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Strings, Conformal Field Theory and Noncommutative Geometry
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics.
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis describes some aspects of noncommutative geometry and conformal field theory. The motivation for the investigations made comes to a large extent from string theory. This theory is today considered to be the most promising way to find a solution to the problem of unifying the four fundamental interactions in one single theory. The thesis gives a short background presentation of string theory and points out how noncommutative geometry and conformal field theory are of relevance within the string theoretical framework. There is also given some further information on noncommutative geometry and conformal field theory. The results from the three papers on which the thesis is based are presented in the text. It is shown in Paper 1 that, for a gauge theory in a flat noncommutative background only the gauge groups U(N) can be used in a straightforward way. These theories can arise as low energy limits of string theory. Paper 2 concerns boundary conformal field theory, which can be used to describe open strings in various backgrounds. Here different orbifold theories which are described using simple currents of the chiral algebra are investigated. The formalism is applied to ``branes´´ in Z2 orbifolds of the SU(2) WZW-model and to the D-series of unitary minimal models. In Paper 3 two different descriptions of an invariant star-product on are compared and the characteristic class that classifies the star-product is calculated. The Fedosov-Nest-Tsygan index theorem is used to compute the characteristic class.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis , 2004. , p. 54
Series
Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1104-232X ; 1004
Keyword [en]
Theoretical physics, Theoretical physics, String theory, Conformal field theory, Noncommutative geometry, Star-products
Keyword [sv]
Teoretisk fysik
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:uu:diva-4508ISBN: 91-554-6019-4 (print)OAI: oai:DiVA.org:uu-4508DiVA, id: diva2:164975
Public defence
2004-10-02, Polhemssalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 09:15
Opponent
Supervisors
Available from: 2004-09-09 Created: 2004-09-09 Last updated: 2013-07-10Bibliographically approved
List of papers
1. Restrictions on gauge groups in noncommutative gauge theory
Open this publication in new window or tab >>Restrictions on gauge groups in noncommutative gauge theory
2000 In: Physics Letters B, ISSN 0370-2693, Vol. 482, no 4, p. 417-419Article in journal (Refereed) Published
Identifiers
urn:nbn:se:uu:diva-92031 (URN)
Available from: 2004-09-09 Created: 2004-09-09Bibliographically approved
2. Opens strings in simple current orbifolds
Open this publication in new window or tab >>Opens strings in simple current orbifolds
2002 (English)In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 626, no 1-2, p. 53-72Article in journal (Refereed) Published
Abstract [en]

We study branes and open strings in a large class of orbifold backgrounds using microscopic techniques of boundary conformal field theory. In particular, we obtain factorizing operator product expansions of open string vertex operators for such branes. Applications include branes in orbifolds of the SU(2) WZW model and in the D-series of unitary minimal models considered previously by Runkel.

National Category
Natural Sciences
Identifiers
urn:nbn:se:uu:diva-92032 (URN)10.1016/S0550-3213(02)00054-8 (DOI)
Available from: 2004-09-09 Created: 2004-09-09 Last updated: 2017-12-14Bibliographically approved
3. Invariant Star Products on S 2 and the Canonical Trace
Open this publication in new window or tab >>Invariant Star Products on S 2 and the Canonical Trace
2004 (English)In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 70, no 2, p. 109-120Article in journal (Refereed) Published
Abstract [en]

We calculate the canonical trace and use the Fedosov–Nest–Tsygan index theorem to obtain the characteristic class for a star product on S 2. We show how, for this simple example, it is possible to extract the relevant information needed to use the Fedosov–Nest–Tsygan index theorem from a local calculation.

National Category
Natural Sciences
Identifiers
urn:nbn:se:uu:diva-92416 (URN)10.1007/s11005-004-4290-7 (DOI)
Available from: 2004-11-22 Created: 2004-11-22 Last updated: 2017-12-14Bibliographically approved

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