Implications of ANEC for SCFTs in four dimensions

Abstract

We explore consequences of the Averaged Null Energy Condition (ANEC) for scaling dimensions $\Delta$ of operators in four-dimensional $\mathcal{N}=1$ superconformal field theories. We show that in many cases the ANEC bounds are stronger than the corresponding unitarity bounds on $\Delta$. We analyze in detail chiral operators in the $(\frac{1}{2}j,0)$ Lorentz representation and prove that the ANEC implies the lower bound $\Delta \ge \frac{3}{2}j$, which is stronger than the corresponding unitarity bound for $j>1$. We also derive ANEC bounds on $(\frac{1}{2}j,0)$ operators obeying other possible shortening conditions, as well as general $(\frac{1}{2}j,0)$ operators not obeying any shortening condition. In both cases we find that they are typically stronger than the corresponding unitarity bounds. Finally, we elucidate operator-dimension constraints that follow from our $\mathcal{N}=1$ results for multiplets of $\mathcal{N}=2,4$ superconformal theories in four dimensions. By recasting the ANEC as a convex optimization problem and using standard semidefinite programming methods we are able to improve on previous analyses in the literature pertaining to the nonsupersymmetric case.

arXiv comment30 pages + appendices, 6 figures

References in corpus (27)

• The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
• Conformal collider physics: Energy and charge correlations
• Chiral Rings and Anomalies in Supersymmetric Gauge Theory
• On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
• Light-ray operators in conformal field theory
• Averaged Null Energy Condition from Causality
• Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
• Comments on Supercurrent Multiplets, Supersymmetric Field Theories and Supergravity
• Comments on Unparticles
• Spectrum of Type IIB Supergravity on AdS_5 x T^{11}: Predictions on N = 1 SCFT's
• Correlation Functions of Conserved Currents in N = 2 Superconformal Theory
• N=1 Superconformal Symmetry in Four Dimensional Quantum Field Theory
• Jets and Quantum Field Theory
• Energy flow in QCD and event shape functions
• Constraining conformal field theories with a higher spin symmetry in d> 3 dimensions
• N=1 Superconformal Symmetry in Four Dimensions
• Bounds on OPE Coefficients from Interference Effects in the Conformal Collider
• Constraints on Chiral Operators in N=2 SCFTs
• Conformal Field Theories and Deep Inelastic Scattering
• On Conformal Field Theories With Extremal a/c Values
• Higher Spin ANEC and the Space of CFTs
• Universal Bounds on Operator Dimensions from the Average Null Energy Condition
• Universality of Nonperturbative Effects in Event Shapes
• Two-point functions of conformal primary operators in $\mathcal{N}=1$ superconformal theories
• Mixed OPEs in $\mathcal{N}=2$ Superconformal Theories
• R-current three-point functions in 4d $\mathcal{N}=1$ superconformal theories
• Infeasibility certificates for linear matrix inequalities

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