论文标题
四分之一基质模型中非交通曲率的近似处理
Approximate treatment of noncommutative curvature in quartic matrix model
论文作者
论文摘要
我们研究了一个Hermitian矩阵模型，其标准四分之一电位由$ \ mathrm {tr}（rφ^2）$ term $ term term固定外部矩阵$ r $。这是由截断的grosse-wulkenhaar模型的截断的海森贝格代数公式中的曲率项的动机 - 可重新分布的非交通性场理论。额外的术语打破了动作的统一对称性，并在对单位积分的扰动计算后引导到有效的多领矩阵模型。伴随着该多头近似的分析处理，我们还通过Monte Carlo Simulates进行数值研究。研究了模型的相结构，并确定了修改的相图。我们观察到该理论的1切割和2切相之间的过渡线的变化，该阶段与先前的数值模拟一致，并且与Grosse-Wulkenhaar模型中的非交通阶段的去除。
We study a Hermitian matrix model with the standard quartic potential amended by a $\mathrm{tr}(RΦ^2)$ term for fixed external matrix $R$. This is motivated by a curvature term in the truncated Heisenberg algebra formulation of the Grosse-Wulkenhaar model -- a renormalizable noncommutative field theory. The extra term breaks the unitary symmetry of the action and leads, after perturbative calculation of the unitary integral, to an effective multitrace matrix model. Accompanying the analytical treatment of this multitrace approximation, we also study the model numerically by Monte Carlo simulations. The phase structure of the model is investigated, and a modified phase diagram is identified. We observe a shift of the transition line between the 1-cut and 2-cut phases of the theory that is consistent with the previous numerical simulations and also with the removal of the noncommutative phase in the Grosse-Wulkenhaar model.
