M-theoretic Genesis of Topological Phases

TL;DR

This paper introduces an M-theoretic framework linking 3-manifolds to topological phases of matter, enabling systematic classification and generation of diverse topological orders, including fermionic and non-unitary types.

Contribution

It develops a novel M-theoretic approach connecting 3-manifold topology with topological phases, providing an algorithm for classification and extending to non-unitary and fermionic phases.

Findings

Reproduces all known unitary bosonic topological orders up to rank 4.

Establishes a correspondence between 3-manifolds and topological phases.

Demonstrates the generation of fermionic and non-unitary phases.

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 topological phases in an equivalent fashion. Hence, we pave a new route toward the classification of topological phases of matter.