Branes between geometry and gauge theory

The subject of this work is part of the theory of strings and in particular concerned with geometrical aspects of the realization or gauge theory with in string theory. In particular we study the gauge theory of D3-branes at g eneralised singularities like orbifolds and the orbifolded conifold singula rities. The introduction of the so called diamonds leads to a consistent pi cture. The action of mirror symmetry for this class of models is discussed. In a second part the field theory of the M5-brane will be investigated on t he basis of the superembedding approach. The main result here will be a rat tler explicit identification of the self dual three form field with the par ameters of the complex structure of the embedding space. The heuristic material collected from the previous chapters states that the information contained in supersymmetric 3-cycles can be partially extracte d from supersymmetric 2-cycles. Thus we study dir case of brane boxes, whic h can be obtained by sewing together usual N = 2 setups of D4 and NS5- bran es. These systems satisfy the condition of uniform bending and the lift to a supersymmetric 3-cycle can be performed explicitly. In the last part a new superconformal N = 1 gauge theories will be construc ted which arise as certain deformations of N = 4 SYM and have a dual descri ption due to the AdS/CFT correspondence.