论文标题
CFT中带电的运算符的凸度，具有多个Abelian对称性
Convexity of Charged Operators in CFTs with Multiple Abelian Symmetries
论文作者
论文摘要
在ADS中全息图的背景下，是由弱重力猜想的动机，有人提出，在CFT中被控的操作员在三个维度或更高的CFT中，应满足其频谱上的某些凸特性。该提案的一个关键要素是必须出现凸度的电荷，这被提议在参数上永远不会大。在本文中，我们在多个Abelian全球对称性的背景下制定了这种约束。我们提出这样的陈述，即多维电荷空间中的凸方向应产生带电运算符的总晶格的子晶格，因此该子晶格的索引不能在参数上大大。在二维CFT的特殊情况下，可以将索引在参数上大大，我们通过一个明确的示例证明了索引。但是，我们还证明，在两个维度上，始终存在凸方向，生成一个子晶格，其索引具有由全局对称的当前级别界定的索引。因此，在两个维度上，应该对猜想进行稍微修改以说明当前水平，然后可以证明它。在两个以上的维度中，我们表明，仅与BPS运算符相关的边凸电荷向量产生的子晶格的索引可以成为参数较大。但是，一旦考虑了所有操作员，我们就找不到凸的参数延迟的证据。
Motivated by the Weak Gravity Conjecture in the context of holography in AdS, it has been proposed that operators charged under global symmetries in CFTs, in three dimensions or higher, should satisfy certain convexity properties on their spectrum. A key element of this proposal is the charge at which convexity must appear, which was proposed to never be parametrically large. In this paper, we develop this constraint in the context of multiple Abelian global symmetries. We propose the statement that the convex directions in the multi-dimensional charge space should generate a sub-lattice of the total lattice of charged operators, such that the index of this sub-lattice cannot be made parametrically large. In the special case of two-dimensional CFTs, the index can be made parametrically large, which we prove by an explicit example. However, we also prove that in two dimensions there always exist convex directions generating a sub-lattice with an index bounded by the current levels of the global symmetry. Therefore, in two dimensions, the conjecture should be slightly modified to account for the current levels, and then it can be proven. In more than two dimensions, we show that the index of the sub-lattice generated by marginally convex charge vectors associated to BPS operators only, can be made parametrically large. However, we do not find evidence for parametric delay in convexity once all operators are considered.
