Papers › Implications of ANEC for SCFTs in four dimensions
Implications of ANEC for SCFTs in four dimensions
Andrea Manenti, Andreas Stergiou, Alessandro Vichi
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We explore consequences of the Averaged Null Energy Condition (ANEC) for scaling dimensions Δ of operators in four-dimensional 𝒩=1 superconformal field theories. We show that in many cases the ANEC bounds are stronger than the corresponding unitarity bounds on Δ. We analyze in detail chiral operators in the (1/2 j,0) Lorentz representation and prove that the ANEC implies the lower bound Δ≥3/2j, which is stronger than the corresponding unitarity bound for j>1. We also derive ANEC bounds on (1/2 j,0) operators obeying other possible shortening conditions, as well as general (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 𝒩=1 results for multiplets of 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.
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