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The Complex World of Superstrings: On Semichiral Sigma Models and N=(4,4) Supersymmetry
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2012 (English)Doctoral thesis, comprehensive summary (Other academic)Alternative title
Supersträngars komplexa värld : Om semikirala sigmamodeller och N=(4,4) supersymmetri (Swedish)
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. , p. 131
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 989
Keyword [en]
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
Identifiers
URN: urn:nbn:se:uu:diva-183407ISBN: 978-91-554-8519-1 (print)OAI: oai:DiVA.org:uu-183407DiVA, id: diva2:562965
Public defence
2012-12-14, Häggsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2012-11-23 Created: 2012-10-25 Last updated: 2013-02-11Bibliographically approved
List of papers
1. Pseudo-Hyperkähler Geometry and Generalized Kähler Geometry
Open this publication in new window or tab >>Pseudo-Hyperkähler Geometry and Generalized Kähler Geometry
2011 (English)In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 95, no 3, p. 211-222Article 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.

Keyword
supersymmetry, semi-chiral fields, sigma models, pseudo-hyperkahler geometry
National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-149587 (URN)10.1007/s11005-010-0456-7 (DOI)000287856800001 ()
Available from: 2012-10-26 Created: 2011-03-21 Last updated: 2017-12-11Bibliographically approved
2. Sigma models with off-shell N = (4,4) supersymmetry and non-commuting complex structures
Open this publication in new window or tab >>Sigma models with off-shell N = (4,4) supersymmetry and non-commuting complex structures
2010 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 9, p. 055-Article in journal (Refereed) Published
Abstract [en]

We describe the conditions for extra supersymmetry in N = (2, 2) supersymmetric nonlinear sigma models written in terms of semichiral superfields. We find that some of these models have additional off-shell supersymmetry. The (4, 4) supersymmetry introduces geometrical structures on the target-space which are conveniently described in terms of Yano f-structures and Magri-Morosi concomitants. On-shell, we relate the new structures to the known bi-hypercomplex structures.

Keyword
Extended Supersymmetry, Sigma Models, Differential and Algebraic Geometry
National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-135092 (URN)10.1007/JHEP09(2010)055 (DOI)000282370900002 ()
Available from: 2010-12-06 Created: 2010-12-03 Last updated: 2017-12-11Bibliographically approved
3. Off-shell N = (4,4) supersymmetry for new (2,2) vector multiplets
Open this publication in new window or tab >>Off-shell N = (4,4) supersymmetry for new (2,2) vector multiplets
2011 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 3, p. 088-Article in journal (Refereed) Published
Abstract [en]

We discuss the conditions for extra supersymmetry of the N = (2, 2) super-symmetric vector multiplets described in arXiv:0705.3201 [hep-th] and in arXiv:0808.1535 [hep-th]. We find (4, 4) supersymmetry for the semichiral vector multiplet but not for the Large Vector Multiplet.

Keyword
Supersymmetry and Duality, Superspaces, Differential and Algebraic Geometry
National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-153951 (URN)10.1007/JHEP03(2011)088 (DOI)000289295300016 ()
Available from: 2011-05-26 Created: 2011-05-23 Last updated: 2017-12-11Bibliographically approved
4. Semichiral Sigma Models with 4D Hyperkähler Geometry
Open this publication in new window or tab >>Semichiral Sigma Models with 4D Hyperkähler Geometry
2013 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 1, p. 073-Article in journal (Refereed) Published
Abstract [en]

Semichiral sigma models with a four-dimensional target space do not support, extended N = (4, 4) supersymmetries off-shell [1, 2]. We contribute towards the understanding of the non-manifest on-shell transformations in (2,2) superspace by analyzing the extended on-shell supersymmetry of such models and find that a rather general ansatz for the additional supersymmetry (not involving central charge transformations) leads to hyperkahler geometry. We give non-trivial examples of these models.

National Category
Other Physics Topics
Identifiers
urn:nbn:se:uu:diva-183358 (URN)10.1007/JHEP01(2013)073 (DOI)000315583200073 ()
Available from: 2012-10-24 Created: 2012-10-24 Last updated: 2017-12-07Bibliographically approved
5. N=(4,4) supersymmetry and T-duality
Open this publication in new window or tab >>N=(4,4) supersymmetry and T-duality
2012 (English)In: Symmetry, ISSN 2073-8994, Vol. 4, no 4, p. 603-625Article in journal (Refereed) Published
Place, publisher, year, edition, pages
MDPI, 2012
Keyword
supersymmetry, sigma models, semichiral superfields, T-duality
National Category
Other Physics Topics
Research subject
High Energy Physics; Mathematics
Identifiers
urn:nbn:se:uu:diva-183406 (URN)10.3390/sym4040603 (DOI)000208832800003 ()
Available from: 2012-10-26 Created: 2012-10-25 Last updated: 2015-01-28Bibliographically approved

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