Fusion category symmetry. Part I. Anomaly in-flow and gapped phases

被引:72
作者
Thorngren, Ryan [1 ,3 ,6 ]
Wang, Yifan [2 ,3 ,4 ,5 ]
机构
[1] Weizmann Inst Sci, Dept Condensed Matter Phys, Rehovot, Israel
[2] Princeton Univ, Joseph Henry Labs, Princeton, NJ 08544 USA
[3] Harvard Univ, Ctr Math Sci & Applicat, Cambridge, MA 02138 USA
[4] Harvard Univ, Jefferson Phys Lab, Cambridge, MA 02138 USA
[5] NYU, Ctr Cosmol & Particle Phys, Broadway, NY USA
[6] Univ Calif Los Angeles, Dept Phys & Astron, Mani L Bhaumik Inst Theoret Phys, Portola Plaza, Los Angeles, CA 90095 USA
关键词
Anomalies in Field and String Theories; Global Symmetries; Topological Field Theories; Topological States of Matter; TENSOR CATEGORIES; SELF-DUALITY; INVARIANTS; RULES;
D O I
10.1007/JHEP04(2024)132
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
We study generalized discrete symmetries of quantum field theories in 1+1D generated by topological defect lines with no inverse. In particular, we describe 't Hooft anomalies and classify gapped phases stabilized by these symmetries, including new 1+1D topological phases. The algebra of these operators is not a group but rather is described by their fusion ring and crossing relations, captured algebraically as a fusion category. Such data defines a Turaev-Viro/Levin-Wen model in 2+1D, while a 1+1D system with this fusion category acting as a global symmetry defines a boundary condition. This is akin to gauging a discrete global symmetry at the boundary of Dijkgraaf-Witten theory. We describe how to "ungauge" the fusion category symmetry in these boundary conditions and separate the symmetry-preserving phases from the symmetry-breaking ones. For Tambara-Yamagami categories and their generalizations, which are associated with Kramers-Wannier-like self-dualities under orbifolding, we develop gauge theoretic techniques which simplify the analysis. We include some examples of CFTs with fusion category symmetry derived from Kramers-Wannier-like dualities as an appetizer for the Part II companion paper.
引用
收藏
页数:42
相关论文
共 54 条
[1]  
Aasen D, 2018, Arxiv, DOI arXiv:1709.01941
[2]   Topological defects on the lattice: I. The Ising model [J].
Aasen, David ;
Mong, Roger S. K. ;
Fendley, Paul .
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2016, 49 (35)
[3]   Symmetry fractionalization, defects, and gauging of topological phases [J].
Barkeshli, Maissam ;
Bonderson, Parsa ;
Cheng, Meng ;
Wang, Zhenghan .
PHYSICAL REVIEW B, 2019, 100 (11)
[4]  
Bhardwaj L, 2017, Arxiv, DOI arXiv:1704.02330
[5]   Anomalies and entanglement renormalization [J].
Bridgeman, Jacob C. ;
Williamson, Dominic J. .
PHYSICAL REVIEW B, 2017, 96 (12)
[6]  
Brown K. S., 2012, Graduate Texts in Mathematics
[7]   Anyonic Chains, Topological Defects, and Conformal Field Theory [J].
Buican, Matthew ;
Gromov, Andrey .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2017, 356 (03) :1017-1056
[8]   Anyons and matrix product operator algebras [J].
Bultinck, N. ;
Marien, M. ;
Williamson, D. J. ;
Sahinoglu, M. B. ;
Haegeman, J. ;
Verstraete, F. .
ANNALS OF PHYSICS, 2017, 378 :183-233
[9]   Topological defect lines and renormalization group flows in two dimensions [J].
Chang, Chi-Ming ;
Lin, Ying-Hsuan ;
Shao, Shu-Heng ;
Wang, Yifan ;
Yin, Xi .
JOURNAL OF HIGH ENERGY PHYSICS, 2019, 2019 (01)
[10]   Symmetry protected topological orders and the group cohomology of their symmetry group [J].
Chen, Xie ;
Gu, Zheng-Cheng ;
Liu, Zheng-Xin ;
Wen, Xiao-Gang .
PHYSICAL REVIEW B, 2013, 87 (15)