arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1610.00526math-phhep-thmath.MP
收藏

矩阵$Φ^3_2$量子场论的精确解

Exact solution of matricial $Φ^3_2$ quantum field theory

Harald Grosse, Akifumi Sako, Raimar Wulkenhaar

备注：
30 pages, LaTeX. v2: some formulae generalised to avoid duplication in arXiv:1612.07584
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

我们应用最近发展的方法来精确地解决$Φ^3$矩阵模型与协方差的二维理论，也被称为正则化Kontsevich模型。它的关联函数共同描述了多穿孔2-球面上的图。我们将展示如何沃德-高桥身份和Schwinger-Dyson方程导致一个特殊的大- $\mathcal{N}$限制积分方程，我们完全解决所有的关联函数。值得注意的是，这些功能是解析的$Φ^3$耦合常数，虽然个别图表上的界限证明只有博雷尔求和。求解的模型是在强变形参数的特殊极限下由非对易场论导出的。该极限定义了普通的2D Schwinger函数，然而，不满足反射正性。

英文摘要：

We apply a recently developed method to exactly solve the $Φ^3$ matrix model with covariance of a two-dimensional theory, also known as regularised Kontsevich model. Its correlation functions collectively describe graphs on a multi-punctured 2-sphere. We show how Ward-Takahashi identities and Schwinger-Dyson equations lead in a special large-$\mathcal{N}$ limit to integral equations that we solve exactly for all correlation functions. Remarkably, these functions are analytic in the $Φ^3$ coupling constant, although bounds on individual graphs justify only Borel summability. The solved model arises from noncommutative field theory in a special limit of strong deformation parameter. The limit defines ordinary 2D Schwinger functions which, however, do not satisfy reflection positivity.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