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Fjelstad, J. & Månsson, T. (2012). New symmetries of the chiral Potts model. Journal of Physics A: Mathematical and General, 45(15), Article ID 155208.
Open this publication in new window or tab >>New symmetries of the chiral Potts model
2012 (English)In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 45, no 15, article id 155208Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2012
National Category
Subatomic Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:oru:diva-57721 (URN)10.1088/1751-8113/45/15/155208 (DOI)000302572000012 ()2-s2.0-84859219997 (Scopus ID)
Funder
Swedish Research Council, 348-2008-6049
Note

Funding Agencies:

NSFC  10775067

Swedish Science Research Council  

Göran Gustafsson foundation 

Available from: 2014-11-25 Created: 2017-05-17 Last updated: 2017-10-18Bibliographically approved
Fjelstad, J., Fuchs, J., Stigner, C. & Schweigert, C. (2012). Partition functions, mapping class groups and Drinfeld doubles. In: Symmetries and Groups in Contemporary Physics: Proceedings of the XXIX International Colloquium on Group-Theoretical Methods in PhysicsTianjin, China, 20 – 26 August 2012. Paper presented at The XXIX International Colloquium on Group-Theoretical Methods in Physics, Tianjin, China, August 20-26, 2012 (pp. 405-410). Shanghai: World Scientific
Open this publication in new window or tab >>Partition functions, mapping class groups and Drinfeld doubles
2012 (English)In: Symmetries and Groups in Contemporary Physics: Proceedings of the XXIX International Colloquium on Group-Theoretical Methods in PhysicsTianjin, China, 20 – 26 August 2012, Shanghai: World Scientific, 2012, p. 405-410Conference paper, Published paper (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
Shanghai: World Scientific, 2012
Series
Nankai Series in Pure, Applied Mathematics and Theoretical Physics ; 11
Keywords
Mapping class group; factorizable Hopf algebra; Drinfeld double; conformal field theory
National Category
Subatomic Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:oru:diva-57725 (URN)10.1142/9789814518550_0055 (DOI)978-981-4518-54-3 (ISBN)978-981-4518-56-7 (ISBN)
Conference
The XXIX International Colloquium on Group-Theoretical Methods in Physics, Tianjin, China, August 20-26, 2012
Available from: 2014-11-25 Created: 2017-05-17 Last updated: 2019-04-02Bibliographically approved
Fjelstad, J., Fuchs, J. & Stigner, C. (2012). RCFT with defects: Factorization and fundamental world sheets. Nuclear Physics B, 863(1), 213-259
Open this publication in new window or tab >>RCFT with defects: Factorization and fundamental world sheets
2012 (English)In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 863, no 1, p. 213-259Article in journal (Refereed) Published
Abstract [en]

It is known that for any full rational conformal field theory, the correlation functions that are obtained by the TFT construction satisfy all locality, modular invariance and factorization conditions, and that there is a small set of fundamental correlators to which all others are related via factorization - provided that the world sheets considered do not contain any non-trivial defect lines. In this paper we generalize both results to oriented world sheets with an arbitrary network of topological defect lines.

Place, publisher, year, edition, pages
Elsevier, 2012
National Category
Subatomic Physics
Identifiers
urn:nbn:se:oru:diva-57719 (URN)10.1016/j.nuclphysb.2012.05.011 (DOI)000306028700007 ()2-s2.0-84861809109 (Scopus ID)
Funder
Swedish Research Council, 348-2008-6049
Note

Funding Agencies:

ESF network "Interactions of Low-Dimensional Topology and Geometry with Mathematical Physics (ITGP)"  

China Science Postdoc  020400383 

Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD)  

NSFC  10775067 

Chinese Central Government  

VR  621-2009-3993 

Available from: 2014-11-25 Created: 2017-05-17 Last updated: 2017-10-18Bibliographically approved
Björnsson, J. & Fjelstad, J. (2011). Modular invariant partition functions for noncompact G/Ad(H) models. Physical Review D, 83(8), Article ID 086007.
Open this publication in new window or tab >>Modular invariant partition functions for noncompact G/Ad(H) models
2011 (English)In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 83, no 8, article id 086007Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
American Physical Society, 2011
National Category
Subatomic Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:oru:diva-57704 (URN)10.1103/PhysRevD.83.086007 (DOI)000290112200009 ()2-s2.0-79956112789 (Scopus ID)
Funder
Swedish Research Council, 623-2008-7048 348-2008-6049
Note

Funding Agency:

