发表机构
Abdus Salam Centre for Theoretical Physics, Imperial College London; Department of Theoretical Physics, Tata Institute of Fundamental Research; Princeton University（阿卜杜斯·萨拉姆理论物理中心，伦敦帝国理工学院; 塔塔基础研究所理论物理系; 普林斯顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出将M理论矩阵理论嵌入AdS/CFT对应，建立BMN矩阵模型、ABJM大电荷单极子扇区与pp波M理论的三重性，通过指标匹配提供证据，并揭示BPS偶然性的新机制。
AI 中文摘要
我们提出一种将M理论的矩阵理论嵌入AdS/CFT对应的方案，使得前者能够通过后者进行检验。核心主张是秩为$m$的BMN矩阵模型、具有电荷$J$的ABJM理论的大电荷单极子扇区，以及具有紧致类光方向的极大超对称十一维pp波上的M理论三者之间存在三重性。相关的ABJM极限取$N,k,J\to\infty$，同时保持$N/k^2$和$m=J/k$固定。我们通过展示在该三重标度极限下，ABJM超共形指标与$U(m)$ BMN矩阵模型的Witten指标的大正则求和精确一致，为该三重性提供了定量证据。这一关系还给出了BMN指标的紧凑大正则表达式，我们利用它重新审视其大$m$行为。我们的解析和数值结果揭示了强烈的玻色子-费米子抵消，并且当BMN电荷按$Q \sim m^2$标度时，没有证据表明先前声称的$e^{O(m^2)}$增长。我们进一步通过构建字母级词典来研究两种理论的BPS上同调之间的对应关系。这导致了ABJM理论中BPS偶然性（fortuity）的新概念，即使在严格的$N=\infty$下依然存在：尽管与有限$N$迹关系相关的通常偶然性在三重标度极限下消失，但每个固定单极子扇区由有效秩$m$控制，有限$m$迹关系产生的偶然态直接映射到BMN矩阵模型的偶然态。最后，我们讨论了与相关概念的联系，如大电荷矩阵模型、开-闭-开三重性和世界线全息原理。
英文摘要
We propose a setup that embeds Matrix Theory for M-theory into the AdS/CFT correspondence, allowing the former to be tested using the latter. The central claim is a triality among the BMN matrix model of rank $m$, a large-charge monopole sector of ABJM theory with charge $J$, and M-theory on the maximally supersymmetric eleven-dimensional pp-wave with a compact lightlike direction. The relevant ABJM limit sends $N,k,J\to\infty$ while keeping $N/k^2$ and $m=J/k$ fixed. We provide quantitative evidence for this triality by showing that, in this triple-scaling limit, the ABJM superconformal index agrees precisely with a grand-canonical sum of Witten indices of the $U(m)$ BMN matrix model. This relation also yields a compact grand-canonical expression for the BMN index, which we use to revisit its large-$m$ behavior. Our analytic and numerical results reveal strong boson--fermion cancellations and show no evidence for the previously claimed $e^{O(m^2)}$ growth when the BMN charge scales as $Q \sim m^2$. We further study the correspondence between the BPS cohomologies of the two theories by constructing a letter-level dictionary. This leads to a new notion of BPS fortuity in ABJM theory that survives even at strict $N=\infty$: although the usual fortuity associated with finite-$N$ trace relations disappears in the triple-scaling limit, each fixed-monopole sector is governed by the effective rank $m$, and finite-$m$ trace relations generate fortuitous states that map directly to fortuitous states of the BMN matrix model. Finally, we discuss connections to related concepts such as large-charge matrix models, open--closed--open triality, and worldline holography.
Comments62 pages, 6 figures
