AI 中文总结
研究质量变形杨 - 米尔斯矩阵模型的强耦合极限，发现费米子改变矩阵对易性竞争，超对称杨 - 米尔斯矩阵模型在临界值\(\mathcal N_c = 2(D - 2)\)时矩阵强耦合下对易，且临界模型有大算子普遍性。
AI 中文摘要
我们研究质量变形的杨 - 米尔斯矩阵模型的强耦合极限，旨在理解矩阵何时有效对易。经典的杨 - 米尔斯相互作用驱使矩阵趋向相互对易的谷值，在此矩阵可被视为新兴空间的坐标。但考虑积分测度，对易性并非自动达成，因为对易轨迹在熵上受到抑制，在\(D\geq3\)的玻色子模型中强耦合极限仍是非对易的。我们发现费米子极大地改变了这种竞争。随着费米自由度数量增加，存在一个临界值\(\mathcal N_c = 2(D - 2)\)，由超对称杨 - 米尔斯矩阵模型实现，在该临界值处矩阵在强耦合下对易。相同的临界模型在\(O(N^2)\)或大算子变形下也表现出普遍性：归一化本征值密度对大算子的微观细节不敏感。费米子数量超过临界点仍使矩阵对易，但大算子普遍性丧失。因此，对易性和普遍性相关但不同：具有超对称场内容的矩阵模型处于同时具备两者的临界边界。
英文摘要
We study the strong coupling limit of mass deformed Yang--Mills matrix models, with the aim of understanding when the matrices become effectively commuting. The Yang--Mills interaction classically drives the matrices toward mutually commuting valleys, where the matrices can potentially be interpreted as coordinates of an emergent space. However, taking into consideration the integration measure, commutativity is not automatic since the commuting locus is entropically suppressed, and in the bosonic models with $D\geq3$ the strong coupling limit remains non-commuting. We find that fermions change this competition in a sharp way. As the number of fermionic degrees of freedom is increased, there is a critical value $\mathcal N_c=2(D-2)$, realized by the supersymmetric Yang--Mills matrix models, at which the matrices commute at strong coupling. The same critical models also exhibit universality under deformations by $O(N^2)$, or huge, operators: the normalized eigenvalue densities are insensitive to the microscopic details of the huge operators. Increasing the number of fermions beyond the critical point still gives commuting matrices, but the huge-operator universality is lost. Thus commutativity and universality are related but distinct: the matrix models with supersymmetric field content sit at the critical boundary where we have both.
Comments42 pages, 14 figures
