Narrow Results

We propose an N = 2 twisted superspace formalism with a central charge in four dimensions by introducing a Dirac–Kähler twist. Using this formalism, we construct an off-shell twisted hypermultiplet action and find an explicit form of fermionic scalar, vector and tensor transformations. We construct an off-shell Donaldson–Witten theory coupled to the twisted hypermultiplet. We show that this action possesses N = 4 twisted supersymmetry at the on-shell level. It turns out that the four-dimensional Dirac–Kähler twist is equivalent to Marcus' twist.

We propose a twisted D=N=2 superspace formalism. The relation between the twisted super charges including the BRST charge, vector and pseudoscalar super charges and the N=2 spinor super charges is established. We claim that this relation is essentially related with the Dirac–Kähler fermion mechanism. We show that a fermionic bilinear form of twisted N=2 chiral and anti-chiral superfields is equivalent to the quantized version of BF theory with the Landau type gauge fixing while a bosonic bilinear form leads to the N=2 Wess–Zumino action. We then construct a Yang–Mills action described by the twisted N=2 chiral and vector superfields, and show that the action is equivalent to the twisted version of the D=N=2 super Yang–Mills action, previously obtained from the quantized generalized topological Yang–Mills action with instanton gauge fixing.

Although the meaning of twisted symmetry is still not fully understood, the twist approach has its advantages in the construction of field theories on noncommutative spaces. We discuss these advantages on the example of κ-Minkowski space-time. We construct the noncommutative U(1) gauge field theory. Especially the action is written as an integral of a maximal form, thus solving the cyclicity problem of the integral in κ-Minkowski. Using the Seiberg-Witten map to relate noncommutative and commutative degrees of freedom the effective action with the first order corrections in the deformation parameter is obtained.

This is intend to provide an overview of the theory and phenomenology parts of the TMD (Transverse Momentum Dependent parton distribution and fragmentation functions) studies. By comparing with the theoretical framework that we have for the inclusive deep inelastic lepton-nucleon scattering and the one-dimensional imaging of the nucleon, I try to outline what we need to do in order to construct a comprehensive theoretical framework for semi-inclusive reactions and the three dimensional imaging of the nucleon. After that, I try to give an overview of what we have already achieved and make an outlook for the future.