Abstract
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.
Highlights
Compactification from higher dimensional field theories is a powerful tool for engineering consistent lower dimensional theories
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
The (2+1)d field theories constructed out of non-hyperbolic manifolds do not, in general, flow to conformal theories. We show that such theories of non-hyperbolic manifolds flow to topological quantum field theories (TQFT) with anyons at the infrared (IR) fixed point
Summary
Compactification from higher dimensional field theories is a powerful tool for engineering consistent lower dimensional theories. It is desirable to develop an entirely new, physicsoriented approach for generating the consistent anyon theories, which is independent with the previous algebraic approaches We achieve this by establishing a novel correspondence between (2+1)d topological field theory and geometry of non-hyperbolic 3-manifolds. One advantage of our approach is that it can immediately generate a UV-complete, consistent field theory description for the anyon theories They were described only by abstract modular data (and c2d) or lattice constructions for limited cases. Similar non-unitary sub-sectors appear in various supersymmetric models, e.g., the Schur operators in 4d N = 2 SCFTs equipped with 2d chiral algebra structure [20] Keeping this in mind, in this paper we build unitary embeddings and classification of the non-unitary MTCs up to rank ≤ 4 as a concrete demonstration of our proposal.
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