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arXiv 2012.15830hep-thcs.ITmath.ITquant-ph
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关于 Narain 理论全息描述的评论

Comments on the holographic description of Narain theories

Anatoly Dymarsky, Alfred Shapere

AI总结:

本文提出在大中心荷极限下 Narain CFT 的态密度由 $U(1)$ 引力态密度下界约束,并据此得到谱隙最大值 $Δ_1=c/(2πe)$,同时利用稳定子码和手征 CFT 验证了该猜想的自洽性。

摘要:

我们讨论 Narain $U(1)^c\ imes U(1)^c$ 共形场论的全息描述,以及它们与传统弱耦合体引力在如下意义上的潜在相似性:有效的红外体描述包含“$U(1)$ 引力”,并补充了额外的轻自由度。从这一图像出发,我们提出如下假设:在大中心荷极限下,任何 Narain 理论的态密度都由下方受 $U(1)$ 引力的态密度约束。这立即意味着初级场的谱隙最大值为 $Δ_1=c/(2πe)$。为了检验该提议的自洽性,我们利用手性格点 CFT 和基于量子稳定子码的 CFT 研究其推论。首先我们注意到,该猜想给出了量子稳定子码的一个新界,并且该界与文献中先前已知的界相容。接着我们讨论态密度的方差,为满足自洽性,该方差在大 $c$ 极限下必须趋于零。我们考虑码理论和手征理论的系综,并证明在两种情况下态密度方差都随中心荷呈指数级小。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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