Supersymmetry Theory in Warped Extra Dimension
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Date
2013-09-20
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Johns Hopkins University
Abstract
We study supersymmetry theory in higher dimensions. In five dimensional anti-de Sitter space, we construct the most general supersymmetric matter coupling in the rigid and gauged cases.
We use the component and warped N=1 superspace formalism. By comparing their results, we find several interesting issues related to boundary effects. For instance, Gibbons-Hawking-York terms are necessary on the AdS5 boundary.
We find the warped space version of spontaneous superpotential generation and reinterpret it as a tuning of a surface-localized Fayet-Iliopoulos term at the component level, or equivalently as a tuning of a boundary-localized superpotential in superspace. On the other hand, in the bulk, we find the N=2 Fayet-Iliopoulos term must be fixed.
We study boundary problems systematically from the variational principle. We find proper boundary conditions and consistent constraints so that all 8 supercharges are preserved on the boundary. The bulk action is then truly invariant under both supersymmetries; and super-multiplets on the boundary have close relations with the superconformal theory in four flat dimensions.
We also investigate some geometric aspects in this thesis. We discover a special type of hyper-Kahler manifold required by the AdS5 supersymmetry. Such a manifold admits an essential isometry along which two complex structures rotate into each other. We also discuss the complex geometry on the Darboux patch, which plays an important role in hypermultiplets' boundary problems.
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Keywords
supersymmetry, extra dimensions, field theory