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Pseudo-Hyperkähler Geometry and Generalized Kähler Geometry
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2011 (English)In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 95, no 3, 211-222 p.Article in journal (Refereed) Published
Abstract [en]

We discuss the conditions for additional supersymmetry and twisted super-symmetry in N = (2, 2) supersymmetric nonlinear sigma models described by one left and one right semi-chiral superfield and carrying a pair of non-commuting complex structures. Focus is on linear non-manifest transformations of these fields that have an algebra that closes off-shell. We find that additional linear supersymmetry has no interesting solution, whereas additional linear twisted supersymmetry has solutions with interesting geometrical properties. We solve the conditions for invariance of the action and show that these solutions correspond to a bi-hermitian metric of signature (2, 2) and a pseudo-hyperkahler geometry of the target space.

Place, publisher, year, edition, pages
2011. Vol. 95, no 3, 211-222 p.
Keyword [en]
supersymmetry, semi-chiral fields, sigma models, pseudo-hyperkahler geometry
National Category
Physical Sciences
URN: urn:nbn:se:uu:diva-149587DOI: 10.1007/s11005-010-0456-7ISI: 000287856800001OAI: oai:DiVA.org:uu-149587DiVA: diva2:405131
Available from: 2012-10-26 Created: 2011-03-21 Last updated: 2013-02-11Bibliographically approved
In thesis
1. The Complex World of Superstrings: On Semichiral Sigma Models and N=(4,4) Supersymmetry
Open this publication in new window or tab >>The Complex World of Superstrings: On Semichiral Sigma Models and N=(4,4) Supersymmetry
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Supersträngars komplexa värld : Om semikirala sigmamodeller och N=(4,4) supersymmetri
Abstract [en]

Non-linear sigma models with extended supersymmetry have constrained target space geometries, and can serve as effective tools for investigating and constructing new geometries. Analyzing the geometrical and topological properties of sigma models is necessary to understand the underlying structures of string theory.

The most general two-dimensional sigma model with manifest N=(2,2) supersymmetry can be parametrized by chiral, twisted chiral and semichiral superfields. In the research presented in this thesis, N=(4,4) (twisted) supersymmetry is constructed for a semichiral sigma model. It is found that the model can only have additional supersymmetry off-shell if the target space has a dimension larger than four. For four-dimensional target manifolds, supersymmetry can be introduced on-shell, leading to a hyperkähler manifold, or pseudo-supersymmetry can be imposed off-shell, implying a target space which is neutral hyperkähler.

Different sigma models and corresponding geometries can be related to each other by T-duality, obtained by gauging isometries of the Lagrangian. The semichiral vector multiplet and the large vector multiplet are needed for gauging isometries mixing semichiral superfields, and chiral and twisted chiral superfields, respectively. We find transformations that close off-shell to a N=(4,4) supersymmetry on the field strengths and gauge potentials of the semichiral vector multiplet, and show that this is not possible for the large vector multiplet.

A sigma model parametrized by chiral and twisted chiral superfields can be related to a semichiral sigma model by T-duality. The N=(4,4) supersymmetry transformations of the former model are linear and close off-shell, whereas those of the latter are non-linear and close only on-shell. We show that this discrepancy can be understood from T-duality, and find the origin of the non-linear terms in the transformations.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2012. 131 p.
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 989
Non-linear sigma models, extended supersymmetry, semichiral superfields, (neutral) hyperkähler geometry, generalized Kähler geometry, T-duality, vector multiplets
National Category
Other Physics Topics
Research subject
Theoretical Physics
urn:nbn:se:uu:diva-183407 (URN)978-91-554-8519-1 (ISBN)
Public defence
2012-12-14, Häggsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Available from: 2012-11-23 Created: 2012-10-25 Last updated: 2013-02-11Bibliographically approved

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