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M-theoretic Genesis of Topological Phases

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arxiv 2007.01532 v1 pith:OVPOEXJP submitted 2020-07-03 hep-th cond-mat.str-elmath.GT

M-theoretic Genesis of Topological Phases

Gil Young Cho , Dongmin Gang , Hee-Cheol Kim This is my paper
classification hep-th cond-mat.str-elmath.GT
keywords topologicalphasesmanifoldsapproachbosonicconstructionm-theoreticmatter
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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 topological phases in an equivalent fashion. Hence, we pave a new route toward the classification of topological phases of matter.

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