NSFC  10775067

Available from: 2014-11-25 Created: 2017-05-17 Last updated: 2018-09-06Bibliographically approved
Fjelstad, J. (2011). On duality and extended chiral symmetry in the SL(2,R) WZW model. Journal of Physics A: Mathematical and General, 44(23), Article ID 235404.
Open this publication in new window or tab >>On duality and extended chiral symmetry in the SL(2,R) WZW model
2011 (English)In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 44, no 23, article id 235404Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2011
National Category
Subatomic Physics
Identifiers
urn:nbn:se:oru:diva-57706 (URN)10.1088/1751-8113/44/23/235404 (DOI)000290518800011 ()2-s2.0-79956147278 (Scopus ID)
Funder
Swedish Research Council, 348-2008-6049
Note

Funding Agency:

NSFC  10775067

Available from: 2014-11-25 Created: 2017-05-17 Last updated: 2017-10-18Bibliographically approved
Andersen, J. E. & Fjelstad, J. (2010). On Reducibility of Mapping Class Group Representations: The SU(N) case. In: Stefaan Caenepeel, Jürgen Fuchs, Simone Gutt, Christophe Schweigert, Alexander Stolin, Freddy Van Oystaeyen (Ed.), Noncommutative structures in mathematics and physics: . Paper presented at Noncommutative Structures in Mathematics and Physics, Brussels, Belgium, July 22-26, 2008 (pp. 27-45). Brussels: Koninklijke vlaamse academie van Belgie voor Wetenschappen en kunsten
Open this publication in new window or tab >>On Reducibility of Mapping Class Group Representations: The SU(N) case
2010 (English)In: Noncommutative structures in mathematics and physics / [ed] Stefaan Caenepeel, Jürgen Fuchs, Simone Gutt, Christophe Schweigert, Alexander Stolin, Freddy Van Oystaeyen, Brussels: Koninklijke vlaamse academie van Belgie voor Wetenschappen en kunsten, 2010, p. 27-45Conference paper, Published paper (Refereed)
Abstract [en]

We review and extend the results of [1] that gives a condition for reducibility of quantum representations of mapping class groups constructed from Reshetikhin-Turaev type topological quantum field theories based on modular categories. This criterion is derived using methods developed to describe rational conformal field theories, making use of Frobenius algebras and their representations in modular categories. Given a modular category C, a rational conformal field theory can be constructed from a Frobenius algebra A in C. We show that if C contains a symmetric special Frobenius algebra A such that the torus partition function Z(A) of the corresponding conformal field theory is non-trivial, implying reducibility of the genus 1 representation of the modular group, then the representation of the genus g mapping class group constructed from C is reducible for every g\geq 1. We also extend the number of examples where we can show reducibility significantly by establishing the existence of algebras with the required properties using methods developed by Fuchs, Runkel and Schweigert. As a result we show that the quantum representations are reducible in the SU(N) case, N>2, for all levels k\in \mathbb{N}. The SU(2) case was treated explicitly in [1], showing reducibility for even levels k\geq 4.

Place, publisher, year, edition, pages
Brussels: Koninklijke vlaamse academie van Belgie voor Wetenschappen en kunsten, 2010
National Category
Other Mathematics
Identifiers
urn:nbn:se:oru:diva-57717 (URN)978-90-6569-061-6 (ISBN)
Conference
Noncommutative Structures in Mathematics and Physics, Brussels, Belgium, July 22-26, 2008
Available from: 2014-11-25 Created: 2017-05-17 Last updated: 2018-02-27Bibliographically approved
Andersen, J. E. & Fjelstad, J. (2010). Reducibility of quantum representations of mapping class groups. Letters in Mathematical Physics, 91(3), 215-239
Open this publication in new window or tab >>Reducibility of quantum representations of mapping class groups
2010 (English)In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 91, no 3, p. 215-239Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Springer, 2010
Keywords
topological quantum field theory; mapping class group; quantum representation
National Category
Other Mathematics Physical Sciences
Identifiers
urn:nbn:se:oru:diva-57703 (URN)10.1007/s11005-009-0367-7 (DOI)000275122700002 ()2-s2.0-77949774852 (Scopus ID)
Note

Funding Agency:

Danish National Research Foundation Center of Excellence

Available from: 2014-11-25 Created: 2017-05-17 Last updated: 2017-10-18Bibliographically approved
Chen, G., Cheung, Y.-K. E., Fan, Z., Fjelstad, J. & Hwang, S. (2009). No-ghost theorem for the bosonic Nappi-Witten string. Physical Review D, 80(8), Article ID 086003.
Open this publication in new window or tab >>No-ghost theorem for the bosonic Nappi-Witten string
Show others...
2009 (English)In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 80, no 8, article id 086003Article in journal (Refereed) Published
Abstract [en]

We prove a no-ghost theorem for a bosonic string propagating in Nappi-Witten spacetime. This is achieved in two steps. We first demonstrate unitarity for a class of NW/U(1) modules: the norm of any state which is primary with respect to a chosen timelike U(1) is non-negative. We then show that physical states - states satisfying the Virasoro constraints - in a class of modules of an affinisation of the Nappi-Witten algebra are contained in the NW/U(1) modules. Similar to the case of strings on AdS3, in order to saturate the spectrum obtained in light-cone quantization we are led to include modules with energy not bounded from below, which are related to modules with energy bounded from below by spectral flow automorphisms.

