String condensations in 3+1D and Lagrangian algebras

Zhao, Jiaheng1,2; Lou, Jia-Qi3,4,5; Zhang, Zhi-Hao6,7; Hung, Ling-Yan3,4,5,8; Kong, Liang7,9,10; Tian, Yin11

2023

ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS   影响因子和分区

1095-0761

1095-0753

We present three Lagrangian algebras in the modular 2-category associated to the 3+1D Z(2) topological order and discuss their physical interpretations, connecting algebras with gapped boundary conditions, and interestingly, maps (braided autoequivalences) exchanging algebras with bulk domain walls. A Lagrangian algebra, together with its modules and local modules, encapsulates detailed physical data of strings condensing at a gapped boundary. In particular, the condensed strings can terminate at boundaries in non-trivial ways. This phenomenon has no lower dimensional analogue and corresponds to novel mathematical structures associated to higher algebras. We provide a layered construction and also explicit lattice realizations of these boundaries and illustrate the correspondence between physics and mathematics of these boundary conditions. This is a first detailed study of the mathematics of Lagrangian algebras in modular 2-categories and their corresponding physics, that brings together rich phenomena of string condensations, gapped boundaries and domain walls in 3+1D topological orders.

SCI

英语

其他

Physics

Physics, Particles & Fields ; Physics, Mathematical

WOS:001156096900005

INT PRESS BOSTON, INC

Web of Science

1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
3.Fudan Univ, State Key Lab Surface Phys, Shanghai 200433, Peoples R China
4.Fudan Univ, Dept Phys, Shanghai 200433, Peoples R China
5.Fudan Univ, Ctr Field Theory & Particle Phys, Shanghai 200433, Peoples R China
6.Univ Sci & Technol China, Chinese Acad Sci, Sch Math Sci, Wu Wen Tsun Key Lab Math, Hefei 230026, Peoples R China
7.Southern Univ Sci & Technol, Shenzhen Inst Quantum Sci & Engn, Shenzhen 518055, Peoples R China
8.Tsinghua Univ, Yau Math Sci Ctr YMSC, Beijing 100084, Peoples R China
9.Int Quantum Acad, Shenzhen 518048, Peoples R China
10.Southern Univ Sci & Technol, Guangdong Prov Key Lab Quantum Sci & Engn, Shenzhen 518055, Peoples R China
11.Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Beijing 100875, Peoples R China

Zhao, Jiaheng,Lou, Jia-Qi,Zhang, Zhi-Hao,et al. String condensations in 3+1D and Lagrangian algebras[J]. ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS,2023,27(2).

Zhao, Jiaheng,Lou, Jia-Qi,Zhang, Zhi-Hao,Hung, Ling-Yan,Kong, Liang,&Tian, Yin.(2023).String condensations in 3+1D and Lagrangian algebras.ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS,27(2).

Zhao, Jiaheng,et al."String condensations in 3+1D and Lagrangian algebras".ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS 27.2(2023).