论文标题
关于Narain理论的全息描述的评论
Comments on the holographic description of Narain theories
论文作者
论文摘要
我们讨论了Narain $ u（1）^C \ times U（1）^c $保形场理论的全息描述，以及它们与批量相传的常规弱耦合重力的潜在相似性，因为有效的IR批量描述包括“ $ u（1）$ GRAVITITY”，以额外的自由度进行了修改。从这张图片开始，我们提出了以下假设：在大型中央电荷中，任何纳林理论的状态密度都受到$ u（1）$重力的密度的限制。这立即暗示，对于主要字段的光谱差距的最大值为$δ_1= c/（2πe）$。为了测试该提案的自洽性，我们根据量子稳定器代码使用手性晶格CFT和CFT研究了它的含义。首先，我们注意到猜想产生了量子稳定器代码的新结合，这与文献中先前已知的边界兼容。我们开始讨论国家密度的差异，因为一致性必须在较大的$ c $限制中消失。我们考虑代码和手性理论的集合，并表明在这两种情况下，密度方差在中心电荷中呈指数较小。
We discuss the holographic description of Narain $U(1)^c\times U(1)^c$ conformal field theories, and their potential similarity to conventional weakly coupled gravity in the bulk, in the sense that the effective IR bulk description includes "$U(1)$ gravity" amended with additional light degrees of freedom. Starting from this picture, we formulate the hypothesis that in the large central charge limit the density of states of any Narain theory is bounded by below by the density of states of $U(1)$ gravity. This immediately implies that the maximal value of the spectral gap for primary fields is $Δ_1=c/(2πe)$. To test the self-consistency of this proposal, we study its implications using chiral lattice CFTs and CFTs based on quantum stabilizer codes. First we notice that the conjecture yields a new bound on quantum stabilizer codes, which is compatible with previously known bounds in the literature. We proceed to discuss the variance of the density of states, which for consistency must be vanishingly small in the large-$c$ limit. We consider ensembles of code and chiral theories and show that in both cases the density variance is exponentially small in the central charge.
