(Non-)Abelian Kramers-Wannier Duality And Topological Field Theory | Zendy

Pavol Ševera | Zendy

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(Non-)Abelian Kramers-Wannier Duality And Topological Field Theory

Author(s) -

Pavol Ševera

Publication year - 2002

Publication title -

journal of high energy physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.998

H-Index - 261

eISSN - 1126-6708

pISSN - 1029-8479

DOI - 10.1088/1126-6708/2002/05/049

Subject(s) - abelian group , duality (order theory) , topological quantum field theory , mathematics , connection (principal bundle) , generalization , pure mathematics , symplectic geometry , field (mathematics) , topology (electrical circuits) , mathematical analysis , combinatorics , geometry

We study a connection between duality and topological field theories. First,2d Kramers-Wannier duality is formulated as a simple 3d topological claim (moreor less Poincare duality), and a similar formulation is given forhigher-dimensional cases. In this form they lead to simple TFTs with boundarycoloured in two colours. The statistical models live on the boundary of theseTFTs, as in the CS/WZW or AdS/CFT correspondence. Classical models (Poisson-LieT-duality) suggest a non-abelian generalization in the 2dcase, with abeliangroups replaced by quantum groups. Amazingly, the TFT formulation solves theproblem without computation: quantum groups appear in pictures, independentlyof the classical motivation. Connection with Chern-Simons theory appears at thesymplectic level, and also in the pictures of the Drinfeld double:Reshetikhin-Turaev invariants of links in 3-manifolds, computed from thedouble, are included in these TFTs. All this suggests nice phenomena in higherdimensions.Comment: 9 pages, 9 figure

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