서강대학교

초록/요약

Duality aspects of string dynamics, its topological objects and their relations with lower and higher dimensional super symmetric Yang Mill theories in curved space and time are studied using languages of supersymmetric gauged nonlinear sigma model. Super space formulation is adopted rather than super coset formalism for its explicit realization. Bearing in mind T-duality we investigate vortex solutions on string world sheet embedded in two dimensional curved target space. Four-dimensional N=1 SYM theory with arbitray holomorphic superpotential and its membrane description in plane wave background are stated revealing implications of super potential on the lower dimensional field theories and especially on string world sheet. Two new theories of interacting membranes were proposed by Bagger, Lambert and Gustavsson in the late 2007 and Aharony-Bergman-Jafferis-Maldacena in 2008. Bagger-Lambert- Gustavsson theory set a new start on the subject but has been unsuccessful failing to give generic finite representations for the three algebra structure by which the membrane interaction is described. Aharony-Bergman-Jafferis-Maldacena theory cured this problem proposing generic representations but has failed to give explicit realization of the maximally supersymmetric theory. In spite of such weaknesses, still the new membrane theory include abundant structures to explore. It has several classes of BPS configurations according to its unbroken global symmetries and each classes have large number of different objects. We investigate various supersymmetric objects of the theory and examine several possibilities for the existence of regular solutions. Finally we find an Abelian vortex in the interacting membrane theory with regular and finite energy profile in funny structures.