Place, publisher, year, edition, pages
American Physical Society, 2009
National Category
Subatomic Physics
Identifiers
urn:nbn:se:oru:diva-57705 (URN)10.1103/PhysRevD.80.086003 (DOI)000271353700126 ()2-s2.0-70449728413 (Scopus ID)
Funder
Swedish Research Council, 348-2008-6049
Note

Funding Agencies:

NSFC  10535010  10775068 

973 National Major State Basic Research and Development of China  2007CB815004 

National Science Foundation of China  0204131361 

Nanjing University  

Chinese Government  020422420100 

Available from: 2014-11-25 Created: 2017-05-17 Last updated: 2017-10-18Bibliographically approved
Fjelstad, J., Fuchs, J., Runkel, I. & Schweigert, C. (2008). Uniqueness of open/closed rational CFT with given algebra of open states. Advances in Theoretical and Mathematical Physics, 12(6), 1283-1375
Open this publication in new window or tab >>Uniqueness of open/closed rational CFT with given algebra of open states
2008 (English)In: Advances in Theoretical and Mathematical Physics, ISSN 1095-0761, E-ISSN 1095-0753, Vol. 12, no 6, p. 1283-1375Article in journal (Refereed) Published
Abstract [en]

We study the sewing constraints for rational two-dimensional conformal field theory on oriented surfaces with possibly non-empty boundary. The boundary condition is taken to be the same on all segments of the boundary. The following uniqueness result is established: For a solution to the sewing constraints with nondegenerate closed state vacuum and nondegenerate two-point correlators of boundary fields on the disk and of bulk fields on the sphere, up to equivalence all correlators are uniquely determined by the one-, two,- and three-point correlators on the disk.

Thus for any such theory every consistent collection of correlators can be obtained by the TFT approach of hep-th/0204148, hep-th/0503194. As morphisms of the category of world sheets we include not only homeomorphisms, but also sewings; interpreting the correlators as a natural transformation then encodes covariance both under homeomorphisms and under sewings of world sheets.

Place, publisher, year, edition, pages
International Press, 2008
National Category
Subatomic Physics
Identifiers
urn:nbn:se:oru:diva-57718 (URN)10.4310/ATMP.2008.v12.n6.a4 (DOI)000260104200004 ()2-s2.0-55449124838 (Scopus ID)
Available from: 2014-11-25 Created: 2017-05-17 Last updated: 2017-10-18Bibliographically approved
Runkel, I., Fjelstad, J., Fuchs, J. & Schweigert, C. (2007). Topological and conformal field theory as Frobenius algebras. In: Alexei Davydov, Michael Batanin, Michael Johnson, Stephen Lack and Amnon Neeman (Ed.), Categories in Algebra, Geometry and Mathematical Physics: (pp. 225-248). American Mathematical Society (AMS)
Open this publication in new window or tab >>Topological and conformal field theory as Frobenius algebras
2007 (English)In: Categories in Algebra, Geometry and Mathematical Physics / [ed] Alexei Davydov, Michael Batanin, Michael Johnson, Stephen Lack and Amnon Neeman, American Mathematical Society (AMS), 2007, p. 225-248Chapter in book (Refereed)
Abstract [en]

Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a (rational) CFT can be divided into two steps, of which one is complex-analytic and one purely algebraic. We realise the algebraic part of the construction with the help of three-dimensional topological field theory and show that any symmetric special Frobenius algebra in the appropriate braided monoidal category gives rise to a solution. A special class of examples is provided by two-dimensional topological field theories, for which the relevant monoidal category is the category of vector spaces

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2007
Series
Contemporary Mathematics, ISSN 0271-4132 ; 431
National Category
Physical Sciences
Research subject
Physics
Identifiers
urn:nbn:se:oru:diva-57727 (URN)000247366900013 ()9780821839706 (ISBN)
Available from: 2013-01-22 Created: 2017-05-17 Last updated: 2017-10-18Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-0372-5093

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