A Monoidal Category for Perturbed Defects in Conformal Field Theory

Details A Monoidal Category for Perturbed Defects in Conformal Field Theory A Monoidal Category for Perturbed Defects in Conformal Field Theory

2009-04-07

arxiv.org/abs/0904.1122v2

Commun.Math.Phys.295:327-362,2010

Physics

High Energy Physics

High Energy Physics - Theory

38 pages; v2: corrected typos and expanded section 3.2, version to appear in CMP

Scientific paper

10.1007/s00220-009-0958-2

Starting from an abelian rigid braided monoidal category C we define an abelian rigid monoidal category 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 C = Rep(V) and an object in C_F corresponds to a conformal defect condition together with a direction of perturbation. We assign to each object in 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 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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