Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modular extensions of unitary braided fusion categories and 2+1D
  topological/SPT orders with symmetries   A finite bosonic or fermionic symmetry can be described uniquely by a
symmetric fusion category $\mathcal{E}$. In this work, we propose that 2+1D
topological/SPT orders with a fixed finite symmetry $\mathcal{E}$ are
classified, up to $E_8$ quantum Hall states, by the unitary modular tensor
categories $\mathcal{C}$ over $\mathcal{E}$ and the modular extensions of each
$\mathcal{C}$. In the case $\mathcal{C}=\mathcal{E}$, we prove that the set
$\mathcal{M}_{ext}(\mathcal{E})$ of all modular extensions of $\mathcal{E}$ has
a natural structure of a finite abelian group. We also prove that the set
$\mathcal{M}_{ext}(\mathcal{C})$ of all modular extensions of $\mathcal{C}$, if
not empty, is equipped with a natural $\mathcal{M}_{ext}(\mathcal{E})$-action
that is free and transitive. Namely, the set $\mathcal{M}_{ext}(\mathcal{C})$
is an $\mathcal{M}_{ext}(\mathcal{E})$-torsor. As special cases, we explain in
details how the group $\mathcal{M}_{ext}(\mathcal{E})$ recovers the well-known
group-cohomology classification of the 2+1D bosonic SPT orders and Kitaev's 16
fold ways. We also discuss briefly the behavior of the group
$\mathcal{M}_{ext}(\mathcal{E})$ under the symmetry-breaking processes and its
relation to Witt groups.

30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs