| 1. |
- Andersen, Jørgen Ellegaard, et al.
(författare)
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Reducibility of quantum representations of mapping class groups
- 2010
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Ingår i: Letters in Mathematical Physics. - : Springer. - 0377-9017 .- 1573-0530. ; 91:3, s. 215-239
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we provide a general condition for the reducibility of the Reshetikhin–Turaev quantum representations of the mapping class groups. Namely, for any modular tensor category with a special symmetric Frobenius algebra with a non-trivial genus one partition function, we prove that the quantum representations of all the mapping class groups built from the modular tensor category are reducible. In particular, for SU(N) we get reducibility for certain levels and ranks. For the quantum SU(2) Reshetikhin–Turaev theory we construct a decomposition for all even levels. We conjecture this decomposition is a complete decomposition into irreducible representations for high enough levels.
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| 2. |
- Björnsson, Jonas, et al.
(författare)
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Modular invariant partition functions for noncompact G/Ad(H) models
- 2011
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Ingår i: Physical Review D. - : American Physical Society. - 1550-7998 .- 1550-2368. ; 83:8
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Tidskriftsartikel (refereegranskat)abstract
- We propose a spectrum for a class of gauged non-compact G/Ad(H) WZNW models, including spectrally flowed images of highest, lowest, and mixed extremal weight modules. These are combined into blocks whose characters, due to the Lorentzian signature of the target space, are divergent and treated as formal expressions in need of regularisation. Assuming that this is possible, we show that these extended characters transform linearly under modular transformations, and can be used to write down modular invariant partition functions.
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| 3. |
- Fjelstad, Jens, 1971-, et al.
(författare)
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CFT description of three-dimensional Kerr-de Sitter space-time
- 2002
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Ingår i: Nuclear Physics B. - : Elsevier. - 0550-3213 .- 1873-1562. ; 641:1-2, s. 376-392
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Tidskriftsartikel (refereegranskat)abstract
- We describe three-dimensional Kerr-de Sitter space using similar methods as recently applied to the BTZ black hole. A rigorous form of the classical connection between gravity in three dimensions and two-dimensional conformal field theory is employed, where the fundamental degrees of freedom are described in terms of two dependent SL(2,C) currents. In contrast to the BTZ case, however, quantization does not give the Bekenstein-Hawking entropy connected to the cosmological horizon of Kerr-de Sitter space.
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| 4. |
- Fjelstad, Jens, 1971-, et al.
(författare)
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Equivalence of Chern-Simons gauge theory and WZNW model using a BRST symmetry
- 1999
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Ingår i: Physics Letters B. - : Elsevier. - 0370-2693 .- 1873-2445. ; 466:2-4, s. 227-233
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Tidskriftsartikel (refereegranskat)abstract
- The equivalence between the Chern-Simons gauge theory on a three-dimensional manifold with boundary and the WZNW model on the boundary is established in a simple and general way using the BRST symmetry. Our approach is based on restoring gauge invariance of the Chern-Simons theory in the presence of a boundary. This gives a correspondence to the WZNW model that does not require solving any constraints, fixing the gauge or specifying boundary conditions.
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| 5. |
- Fjelstad, Jens, 1971-, et al.
(författare)
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Logarithmic conformal field theories via logarithmic deformations
- 2002
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Ingår i: Nuclear Physics B. - : Elsevier. - 0550-3213 .- 1873-1562. ; 633:3, s. 379-413
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Tidskriftsartikel (refereegranskat)abstract
- We construct logarithmic conformal field theories starting from an ordinary conformal field theory -- with a chiral algebra C and the corresponding space of states V -- via a two-step construction: i) deforming the chiral algebra representation on V\tensor End K[[z,1/z]], where K is an auxiliary finite-dimensional vector space, and ii) extending C by operators corresponding to the endomorphisms End K. For K=C^2, with End K being the two-dimensional Clifford algebra, our construction results in extending C by an operator that can be thought of as \partial^{-1}E, where \oint E is a fermionic screening. This covers the (2,p) Virasoro minimal models as well as the sl(2) WZW theory.
