Abstract
We explore consequences of the Averaged Null Energy Condition (ANEC) for scaling dimensions ∆ 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 ∆. We analyze in detail chiral operators in the \( \left(\frac{1}{2}j,0\right) \) 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 \( \left(\frac{1}{2}j,0\right) \) operators obeying other possible shortening conditions, as well as general \( \left(\frac{1}{2}j,0\right) \) 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.
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Manenti, A., Stergiou, A. & Vichi, A. Implications of ANEC for SCFTs in four dimensions. J. High Energ. Phys. 2020, 93 (2020). https://doi.org/10.1007/JHEP01(2020)093
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DOI: https://doi.org/10.1007/JHEP01(2020)093