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Renormalization Group Approach to Matrix Models
2017-11-08  【 】【打印】【关闭

CAS Key Laboratory of Theoretical Physics

Institute of Theoretical Physics

 Chinese Academy of Sciences

Seminar

Title

题目

Renormalization Group Approach to Matrix Models

Speaker

报告人

 Prof. Jean Zinn-Justin

Affiliation

所在单位

CEA, France

Date

日期

3:30pm, Nov 08, 2017, Wednesday

Venue

地点

Room 6620, ITP NEW BUILDING

Abstract

摘要

 The study of the statistical properties of random matrices of large size has a long history. For example, Wigner used Gaussian ensembles to describe statistically   the spectrum of complex Hamiltonians and derived the famous semi-circle law. 't Hooft noticed that, in SU(N) non-Abelian gauge theories, tessalated surfaces can be associated to Feynman diagrams and that the large N expansion is an expansion in successive topologies. Later, some ensembles of random matrices in the large size   and the so-called double scaling limit were used as toy models for 2D quantum gravity coupled to conformal matter and string theory or as examples of statistical models on some random surfaces. This has resulted in a tremendous development of random matrix theory, tackled with increasingly sophisticated mathematical methods and number of matrix models have been solved exactly. However, many matrix problems remain unsolved. Since the solved models exhibit critical points and universal properties, it is tempting to try renormalization group (RG) ideas with the goal of determining universal properties, without solving models explicitly (Brézin, Zinn-Justin 1992, Zinn-Justin 2014).

Contact person

所内联系人

Chushun Tian
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