洛伦兹IIB矩阵模型中受约束非对易模上的单圈涨落响应
One-Loop Fluctuation Response Along a Constrained Noncommutative Modulus in the Lorentzian IIB Matrix Model
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中文总结 AI 辅助
研究洛伦兹IIB矩阵模型N=5时的局域约束问题，计算单圈涨落，发现量子涨落数据可区分未被粗二次谱分辨的背景，表明非对易结构与量子涨落或含维度动力学相关信息。
中文摘要 AI 辅助
我们研究洛伦兹IIB（IKKT）矩阵模型中矩阵规模N=5时的局域约束问题，并对一维物理模进行数值延拓。对于精确的固定Q_ρ约束解族，其平稳恒等式意味着经典作用量为常数；23个已接受的背景以所述精度实现了该关系。在采样分支中，洛伦兹延展算子的谱在数值精度下保持一致，而微观非对易不变量发生变化。我们沿该分支计算有限维单圈涨落：在固定玻色背景下，费米子Grassmann积分是精确的，给出PfM_F；其幅度在色规范变换和连通固有洛伦兹变换下不变，且沿模变化。完整的玻色-鬼场-费米子商测度定义了与洛伦兹表示无关的密度一元形式，而非标量势。因此量子涨落数据可区分未被粗二次谱分辨的背景。我们还应用了带框高L SO(5)结构探针：在参考背景下，有序3+6谱分离度在L=2、3时大于L=1时，在规范大L极限下更大；这是框架定义的诊断，而非内禀可观测量或高N解。Pfaffian与高L响应沿采样分支密切相关（我们仅将其视为描述性结果）。这些结果表明，微观非对易结构与量子涨落可能包含与维度动力学相关的信息，但未确立维度选择。
英文摘要
We study a local constrained problem at matrix size $N=5$ in the Lorentzian IIB (IKKT) matrix model and numerically continue a one-dimensional physical modulus. For an exact fixed-$Q_ρ$ constrained solution family, the stationary identity implies constant classical action; the 23 accepted backgrounds realize this relation to the quoted precision. Across the sampled branch, the spectrum of the Lorentzian extent operator remains common to numerical precision while microscopic noncommutative invariants vary. We evaluate finite-dimensional one-loop fluctuations along this branch. At fixed bosonic background, the fermionic Grassmann integral is exact and gives $\operatorname{Pf}\mathcal M_F$; its magnitude is invariant under color-gauge and connected proper-Lorentz transformations and varies along the modulus. The complete boson--ghost--fermion quotient measure defines a Lorentz-representative-independent density one-form rather than a scalar potential. Thus quantum fluctuation data distinguish backgrounds unresolved by the coarse quadratic spectrum. We also apply a framed higher-$L$ SO(5) structural probe. At the reference background, the ordered $3+6$ spectral separation is larger at $L=2,3$ than at $L=1$, and larger still in the canonical large-$L$ limit. This is a frame-defined diagnostic, not an intrinsic observable or a higher-$N$ solution. The Pfaffian and higher-$L$ responses are closely correlated along the sampled branch, which we treat only as descriptive. These results suggest that microscopic noncommutative structure and quantum fluctuations may contain information relevant to dimensional dynamics, without establishing dimensional selection.
发表机构
- Tokai National Higher Education and Research System（东海国立高等教育与研究机构）
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