{"title":"正交和辛随机张量模型的对偶性","authors":"Razvan Gurau, Hannes Keppler","doi":"10.4171/aihpd/177","DOIUrl":null,"url":null,"abstract":"The groups $\\mathrm{O}(N)$ and $\\mathrm{Sp}(N)$ are related by an analytic continuation to negative values of $N$, $\\mathrm{O}(-N)\\simeq\\mathrm{Sp}(N)$. This duality has been studied for vector models, $\\mathrm{SO}(N)$ and $\\mathrm{Sp}(N)$ gauge theories, as well as some random matrix ensembles. We extend this duality to real random tensor models of arbitrary order $D$ with no symmetry under permutation of the indices and with quartic interactions. The $N$ to $-N$ duality is shown to hold graph by graph to all orders in perturbation theory for the partition function, the free energy and the connected two-point function.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Duality of orthogonal and symplectic random tensor models\",\"authors\":\"Razvan Gurau, Hannes Keppler\",\"doi\":\"10.4171/aihpd/177\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The groups $\\\\mathrm{O}(N)$ and $\\\\mathrm{Sp}(N)$ are related by an analytic continuation to negative values of $N$, $\\\\mathrm{O}(-N)\\\\simeq\\\\mathrm{Sp}(N)$. This duality has been studied for vector models, $\\\\mathrm{SO}(N)$ and $\\\\mathrm{Sp}(N)$ gauge theories, as well as some random matrix ensembles. We extend this duality to real random tensor models of arbitrary order $D$ with no symmetry under permutation of the indices and with quartic interactions. The $N$ to $-N$ duality is shown to hold graph by graph to all orders in perturbation theory for the partition function, the free energy and the connected two-point function.\",\"PeriodicalId\":42884,\"journal\":{\"name\":\"Annales de l Institut Henri Poincare D\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2023-10-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales de l Institut Henri Poincare D\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/aihpd/177\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales de l Institut Henri Poincare D","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/aihpd/177","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
Duality of orthogonal and symplectic random tensor models
The groups $\mathrm{O}(N)$ and $\mathrm{Sp}(N)$ are related by an analytic continuation to negative values of $N$, $\mathrm{O}(-N)\simeq\mathrm{Sp}(N)$. This duality has been studied for vector models, $\mathrm{SO}(N)$ and $\mathrm{Sp}(N)$ gauge theories, as well as some random matrix ensembles. We extend this duality to real random tensor models of arbitrary order $D$ with no symmetry under permutation of the indices and with quartic interactions. The $N$ to $-N$ duality is shown to hold graph by graph to all orders in perturbation theory for the partition function, the free energy and the connected two-point function.