M-theoretic genesis of topological phases

Journal of High Energy Physics

Gil Young Cho¹  Dongmin Gang¹  Hee-Cheol Kim¹ 

[1] Department of Physics, Pohang University of Science and Technology (POSTECH), 37673, Pohang, Republic of Korea;Asia Pacific Center for Theoretical Physics (APCTP), 790-784, Pohang, Korea;

关键词: Anyons;    M-Theory;    Topological States of Matter;   

DOI  :  10.1007/JHEP11(2020)115

来源: Springer

【 摘 要 】

We present a novel M-theoretic approach of constructing and classifying anyonic topological phases of matter, by establishing a correspondence between (2+1)d topological field theories and non-hyperbolic 3-manifolds. In this construction, the topological phases emerge as macroscopic world-volume theories of M5-branes wrapped around certain types of non-hyperbolic 3-manifolds. We devise a systematic algorithm for identifying the emergent topological phases from topological data of the internal wrapped 3-manifolds. As a benchmark of our approach, we reproduce all the known unitary bosonic topological orders up to rank 4. Remarkably, our construction is not restricted to an unitary bosonic theory but it can also generate fermionic and/or non-unitary anyon models in an equivalent fashion. Hence, we pave a new route toward the classification of topological phases of matter.

【 授权许可】

CC BY