AI 中文总结
研究𝒩=2超对称SYK模型中BPS态的偶然性，引入解码器D定义度量脆弱性，区分混沌BPS扇区与精确可解塔。
AI 中文摘要
在具有N个费米子的𝒩=2超对称SYK模型中，每个BPS态都是偶然的：在固定电荷下，它仅存在于有限的N范围内。我们证明，当电荷增加时，BPS类可在偶然性窗口内的格点行走中被提升，潜在地达到任意大的N，但不存在规范的提升。因此，我们引入解码器D，其谱量化精确提升及其度量代价，我们将谐波代表的提升失败或代价增加称为度量脆弱性。Chen的单矩阵模型和双味SYK模型的保护塔分别实现了完美提升的裸机制和真正的 dressing 机制。在一般的单味模型中，精确提升最终失败。Lin-Maldacena-Rozenberg-Shan型算子D†D表现出与高斯酉系综一致的能级统计，其本征值量化BPS态在系统尺寸上的度量连续性，而它们的关联探测BPS扇区内的混沌。因此，度量脆弱性和BPS混沌被编码在同一算子的互补可观测量中，从而将混沌BPS扇区与精确可解塔区分开来。
英文摘要
In the $\mathcal N=2$ supersymmetric SYK model with $N$ fermions, every BPS state is fortuitous: at fixed charge, it exists only over a finite range of $N$. Allowing the charge to increase, we show that BPS classes may instead be uplifted along lattice walks inside the fortuity window, potentially to arbitrarily large $N$. However, there is no canonical uplift. We therefore introduce a decoder $D$ whose spectrum quantifies exact uplift and its metric cost. We call the failure or increasing cost of uplifting harmonic representatives metric fragility. Chen's single-matrix model and the protected tower of the two-flavor SYK model realize bare and genuinely dressed mechanisms of perfect uplift, respectively. In the generic one-flavor model, exact uplift eventually fails. The Lin-Maldacena-Rozenberg-Shan-type operator $D^\dagger D$ exhibits level statistics consistent with the Gaussian unitary ensemble. Its eigenvalues quantify the metric continuity of BPS states across system size, while their correlations probe chaos within the BPS sector. Metric fragility and BPS chaos are thus encoded in complementary observables of the same operator, distinguishing chaotic BPS sectors from exactly solvable towers.
Comments44 pages, 15 figures, 2 tables
