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August 2009 Gerbe-holonomy for surfaces with defect networks
Ingo Runkel, Rafal R. Suszek
Adv. Theor. Math. Phys. 13(4): 1137-1219 (August 2009).


We define the sigma-model action for world-sheets with embedded defect networks in the presence of a three-form field strength. We derive the defect gluing condition for the sigma-model fields and their derivatives, and use it to distinguish between conformal and topological defects. As an example, we treat the WZW model with defects labelled by elements of the centre Z(G) of the target Lie group G; comparing the holonomy for different defect networks gives rise to a 3-cocycle on Z(G). Next, we describe the factorization properties of two-dimensional quantum field theories in the presence of defects and compare the correlators for different defect networks in the quantum WZW model. This, again, results in a 3-cocycle on Z(G). We observe that the cocycles obtained in the classical and in the quantum computation are cohomologous.


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Ingo Runkel. Rafal R. Suszek. "Gerbe-holonomy for surfaces with defect networks." Adv. Theor. Math. Phys. 13 (4) 1137 - 1219, August 2009.


Published: August 2009
First available in Project Euclid: 6 July 2010

zbMATH: 1200.81137
MathSciNet: MR2661204

Rights: Copyright © 2009 International Press of Boston

Vol.13 • No. 4 • August 2009
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