Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
arXiv:hep-th/0603098
Abstract
In this thesis, we report on results in non-anticommutative field theory and twistor string theory, trying to be self-contained. We first review the construction of non-anticommutative N=4 super Yang-Mills theory and discuss a Drinfeld-twist which allows to regain a twisted supersymmetry in the non-anticommutative setting. This symmetry then leads to twisted chiral rings and supersymmetric Ward-Takahashi identities, which, when combined with the usual naturalness argument by Seiberg, could yield non-renormalization theorems for non-anticommutative field theories. The major part of this thesis consists of a discussion of various geometric aspects of the Penrose-Ward transform. We present in detail the case of N=4 super Yang-Mills theory and its self-dual truncation. Furthermore, we study reductions of the supertwistor space to exotic supermanifolds having even nilpotent dimensions as well as dimensional reductions to mini-supertwistor and mini-superambitwistor spaces. Eventually, we present two pairs of matrix models in the context of twistor string theory, and find a relation between the ADHM- and Nahm-constructions and topological D-brane configurations.
PhD thesis, 280 pages, 9 figures
References in corpus (12)
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- TASI Lectures on Solitons
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- Deformations of Euclidean Supersymmetries
- BRST quantization of Matrix Chern-Simons Theory
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- Twisted Supersymmetry, Fermion-Boson Mixing and Removal of UV-IR Mixing
- Lorentz invariant supersymmetric mechanism for non(anti)commutative deformations of space-time geometry
- Progress in study of N=4 SYM effective action