ANEC对SCFT在四个维度上的意义
Implications of ANEC for SCFTs in four dimensions
摘要：
我们探讨了四维$\mathcal{N}=1$超共形场论中算子标度维数$Δ$的平均能量条件（ANEC）的后果。我们表明，在许多情况下，ANEC界强于相应的酉界$Δ$。我们详细分析了$(\frac12 j,0)$ Lorentz表示中的手征算子，证明了ANEC蕴涵了$Δ\ge\frac32j$的下界，它比$j>1$相应的么正性界强.我们还推导了$(\frac12 j,0)$算子服从其他可能的缩短条件的ANEC界，以及一般的$(\frac12 j,0)$算子不服从任何缩短条件的ANEC界.在这两种情况下，我们发现它们通常比相应的么正性边界更强。最后，我们阐明运营商尺寸的限制，从我们的$\mathcal{N}=1$结果多重的$\mathcal{N}=2,4$超共形理论在四维。通过重铸的ANEC作为一个凸优化问题，并使用标准的半定规划方法，我们能够改善以前的分析在文献中有关的非超对称的情况下。
英文摘要：
We explore consequences of the Averaged Null Energy Condition (ANEC) for scaling dimensions $Δ$ 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 $Δ$. We analyze in detail chiral operators in the $(\frac12 j,0)$ Lorentz representation and prove that the ANEC implies the lower bound $Δ\ge\frac32j$, which is stronger than the corresponding unitarity bound for $j>1$. We also derive ANEC bounds on $(\frac12 j,0)$ operators obeying other possible shortening conditions, as well as general $(\frac12 j,0)$ 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.
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