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A Monoidal Category for Perturbed Defects in Conformal Field Theory

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Abstract

Starting from an abelian rigid braided monoidal category \({\mathcal{C}}\) we define an abelian rigid monoidal category \({\mathcal{C}_F}\) which captures some aspects of perturbed conformal defects in two-dimensional conformal field theory. Namely, for V a rational vertex operator algebra we consider the charge-conjugation CFT constructed from V (the Cardy case). Then \({\mathcal{C} = {\rm Rep}(V)}\) and an object in \({\mathcal{C}_F}\) corresponds to a conformal defect condition together with a direction of perturbation. We assign to each object in \({\mathcal{C}_F}\) an operator on the space of states of the CFT, the perturbed defect operator, and show that the assignment factors through the Grothendieck ring of \({\mathcal{C}_F}\). This allows one to find functional relations between perturbed defect operators. Such relations are interesting because they contain information about the integrable structure of the CFT.

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  1. Department of Mathematics, King’s College London, Strand, London, WC2R 2LS, United Kingdom

    Dimitrios Manolopoulos & Ingo Runkel

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  1. Dimitrios Manolopoulos
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  2. Ingo Runkel
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Correspondence to Ingo Runkel.

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Communicated by A. Kapustin

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Manolopoulos, D., Runkel, I. A Monoidal Category for Perturbed Defects in Conformal Field Theory. Commun. Math. Phys. 295, 327–362 (2010). https://doi.org/10.1007/s00220-009-0958-2

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