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| 6. |
- Fjelstad, Jens, 1971-, et al.
(författare)
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Mapping class group representations from Drinfeld doubles of finite groups
- 2020
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Ingår i: Journal of knot theory and its ramifications. - : World Scientific Publishing Co. Pte Ltd. - 0218-2165. ; 29:5
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Tidskriftsartikel (refereegranskat)abstract
- We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of such representations in terms of finite group data. This allows us to establish various properties of these representations. In particular we show that they have finite images, and that for surfaces of genus at least 3 their restriction to the Torelli group is non-trivial iff G is non-abelian.
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| 7. |
- Fjelstad, Jens, 1971-, et al.
(författare)
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Mapping class group representations from Drinfeld doubles of finite groups
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We investigate representations of mapping class groups of surfaces that arise from the untwisted Drinfeld double of a finite group G, focusing on surfaces without marked points or with one marked point. We obtain concrete descriptions of such representations in terms of finite group data. This allows us to establish various properties of these representations. In particular we show that they have finite images, and that for surfaces of genus at least 3 their restriction to the Torelli group is non-trivial iff G is non-abelian.
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| 8. |
- Fjelstad, Jens, 1971-, et al.
(författare)
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New symmetries of the chiral Potts model
- 2012
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Ingår i: Journal of Physics A. - : Institute of Physics (IOP). - 0305-4470 .- 1361-6447 .- 1751-8113 .- 1751-8121. ; 45:15
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Tidskriftsartikel (refereegranskat)abstract
- In this paper a hithertho unknown symmetry of the three-state chiral Potts model is found consisting of two coupled Temperley-Lieb algebras. From these we can construct new superintegrable models. One realisation is in terms of a staggered isotropic XY spin chain. Further we investigate the importance of the algebra for the existence of mutually commuting charges. This leads us to a natural generalisation of the boost-operator, which generates the charges.
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| 9. |
- Fjelstad, Jens, 1971-
(författare)
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On duality and extended chiral symmetry in the SL(2,R) WZW model
- 2011
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Ingår i: Journal of Physics A. - : Institute of Physics (IOP). - 0305-4470 .- 1361-6447. ; 44:23
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Tidskriftsartikel (refereegranskat)abstract
- Two chiral aspects of the SL(2,R) WZW model in an operator formalism are investigated. First, the meaning of duality, or conjugation, of primary fields is clarified. On a class of modules obtained from the discrete series it is shown, by looking at spaces of two-point conformal blocks, that a natural definition of contragredient module provides a suitable notion of conjugation of primary fields, consistent with known two-point functions. We find strong indications that an apparent contradiction with the Clebsch-Gordan series of SL(2,R), and proposed fusion rules, is explained by nonsemisimplicity of a certain category. Second, results indicating an infinite cyclic simple current group, corresponding to spectral flow automorphisms, are presented. In particular, the subgroup corresponding to even spectral flow provides part of a hypothetical extended chiral algebra resulting in proposed modular invariant bulk spectra.
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| 10. |
- Fjelstad, Jens, 1971-, et al.
(författare)
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Partition functions, mapping class groups and Drinfeld doubles
- 2012
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Ingår i: Symmetries and Groups in Contemporary Physics. - Shanghai : World Scientific. - 9789814518543 - 9789814518567 ; , s. 405-410
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Konferensbidrag (refereegranskat)abstract
- Higher genus partition functions of two-dimensional conformal field theories have to be invariants under linear actions of mapping class groups. We illustrate recent results [4,6] on the construction of such invariants by concrete expressions obtained for the case of Drinfeld doubles of finite groups. The results for doubles are independent of the characteristic of the underlying field, and the general results do not require any assumptions of semisimplicity.
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