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arXiv 1508.00548hep-th
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一般二维共形场论中算子维数的泛界

Universal Bounds on Operator Dimensions in General 2D Conformal Field Theories

Joshua D. Qualls

备注：
24 pages; extension of (and thus overlap with) arXiv:0902.2790 and arXiv:1312.0038
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摘要：

我们推导出了一般酉二维共形场论中最轻的几个态的共形维数的界，其中包括具有手征电流的CFTs。我们推导出共形维数$Δ_1$和$Δ_2$的一个界，其形式为$c_{\rm tot}/12 + O(1)$。结合形式与arXiv：0902.2790和arXiv：1312.0038中无手性电流的CFTs相同。然后，我们证明了不等式$Δ_n \leq c_{\rm tot}/12 + O(1)$大$c_{\rm tot}$和适当的限制$n$。使用AdS $_3$ /CFT $_2$对应关系，我们的边界对应于最轻的几个状态的质量的上限和状态的数量的下限。最后，我们检查我们的结果对几个候选的共形场论。

英文摘要：

We derive a bound on the conformal dimensions of the lightest few states in general unitary 2d conformal field theories with discrete spectra using modular invariance, including CFTs with chiral currents. We derive a bound on the conformal dimensions $Δ_1$ and $Δ_2$ going as $c_{\rm tot}/12 + O(1)$. The bound is of the same form found for CFTs without chiral currents in arXiv:0902.2790 and arXiv:1312.0038. We then prove the inequality $Δ_n \leq c_{\rm tot}/12 + O(1)$ for large $c_{\rm tot}$ and with appropriate restrictions on $n$. Using the AdS$_3$/CFT$_2$ correspondence, our bounds correspond to upper bounds on the masses of the lightest few states and a lower bound on the number of states. We conclude by checking our results against several candidate conformal field theories.

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