Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cardy condition for open-closed field algebras   Let $V$ be a vertex operator algebra satisfying certain reductivity and
finiteness conditions such that $\mathcal{C}_V$, the category of V-modules, is
a modular tensor category. We study open-closed field algebras over V equipped
with nondegenerate invariant bilinear forms for both open and closed sectors.
We show that they give algebras over certain $\C$-extension of the Swiss-cheese
partial dioperad, and we obtain Ishibashi states easily in such algebras. We
formulate Cardy condition algebraically in terms of the action of the modular
transformation $S: \tau \mapsto -\frac{1}{\tau}$ on the space of intertwining
operators. We then derive a graphical representation of S in the modular tensor
category $\mathcal{C}_V$. This result enables us to give a categorical
formulation of Cardy condition and modular invariant conformal full field
algebra over $V\otimes V$. Then we incorporate the modular invariance condition
for genus-one closed theory, Cardy condition and the axioms for open-closed
field algebra over V equipped with nondegenerate invariant bilinear forms into
a tensor-categorical notion called Cardy $\mathcal{C}_V|\mathcal{C}_{V\otimes
V}$-algebra. We also give a categorical construction of Cardy
$\mathcal{C}_V|\mathcal{C}_{V\otimes V}$-algebra in Cardy case.

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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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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: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg