Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Logarithmic Conformal Field Theory: a Lattice Approach   Logarithmic Conformal Field Theories (LCFT) play a key role, for instance, in
the description of critical geometrical problems (percolation, self avoiding
walks, etc.), or of critical points in several classes of disordered systems
(transition between plateaus in the integer and spin quantum Hall effects).
Much progress in their understanding has been obtained by studying algebraic
features of their lattice regularizations. For reasons which are not entirely
understood, the non semi-simple associative algebras underlying these lattice
models - such as the Temperley-Lieb algebra or the blob algebra - indeed
exhibit, in finite size, properties that are in full correspondence with those
of their continuum limits. This applies to the structure of indecomposable
modules, but also to fusion rules, and provides an `experimental' way of
measuring couplings, such as the `number b' quantifying the logarithmic
coupling of the stress energy tensor with its partner. Most results obtained so
far have concerned boundary LCFTs, and the associated indecomposability in the
chiral sector. While the bulk case is considerably more involved (mixing in
general left and right moving sectors), progress has also been made in this
direction recently, uncovering fascinating structures. This article provides a
short general review of our work in this area.

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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci