Juan L. A. Abranches, Antonio D. Pereira, Reiko Toriumi
{"title":"Dually Weighted Multi-matrix Models as a Path to Causal Gravity-Matter Systems","authors":"Juan L. A. Abranches, Antonio D. Pereira, Reiko Toriumi","doi":"10.1007/s00023-024-01442-1","DOIUrl":null,"url":null,"abstract":"<p>We introduce a dually-weighted multi-matrix model that for a suitable choice of weights reproduce two-dimensional Causal Dynamical Triangulations (CDT) coupled to the Ising model. When Ising degrees of freedom are removed, this model corresponds to the CDT-matrix model introduced by Benedetti and Henson (Phys Lett B 678:222, 2009). We present exact as well as approximate results for the Gaussian averages of characters of a Hermitian matrix <i>A</i> and <span>\\(A^2\\)</span> for a given representation and establish the present limitations that prevent us to solve the model analytically. This sets the stage for the formulation of more sophisticated matter models coupled to two-dimensional CDT as dually weighted multi-matrix models providing a complementary view to the standard simplicial formulation of CDT-matter models.</p>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"14 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Henri Poincaré","FirstCategoryId":"4","ListUrlMain":"https://doi.org/10.1007/s00023-024-01442-1","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We introduce a dually-weighted multi-matrix model that for a suitable choice of weights reproduce two-dimensional Causal Dynamical Triangulations (CDT) coupled to the Ising model. When Ising degrees of freedom are removed, this model corresponds to the CDT-matrix model introduced by Benedetti and Henson (Phys Lett B 678:222, 2009). We present exact as well as approximate results for the Gaussian averages of characters of a Hermitian matrix A and \(A^2\) for a given representation and establish the present limitations that prevent us to solve the model analytically. This sets the stage for the formulation of more sophisticated matter models coupled to two-dimensional CDT as dually weighted multi-matrix models providing a complementary view to the standard simplicial formulation of CDT-matter models.
我们介绍了一种双权重多矩阵模型，对于合适的权重选择，它可以重现与伊辛模型耦合的二维因果动态三角模型（CDT）。去掉伊辛自由度后，该模型与贝内代蒂和亨森（Phys Lett B 678:222, 2009）提出的 CDT 矩阵模型相对应。我们给出了给定表示法下赫米矩阵 A 和 \(A^2\)字符的高斯平均值的精确和近似结果，并确定了阻碍我们分析求解模型的现有限制。这为把与二维 CDT 耦合的更复杂的物质模型表述为双重加权多矩阵模型奠定了基础，为 CDT-物质模型的标准简单表述提供了补充视角。
期刊介绍：
The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society.
The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
