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Gerbe-holonomy for surfaces with defect networks

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)1137 - 1219
Number of pages83
JournalAdv.Theor. Math. Phys.
Volume13
Issue number4
Publication statusPublished - Aug 2009

King's Authors

Research Groups

  • King's College London

Abstract

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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