Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homotopy and duality in non-Abelian lattice gauge theory   We propose an approach of lattice gauge theory based on a homotopic
interpretation of its degrees of freedom. The basic idea is to dress the
plaquettes of the lattice to view them as elementary homotopies between nearby
paths. Instead of using a unique $G$-valued field to discretize the connection
1-form, $A$, we use an $\AG$-valued field $U$ on the edges, which plays the
role of the 1-form $\ad_A$, and a $G$-valued field $V$ on the plaquettes, which
corresponds to the Faraday tensor, $F$. The 1-connection, $U$, and the
2-connection, $V$, are then supposed to have a 2-curvature which vanishes. This
constraint determines $V$ as a function of $U$ up to a phase in $Z(G)$, the
center of $G$. The 3-curvature around a cube is then Abelian and is interpreted
as the magnetic charge contained inside this cube. Promoting the plaquettes to
elementary homotopies induces a chiral splitting of their usual Boltzmann
weight, $w=v\bar{v}$, defined with the Wilson action. We compute the Fourier
transform, $\hat{v}$, of this chiral Boltzmann weight on $G=SU_3$ and we obtain
a finite sum of generalized hypergeometric functions. The dual model describes
the dynamics of three spin fields : $\lambda_P\in{\hat{G}}$ and
$m_P\in{\hat{Z(G)}}\simeq\Z_3$, on each oriented plaquette $P$, and
$\epsilon_{ab}\in{\hat{\OG}}\simeq\Z_2$, on each oriented edge $(ab)$. Finally,
we sketch a geometric interpretation of this spin system in a fibered category
modeled on the category of representations of $G$.

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The categories of this paper are: comp-gas
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: q-alg