Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anomalous Quantum Hall Effect of 4D Graphene in Background Fields   Bori\c{c}i-Creutz (\emph{BC}) model describing the dynamics of light quarks
in lattice \emph{QCD} has been shown to be intimately linked to the four
dimensional extension of 2D graphene refereed below to as four dimensional
graphene (\emph{4D-graphene}). Borrowing ideas from the field theory
description of the usual \emph{2D} graphene, we study in this paper the
anomalous quantum Hall effect (AQHE) of the \emph{BC} fermions in presence of a
constant background field strength $\mathcal{F}_{\mu \nu}$ with a special
focuss on the case $\mathcal{F}_{\mu \nu}=\mathcal{B}\epsilon_{\mu \nu
34}+\mathcal{E}\epsilon_{12\mu \nu}$ with $\mathcal{B}$ and $ \mathcal{E}$ two
real\ moduli and $\det \mathcal{F}_{\mu \nu}=\mathcal{B}^{2}\mathcal{\times
E}^{2}$. First, we revisit the anomalous \emph{2D} graphene by using \emph{QFT}
method. Then, we consider the AQHE of \emph{BC}fermions for both regular $\det
\mathcal{F}_{\mu \nu}\neq 0$ and singular $ \det F_{\mu \nu}=0$ cases. We show,
amongst others, that the exact solutions of the \emph{BC} fermions coupled to
constant $\mathcal{F}_{\mu \nu}$ have a 5D interpretation; and the filling
factor $\nu_{BC}$ of the \emph{BC}\ model coupled to constant $\mathcal{F}_{\mu
\nu}$ is given by $24% \frac{(2N+1) (2M+1)}{2}$ with $N,$ $M$ positive
integers. Others features, such as $\mathcal{F}_{\mu \nu}^{QCD}\neq 0$
\textrm{and the extension of the obtained results to the lattice fermions like
Karsten-Wilzeck (KW) fermions and naive ones}, are also discussed.
  Key words: Lattice QCD, Bori\c{c}i-Creutz fermions, Anomalous Quantum Hall
Effect, filling factor, four dimensional graphene, Index theorem, Spectral
flow.

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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: alg-geom