MTC[M3, G]: 3d Topological Order Labeled by Seifert Manifolds

Abstract: We propose a correspondence between topological order in 2+1d, i.e. modular tensor categories (MTCs) and Seifert three-manifolds together with a choice of ADE gauge group G. The correspondence defines for every Seifert manifold and choice of G a fusion category, which we conjecture to be modular whenever the Seifert manifold has trivial first homology group with coefficients in the center of G. The construction determines the spins of anyons and their S-matrix, and provides a constructive way to determine the R- and F-symbols from simple building blocks. We explore the possibility that this correspondence provides an alternative classification of MTCs, which is put to the test by realizing all MTCs (unitary or non-unitary) with rank $r\leq 5$ in terms of Seifert manifolds and a choice of Lie group G.

HEP - phenomenologyHEP - theorymathematical physicscategory theory

Audience: researchers in the topic

Symmetry Seminar

Series comments: Weekly seminar on generalized symmetries in QFT, string theory and related topics.