries
• Stress-tensor OPE in N=2 Superconformal Theories
• Bounds on $\mathcal{N}=1$ Superconformal Theories with Global Symmetries
• Conformal Collider Physics from the Lightcone Bootstrap
• Bootstrapping $\mathcal{N}=3$ superconformal theories
• Covariant Approaches to Superconformal Blocks
• $\mathcal{N}=1$ Superconformal Blocks for General Scalar Operators
• Constraints on Chiral Operators in N=2 SCFTs
• Analytic bootstrap and Witten diagrams for the ABJM Wilson line as defect CFT${}_1$
• Bootstrapping Mixed Correlators in 4D $\mathcal{N}=1$ SCFTs
• Long Multiplet Bootstrap
• Superembedding methods for 4d N=1 SCFTs
• Holographic Correlators for General Gauge Mediation
• Bootstrapping line defects in $\mathcal{N}=2$ theories
• Superembedding Methods for Current Superfields
• Exploring the Minimal 4D $\mathcal{N}=1$ SCFT
• Celestial superamplitude in $\mathcal{N}=4$ SYM theory
• Superconformal Blocks: General Theory
• Two-point functions of conformal primary operators in $\mathcal{N}=1$ superconformal theories
• Quantum Integrable Systems from Conformal Blocks
• Superconformally Covariant OPE and General Gauge Mediation
• The Epsilon-Expansion from Conformal Field Theory
• Differential operators for superconformal correlation functions
• Bootstrapping Coulomb and Higgs branch operators
• OPE Selection Rules for Schur Multiplets in 4D $\mathcal{N}=2$ Superconformal Field Theories
• $\mathcal{N}=(1,0)$ Anomaly Multiplet Relations in Six Dimensions
• S and T for SCFTs
• R-current three-point functions in 4d $\mathcal{N}=1$ superconformal theories
• Bounds on Triangle Anomalies in (3+1)d
• OPE Methods for the Holomorphic Higgs Portal
• Towards general super Casimir equations for $4D$ $\mathcal{N}=1$ SCFTs
• Field-theoretic Methods in Strongly-Coupled Models of General Gauge Mediation
• Relevant deformations and c-extremization
• Superconformal Partial Waves for Stress-tensor Multiplet Correlator in $4D$ $\mathcal{N}=2$ SCFTs
• Local Operators from the Space of Vacua of Four Dimensional SUSY Gauge Theories
• Holomorphic Scalar Portals and the OPE
• Analytic Studies of Fermions in the Conformal Bootstrap