Cardy Algebras, Sewing Constraints and String-Nets

2020/09/24 by Traube, Matthias · 1 citation
#18D10 #18D35 #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Primary: 81T40 #Quantum Algebra (math.QA) #Secondary: 81T45

paper · doi:10.48550/arxiv.2009.11895

Abstract

In \citeSchweigert:2019zwt it was shown how string-net spaces for the Cardy bulk algebra in the Drinfeld center Z(C) of a modular tensor category C give rise to a consistent set of correlators. We extend their results to include open-closed world sheets and allow for more general field algebras, which come in the form of (C|Z(C))-Cardy algebras. To be more precise, we show that a set of fundamental string-nets with input data from a (C|Z(C))-Cardy algebra gives rise to a solution of the sewing constraints formulated in \citeKong₂014 and that any set of fundamental string-nets solving the sewing constraints determine a (C|Z(C))-Cardy algebra up to isomorphism. Hence we give an alternative proof of the results in \citeKong₂014 in terms of string-nets.

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