Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parity Anomaly and Duality Web   We review the parity anomaly and a duality web in 2+1 dimensions. An odd
dimensional non-interacting Dirac fermion theory is not parity invariant at
quantum level. We demonstrate the parity anomaly in a three dimensional
non-interacting Dirac fermion theory and a one dimensional non-interacting
Dirac fermion theory. These theories can generate non-gauge invariant Abelian
Chern-Simons terms at a finite temperature through an effective action. The
parity anomaly also leads us to study the duality web in 2+1 dimensions, in
which the 2+1 dimensional duality web begins from the conjecture of a duality
between a three dimensional Dirac fermion theory and a three dimensional
interacting scalar field theory at the Wilson-Fisher fixed point. We first
review the duality web for the flat background, then we discuss its extension
to the spin$_c$ manifold to avoid inconsistency from the spin structure. This
also leads a global effect. We discuss that the composite fermions approach of
the quantum Hall system also suffers from the same issue of the global
description. Finally, we use perspective of the electric-magnetic duality of
the Abelian gauge theory in 3+1 dimensions to study the 2+1 dimensional duality
web.

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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: math
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg