Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abelian Topological Order on Lattice Enriched with Electromagnetic
  Background   In topological phases of matter, the interplay between intrinsic topological
order and global symmetry is an interesting task. In the study of topological
orders with discrete global symmetry, an important systematic approach is the
construction of exactly soluble lattice models. However, for continuous global
symmetry, in particular the electromagnetic $U(1)$, the lattice approach has
been less systematically developed. In this paper, we introduce a systematic
construction of effective theories for a large class of abelian topological
orders on three-dimensional spacetime lattice with electromagnetic background.
We discuss the associated topological properties, including the Hall
conductivity and the spin-c nature of the electromagnetic background. Some of
these effective spacetime lattice theories can be readily mapped to microscopic
Hamiltonians on spatial lattice; others may also shed light on their possible
microscopic Hamiltonian realizations. Our approach is based on the gauging of
$1$-form $\mathbb{Z}$ symmetries. Our construction is naturally related to the
continuum path integral of (doubled) $U(1)$ Chern-Simons theory, through the
latter's formal description in terms of Deligne-Beilinson cohomology; when the
global symmetry is dropped, our construction can be reduced to the
Dijkgraaf-Witten model of associated abelian topological orders, as expected.

18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an