Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattice realization of compact $U(1)$ Chern-Simons theory with exact
  1-symmetries   We propose a bosonic $U(1)$ rotor model on a three dimensional space-time
lattice. With the inclusion of a Maxwell term, we show that the low-energy
semi-classical behavior of our model is consistent with the Chern-Simons field
theory, $S= \int \text{d}^3 x\ \frac{K_{IJ}}{4\pi} A_I \text{d} A_J$ at low
energies. We require that the action be periodic in the lattice variables,
which enforces the quantization of the $K$-matrix as a symmetric integer matrix
with even diagonals. We also show that our lattice model has the exact
$1$-symmetries. In particular, some of those 1-symmetries are anomalous (i.e.
non-on-site) in the expected way. The anomaly can be probed via the breaking of
those $1$-symmetries by the boundaries of space-time.

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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph