uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Generalized Kähler geometry from supersymmetric sigma models
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Theoretical Physics.
2006 (English)In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 77, no 3, 291-308 p.Article in journal (Refereed) Published
Abstract [en]

We give a physical derivation of generalized Kahler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri (Generalized complex geometry, DPhil thesis, Oxford University, 2004) regarding the equivalence between generalized Kahler geometry and the bi-hermitean geometry of Gates et al. (Nucl Phys B248:157, 1984). When cast in the language of supersymmetric sigma models, this relation maps precisely to that between the Lagrangian and the Hamiltonian formalisms. We also discuss topological twist in this context.

Place, publisher, year, edition, pages
2006. Vol. 77, no 3, 291-308 p.
Keyword [en]
generalized kahler geometry, supersymmetric sigma models
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:uu:diva-94767DOI: 10.1007/s11005-006-0099-xISI: 000240126700006OAI: oai:DiVA.org:uu-94767DiVA: diva2:168740
Available from: 2006-09-08 Created: 2006-09-08 Last updated: 2011-06-21Bibliographically approved
In thesis
1. Tensionless Strings and Supersymmetric Sigma Models: Aspects of the Target Space Geometry
Open this publication in new window or tab >>Tensionless Strings and Supersymmetric Sigma Models: Aspects of the Target Space Geometry
2006 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, two aspects of string theory are discussed, tensionless strings and supersymmetric sigma models.

The equivalent to a massless particle in string theory is a tensionless string. Even almost 30 years after it was first mentioned, it is still quite poorly understood. We discuss how tensionless strings give rise to exact solutions to supergravity and solve closed tensionless string theory in the ten dimensional maximally supersymmetric plane wave background, a contraction of AdS(5)xS(5) where tensionless strings are of great interest due to their proposed relation to higher spin gauge theory via the AdS/CFT correspondence.

For a sigma model, the amount of supersymmetry on its worldsheet restricts the geometry of the target space. For N=(2,2) supersymmetry, for example, the target space has to be bi-hermitian. Recently, with generalized complex geometry, a new mathematical framework was developed that is especially suited to discuss the target space geometry of sigma models in a Hamiltonian formulation. Bi-hermitian geometry is so-called generalized Kähler geometry but the relation is involved. We discuss various amounts of supersymmetry in phase space and show that this relation can be established by considering the equivalence between the Hamilton and Lagrange formulation of the sigma model. In the study of generalized supersymmetric sigma models, we find objects that favor a geometrical interpretation beyond generalized complex geometry.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2006. viii+87 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 209
Keyword
Theoretical physics, Theoretical Physics, String Theory, Tensionless Strings, Supergravity Backgrounds, Plane Wave, Supersymmetry, Non-linear Sigma Models, Generalized Complex Geometry, Teoretisk fysik
Identifiers
urn:nbn:se:uu:diva-7105 (URN)91-554-6632-X (ISBN)
Public defence
2006-09-30, Häggsalen, Ångström Laboratory, Lägerhyddsvägen 1, Uppsala, 13:00
Opponent
Supervisors
Available from: 2006-09-08 Created: 2006-09-08Bibliographically approved
2. Strings as Sigma Models and in the Tensionless Limit
Open this publication in new window or tab >>Strings as Sigma Models and in the Tensionless Limit
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis considers two different aspects of string theory, the tensionless limit of the string and supersymmetric sigma models with extended supersymmetry. First, the tensionless limit is used to find a IIB supergravity background generated by a tensionless string. The background has the characteristics of a gravitational shock-wave. Then, the quantization of the tensionless string in a pp-wave background is performed and the result is found to agree with what is obtained by taking a tensionless limit directly in the quantized theory of the tensile string. Hence, in the pp-wave background the tensionless limit commutes with quantization. Next, supersymmetric sigma models and the relation between extended world-sheet supersymmetry and target space geometry is studied. The sigma model with N=(2,2) extended supersymmetry is considered and the requirement on the target space to have a bi-Hermitean geometry is reviewed. The Hamiltonian formulation of the model is constructed and the target space is shown to have generalized Kähler geometry. The equivalence between bi-Hermitean geometry and generalized Kähler follows, in this context, from the equivalence between the Lagrangian- and Hamiltonian formulation of the sigma model. Then, T-duality in the Hamiltonian formulation of the sigma model is studied and the explicit T-duality transformation is constructed. It is shown that the transformation is a symplectomorphism, i.e. a generalization of a canonical transformation. Under certain assumptions, the amount of extended supersymmetry present in the sigma model is shown to be preserved under the T-duality transformation. Next, extended supersymmetry in a first order formulation of the sigma model is studied. By requiring N=(2,2) extended world-sheet supersymmetry an intriguing geometrical structure arises and in a special case generalized complex geometry is found to be contained in the new framework.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2007. viii+127 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 286
Keyword
Theoretical physics, Theoretical Physics, String Theory, Tensionless Strings, Supergravity Backgrounds, Plane Wave, Extended Supersymmetry, Non-Linear Sigma Models, Generalized Complex Geometry, T-duality, Teoretisk fysik
Identifiers
urn:nbn:se:uu:diva-7783 (URN)978-91-554-6848-4 (ISBN)
Public defence
2007-04-27, Häggsalen, Ångström Laboratory, Lägerhyddsvägen 1, Uppsala, 13:15
Opponent
Supervisors
Available from: 2007-04-03 Created: 2007-04-03 Last updated: 2011-06-21Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Authority records BETA

Bredthauer, AndreasLindström, UlfPersson, JonasZabzine, Maxim

Search in DiVA

By author/editor
Bredthauer, AndreasLindström, UlfPersson, JonasZabzine, Maxim
By organisation
Department of Theoretical Physics
In the same journal
Letters in Mathematical Physics
Physical Sciences

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 484 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf