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Fractional Loop Group and Twisted K-theory
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
2010 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 299, no 3, 741-763 p.Article in journal (Refereed) Published
Abstract [en]

We study the structure of abelian extensions of the group L (q) G of q-differentiable loops (in the Sobolev sense), generalizing from the case of the central extension of the smooth loop group. This is motivated by the aim of understanding the problems with current algebras in higher dimensions. Highest weight modules are constructed for the Lie algebra. The construction is extended to the current algebra of the supersymmetric Wess-Zumino-Witten model. An application to the twisted K-theory on G is discussed.

Place, publisher, year, edition, pages
2010. Vol. 299, no 3, 741-763 p.
Keyword [en]
unitary representations, quantization
National Category
Other Physics Topics
Identifiers
URN: urn:nbn:se:kth:diva-8044DOI: 10.1007/s00220-010-1108-6ISI: 000281711100007Scopus ID: 2-s2.0-84755161215OAI: oai:DiVA.org:kth-8044DiVA: diva2:13260
Note
QC 20100915 Uppdaterad från submitted till published (20101130).Available from: 2008-02-27 Created: 2008-02-27 Last updated: 2010-11-30Bibliographically approved
In thesis
1. Group Extensions, Gerbes and Twisted K-theory
Open this publication in new window or tab >>Group Extensions, Gerbes and Twisted K-theory
2008 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

This thesis reviews the theory of group extensions, gerbes and twisted K-theory. Application to anomalies in gauge theory is briefly discussed. The main results are presented in two appended scientific papers. In the first paper we establish, by construction, a criterion for when an infinite dimensional abelian Lie algebra extension corresponds to a Lie group extension. In the second paper we introduce the fractional loop group L_qG, construct highest weight modules for the Lie algebra and discuss an application to twisted K-theory on G.

Place, publisher, year, edition, pages
Stockholm: KTH, 2008. x, 48 p.
Series
Trita-FYS, ISSN 0280-316X ; 2008:7
National Category
Other Physics Topics
Identifiers
urn:nbn:se:kth:diva-4654 (URN)978-91-7178-893-1 (ISBN)
Presentation
2008-03-13, FA32, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 10:00
Opponent
Supervisors
Note
QC 20101111Available from: 2008-02-27 Created: 2008-02-27 Last updated: 2010-11-11Bibliographically approved
2. Abelian Extensions, Fractional Loop Group and Quantum Fields
Open this publication in new window or tab >>Abelian Extensions, Fractional Loop Group and Quantum Fields
2010 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis deals with the theory of Lie group extensions, Lie conformal algebras and twisted K-theory, in the context of quantum physics. These structures allow for a mathematically precise description of certain aspects of interacting quantum field theories. We review three concrete examples, namely symmetry breaking (or anomalies) in gauge theory, classification of D-brane charges in string theory and the formulation of integrable hierarchies in the language of Poisson vertex algebras. The main results are presented in three appended scientific papers.

In the first paper we establish, by construction, a criterion for when an infinite dimensional abelian Lie algebra extension corresponds to a Lie group extension.

In the second paper we introduce the fractional loop group LqG, that is the group of maps from a circle to a compact Lie group G, with only a small degree of differentiability q ε R+ in the Sobolev sense. We construct abelian extensions and highest weight modules for the Lie algebra Lqg, and discuss an application to equivariant twisted K-theory on G.

In the third paper, we construct a structure of calculus algebra on the Lie conformal algebra complex and provide a more detailed description in the special case of the complex of variational calculus.

Place, publisher, year, edition, pages
Stockholm: KTH, 2010. x, 95 p.
Series
Trita-FYS, ISSN 0280-316X ; 2010:13
Keyword
Lie group extensions, Lie conformal algebras, gerbes, twisted K-theory, renormalization, anomalies, D-brane charges, variational complex
National Category
Other Physics Topics
Identifiers
urn:nbn:se:kth:diva-12155 (URN)978-91-7415-592-1 (ISBN)
Public defence
2010-03-26, FA32, Roslagstullsbacken 21, Albanova universitetscentrum, Stockholm, 13:00 (English)
Opponent
Supervisors
Note
QC 20100915Available from: 2010-03-16 Created: 2010-03-15 Last updated: 2010-09-15Bibliographically approved

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