References$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt152",{id:"formSmash:upper:j_idt152",widgetVar:"widget_formSmash_upper_j_idt152",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:referencesLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt153_j_idt156",{id:"formSmash:upper:j_idt153:j_idt156",widgetVar:"widget_formSmash_upper_j_idt153_j_idt156",target:"formSmash:upper:j_idt153:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

Abelian Extensions, Fractional Loop Group and Quantum FieldsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2010 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Stockholm: KTH , 2010. , x, 95 p.
##### Series

Trita-FYS, ISSN 0280-316X ; 2010:13
##### Keyword [en]

Lie group extensions, Lie conformal algebras, gerbes, twisted K-theory, renormalization, anomalies, D-brane charges, variational complex
##### National Category

Other Physics Topics
##### Identifiers

URN: urn:nbn:se:kth:diva-12155ISBN: 978-91-7415-592-1OAI: oai:DiVA.org:kth-12155DiVA: diva2:303818
##### Public defence

2010-03-26, FA32, Roslagstullsbacken 21, Albanova universitetscentrum, Stockholm, 13:00 (English)
##### Opponent

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##### Supervisors

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#####

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##### Note

QC 20100915Available from: 2010-03-16 Created: 2010-03-15 Last updated: 2010-09-15Bibliographically approved
##### List of papers

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 L_{q}G, 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 L_{qg}, 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.

1. Integrability Criterion for Abelian Extensions of Lie Groups$(function(){PrimeFaces.cw("OverlayPanel","overlay13259",{id:"formSmash:j_idt503:0:j_idt507",widgetVar:"overlay13259",target:"formSmash:j_idt503:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Fractional Loop Group and Twisted K-theory$(function(){PrimeFaces.cw("OverlayPanel","overlay13260",{id:"formSmash:j_idt503:1:j_idt507",widgetVar:"overlay13260",target:"formSmash:j_idt503:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Calculus structure on the Lie conformal algebra complex and the variational complex$(function(){PrimeFaces.cw("OverlayPanel","overlay351689",{id:"formSmash:j_idt503:2:j_idt507",widgetVar:"overlay351689",target:"formSmash:j_idt503:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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