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arXiv · 1310.1875

Cardy algebras and sewing constraints, II

Liang Kong·Qin Li·Ingo Runkel
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Abstract

This is the part II of a two-part work started in arXiv:0807.3356 [math.QA]. In part I, Cardy algebras were studied, a notion which arises from the classification of genus-0,1 open-closed rational conformal field theories. In this part, we prove that a Cardy algebra also satisfies the higher genus factorisation and modular-invariance properties formulated in arXiv:hep-th/0612306 in terms of the notion of a solution to the sewing constraints. We present the proof by showing that the latter notion, which is defined as a monoidal natural transformation, can be expressed in terms of generators and relations, which correspond exactly to the defining data and axioms of a Cardy algebra.

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Liang Kong, Qin Li, Ingo Runkel. 2013-10-07. Cardy algebras and sewing constraints, II. https://doi.org/10.1016/j.aim.2014.05.020

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