All order Seiberg-Witten maps of gauge parameter, gauge field and matter fields are given as a closed recursive formula. These maps are obtained by analyzing the order by order solutions of the gauge consistency and equivalence conditions as well as by directly solving Seiberg-Witten differential equations. The explicit third order non-abelian and fourth order abelian Seiberg-Witten maps of gauge parameter and gauge field are also presented..

In this work we investigate the structure of neutron stars in modified f (T ) gravity models. We find that, unlike the f (R) models, the equations of motion put a rather strict constraint on the possible f (T ) functions. Specifically, after analyzing the problem in two different choice of coordinates with spherical symmetry, we conclude that the relativistic neutron star solution in f (T ) gravity models is possible only if f (T ) is a linear function of the torsion scalar T , that is in the case of Teleparallel Equivalent of General Relativity.

We solve the Einstein equations for the 2+1 dimensions with and without scalar fields. We calculate the entropy, Hawking temperature and the emission probabilities for these cases. We also compute the Newman-Penrose coefficients for different solutions and compare them.

Lagrangians of the Abelian Gauge Theory and its dual are related in terms of a shifted action. We show that in d = 4 constrained Hamiltonian formulation of the shifted action yields Hamiltonian description of the dual theory, without referring to its Lagrangian. We apply this method, at the first order in the noncommutativity parameter θ, to the noncommutative U (1) gauge theory possessing spatial noncommutativity. Its dual theory is effectively a space-time noncommutative U (1) gauge theory. However, we obtain a Hamiltonian formulation where time is commuting. Space-time noncommutative D3brane worldvolume Hamiltonian is derived as the dual of space noncommutative U (1) gauge theory. We show that a BPS like bound can be obtained and it is saturated for configurations which are the same with the ordinary D3-brane BIon and dyon solutions.

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 Θ µν withΘ µν = g 2 ǫ µνρσ Θ ρσ 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.