Dimensional Reduction, Seiberg--Witten Map and Supersymmetry

It is argued that dimensional reduction of Seiberg-Witten map for a gauge field induces Seiberg-Witten maps for the other noncommutative fields of a gauge invariant theory. We demonstrate this observation by dimensionally reducing the noncommutative N=1 SYM theory in 6 dimensions to obtain noncommutative N=2 SYM in 4 dimensions. We explicitly derive Seiberg-Witten maps of the component fields in 6 and 4 dimensions. Moreover, we give a general method to define the deformed supersymmetry transformations that leaves the actions invariant after performing the Seiberg-Witten maps.Comment: 14 pages. One Ref. added. To appear in PR

Supersymmetric field theories and cohomology

Bu çalışmada, genel anlamda süpersimetrik alan teorilerinin kohomolojik yapısı çalışılmıştır. Kohomoloji problemi süpersimetri cebri kullanılarak tanımlanmıştır. Süpersimetrik alan teorilerinin eylemlerinin ilgili çokluların en üst elemanı olduğu kullanılarak elde edilen bu kohomoloji probleminin çözümleri yardımıyla bu eylemlerin düşük boyutlu alan polinomlarının çoklu süpervaryasyonları olarak temsil edilebileceği gösterilmiştir. Bu yaklaşımın bir uygulaması olarak Wess-Zumino modelinin kohomolojik yapısı incelenmiştir. Elde edilen sonuçlardan modelin eyleminin kinetik, kütle ve etkileşme terimlerinin kabuk-dışı süpersimetrik durum için tam olarak düşük boyutlu alan polinomlarının kiral ve/veya anti-kiral çoklu süper varyasyonları ile yazılabileceği gösterilmiştir. Anahtar Kelimeler: Süpersimetri, süpersimetrik alan teorileri, kohomoloji.In this work, the cohomological structure of supersymmetric field theories is studied in a general context. Cohomology problem is defined by using the off-shell structure of the supersymmetry algebra. In order to define a cohomology problem it is crucial to use the two component (Weyl) formalism of the supersymmetry algebra, since each individual component of chiral and anti-chiral supersymmetry generators are nilpotent operators. It is then possible to show that the actions of supersymmetric field theories belong to a class of solutions of this cohomology problem and can be represented as multiple supervariations of some lower dimensional field polynomials due to the fact that the actions of supersymmetric field theories can be viewed as the highest component of respective multiplets. It is also discussed that the aforementioned algebraic structure can be thought as the algebraic source of the well-known non-renormalization theorems of several supersymmetric field theories. As an application of our method, the cohomological structure of Wess-Zumino model is discussed. It is shown that the kinetic, mass and the interaction terms can be constructed from the chiral and/or anti-chiral supervariations of the lower dimensional field polynomials for off-shell supersymmetry. It is then found out that the well known non-renormalization theorems of Wess-Zumino model is related to the terms that can only be written as pure chiral or anti-chiral supervariations of (mass) dimension three fields. Keywords: Supersymmetry, supersymmetric field theories, cohomology

Duals of noncommutative supersymmetric U(1) gauge theory

Parent actions for component fields are utilized to derive the dual of supersymmetric U(1) gauge theory in 4 dimensions. Generalization of the Seiberg-Witten map to the component fields of noncommutative supersymmetric U(1) gauge theory is analyzed. Through this transformation we proposed parent actions for noncommutative supersymmetric U(1) gauge theory as generalization of the ordinary case.Duals of noncommutative supersymmetric U(1) gauge theory are obtained. Duality symmetry under the interchange of fields with duals accompanied by the replacement of the noncommutativity parameter \Theta_{\mu\nu} with \tilde{\Theta}_{\mu \nu} = \epsilon_{\mu\nu\rho\sigma}\Theta^{\rho\sigma} of the non--supersymmetric case is broken at the level of actions. We proposed a noncommutative parent action for the component fields which generates actions possessing this duality symmetry.Comment: Typos corrected. Version which will appear in JHE

Construction of a Wilson action for the Wess-Zumino model

We construct a Wilson action for the Wess-Zumino model by applying the exact renormalization group perturbatively. Using neither superfields nor auxiliary fields, we construct a supersymmetric action only with complex scalar and Majorana spinor fields. We adopt the BRST (antifield) formalism to show the consistency of the construction to all orders in loop expansions. The resulting action has a quadratically divergent scalar mass term which is absent in the superfield formalism.Comment: 33 pages; reformatted using ptptex; accepted for publication in Progress of Theoretical Physic

Duality invariance of non-anticommutative N=1/2 supersymmetric U(1) gauge theory

A parent action is introduced to formulate (S-) dual of non-anticommutative N=1\2 supersymmetric U(1) gauge theory. Partition function for parent action in phase space is utilized to establish the equivalence of partition functions of the theories which this parent action produces. Thus, duality invariance of non-anticommutative N=1\2 supersymmetric U(1) gauge theory follows. The results which we obtained are valid at tree level or equivalently at the first order in the nonanticommutativity parameter C_{\mu\nu}.Comment: 12 pages, some comments and references are added. To appear in JHE

International Conference on Electric Power and Energy Conversion Systems

Energy is very important for countries which are developing rapidly, such as Turkey, during the fossil fuel prices are increasing. In this respect, renewable technologies such as PV systems are gaining importance in the world gradually due to its eco friendliness, easy applicability and increasing efficiency. Today, incentives for PV systems are being provided to private sector companies and people who would like to take benefit from generating energy from PV systems in Turkey. According to General Directorate on Renewable Energy (EIE), while the average annual sunshine and radiation are roundly 6.69 hour and 3.6 kWh/m(2)-day for Istanbul respectively, they are roundly 8.25 hour and 4.5 kWh/m(2)-day for Antalya. This paper makes an overview on PV systems and examines the financial outcome of PV system investment in Turkey. Two locations, Istanbul and Antalya, were taken into account in installing/constructing a PV Plant and these two systems were examined and compared in terms of their prices, feasibility, solar efficiencies regarding the location and future financial performances