A mathematical theory of gapless edges of 2d topological orders. Part I

Kong, Liang1,2; Zheng, Hao1,2,3

2020-02-25

10.1007/JHEP02(2020)150

JOURNAL OF HIGH ENERGY PHYSICS   影响因子和分区

1029-8479

This is the first part of a two-part work on a unified mathematical theory of gapped and gapless edges of 2d topological orders. We analyze all the possible observables on the 1+1D world sheet of a chiral gapless edge of a 2d topological order, and show that these observables form an enriched unitary fusion category, the Drinfeld center of which is precisely the unitary modular tensor category associated to the bulk. This mathematical description of a chiral gapless edge automatically includes that of a gapped edge (i.e. a unitary fusion category) as a special case. Therefore, we obtain a unified mathematical description and a classification of both gapped and chiral gapless edges of a given 2d topological order. In the process of our analysis, we encounter an interesting and reoccurring phenomenon: spatial fusion anomaly, which leads us to propose the Principle of Universality at RG fixed points for all quantum field theories. Our theory also implies that all chiral gapless edges can be obtained from a so-called topological Wick rotations. This fact leads us to propose, at the end of this work, a surprising correspondence between gapped and gapless phases in all dimensions.

Anyons Conformal Field Theory Topological Field Theories Topological States of Matter

SCI

英语

NI论文

第一 ; 通讯

NSFC[11071134] ; NSFC[11971219] ; NSFC[11871078]

Physics

Physics, Particles & Fields

WOS:000518577500001

SPRINGER

PHYSICS

Web of Science

1.Southern Univ Sci & Technol, Shenzhen Inst Quantum Sci & Engn, Shenzhen 518055, Peoples R China
2.Southern Univ Sci & Technol, Dept Phys, Shenzhen 518055, Peoples R China
3.Peking Univ, Dept Math, Beijing 100871, Peoples R China

Kong, Liang,Zheng, Hao. A mathematical theory of gapless edges of 2d topological orders. Part I[J]. JOURNAL OF HIGH ENERGY PHYSICS,2020(2).

Kong, Liang,&Zheng, Hao.(2020).A mathematical theory of gapless edges of 2d topological orders. Part I.JOURNAL OF HIGH ENERGY PHYSICS(2).

Kong, Liang,et al."A mathematical theory of gapless edges of 2d topological orders. Part I".JOURNAL OF HIGH ENERGY PHYSICS .2(2020).