Unraveling spontaneously broken abelian Chern-Simons theories

TL;DR

This work classifies all 2+1D abelian Chern-Simons theories, identifying those arising from spontaneous symmetry breaking and highlighting the interesting nonabelian phenomena and dualities they can produce.

Contribution

It provides a comprehensive classification of abelian Chern-Simons theories in 2+1 dimensions, including those not obtainable from symmetry breaking, revealing their connection to nonabelian phenomena.

Findings

Classified all possible 2+1D abelian Chern-Simons theories.

Identified theories resulting from spontaneous symmetry breaking.

Highlighted theories leading to nonabelian braid statistics and dualities.

Abstract

In this talk I describe recent work (hep-th/9606029) in which I classified all conceivable 2+1 dimensional Chern-Simons (CS) theories with continuous compact abelian gauge group or finite abelian gauge group. The CS theories with finite abelian gauge group that can be obtained from the spontaneous breakdown of a CS theory with gauge group the direct product of various compact U(1) gauge groups were also identified. Those that can not be reached in this way are actually the most interesting since they lead to nonabelian phenomena such as nonabelian braid statistics, Alice fluxes and Cheshire charges and quite generally lead to dualities with 2+1 dimensional theories with a nonabelian finite gauge group.