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Cohomological localization of Chern-Simons theory
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2011 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 8, 8- p.Article in journal (Refereed) Published
Abstract [en]

We generalize the framework introduced by Kapustin et al. for doing path integral localization in Chern-Simons theory to work on any Seifert manifold. This is done by topologically twisting the supersymmetric theory considered by Kapustin et al., after which the theory takes a cohomological form. We also consider Wilson loops which wrap the fiber directions and compute their expectation values. We discuss the relation with other approaches to exact path integral calculations in Chern-Simons theory.

Place, publisher, year, edition, pages
2011. no 8, 8- p.
Keyword [en]
Chern-Simons Theories, Topological Field Theories, Supersymmetric gauge theory
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:uu:diva-160219DOI: 10.1007/JHEP08(2011)008ISI: 000294901400074OAI: oai:DiVA.org:uu-160219DiVA: diva2:448721
Available from: 2011-10-18 Created: 2011-10-18 Last updated: 2017-12-08Bibliographically approved
In thesis
1. Twisting and Gluing: On Topological Field Theories, Sigma Models and Vertex Algebras
Open this publication in new window or tab >>Twisting and Gluing: On Topological Field Theories, Sigma Models and Vertex Algebras
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of two parts, which can be read separately. In the first part we study aspects of topological field theories. We show how to topologically twist three-dimensional N=2 supersymmetric Chern-Simons theory using a contact structure on the underlying manifold. This gives us a formulation of Chern-Simons theory together with a set of auxiliary fields and an odd symmetry. For Seifert manifolds, we show how to use this odd symmetry to localize the path integral of Chern-Simons theory. The formulation of three-dimensional Chern-Simons theory using a contact structure admits natural generalizations to higher dimensions. We introduce and study these theories. The focus is on the five-dimensional theory, which can be understood as a topologically twisted version of N=1 supersymmetric Yang-Mills theory. When formulated on contact manifolds that are circle fibrations over a symplectic manifold, it localizes to contact instantons. For the theory on the five-sphere, we show that the perturbative part of the partition function is given by a matrix model.

In the second part of the thesis, we study supersymmetric sigma models in the Hamiltonian formalism, both in a classical and in a quantum mechanical setup. We argue that the so called Chiral de Rham complex, which is a sheaf of vertex algebras, is a natural framework to understand quantum aspects of supersymmetric sigma models in the Hamiltonian formalism. We show how a class of currents which generate symmetry algebras for the classical sigma model can be defined within the Chiral de Rham complex framework, and for a six-dimensional Calabi-Yau manifold we calculate the equal-time commutators between the currents and show that they generate the Odake algebra.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2012. 95 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 938
Keyword
Topological field theory, Chern-Simons theory, Contact geometry, Sigma models, Poisson vertex algebras, Vertex algebras, String theory
National Category
Other Physics Topics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:uu:diva-173225 (URN)978-91-554-8379-1 (ISBN)
Public defence
2012-06-08, Häggsalen, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2012-05-16 Created: 2012-04-20 Last updated: 2012-08-01Bibliographically approved

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