Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poisson Lie symmetry and D-branes in WZW model on the Heisenberg Lie
  group $H_4$   We show that the WZW model on the Heisenberg Lie group $H_4$ has Poisson-Lie
symmetry only when the dual Lie group is ${ A}_2 \oplus 2{ A}_1$. In this way,
we construct the mutual T-dual sigma models on Drinfel'd double generated by
the Heisenberg Lie group $H_4$ and its dual pair, ${ A}_2 \oplus 2{ A}_1$, as
the target space in such a way that the original model is the same as the $H_4$
WZW model. Furthermore, we show that the dual model is conformal up to two
loops order. Finally, we discuss $D$-branes and the worldsheet boundary
conditions defined by a gluing matrix on the $H_4$ WZW model. Using the duality
map obtained from the canonical transformation description of the Poisson-Lie
T-duality transformations for the gluing matrix which locally defines the
properties of the $D$-brane, we find two different cases of the gluing matrices
for the WZW model based on the Heisenberg Lie group $H_4$ and its dual model.

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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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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: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom