Supersymmetry, supergravity and strings

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The  proposed research, primarily in the area of elementary particle physics with emphasis on string theory  will help in the effort to understand how the physical world, at its most basic constituents, functions. String theory is believed to provide answers to many of the questions that Einstein and many other scientists have puzzled over for at least a century. We need to understand why the elementary particles,  electrons, quarks, etc. have the masses they have, what the forces between them are, and, ultimately, why they are grouped into several families with similar properties.The specific work to be supported by the grant will use certain concepts and techniques that go by such names as superspace, superfields and supergraphs, to perform calculations that should provide insights and partial results about certain quantum fields (quantities which describe mathematicaly specific particles). This research topic is described under the titles  " Non-anticommutative supersymmetric field theories" and  "String-loop calculations in the GS-Berkovits formalism".Other work falls under the topic "Geometric transitions, dualities, non-Kahler manifolds and sigma models." In the string theory description of elementary particles and their interactions, it is believed that our world is ten-dimensional, with six of the dimensions very small and essentially unobservable. These dimensions are curled up, and twisted, and distorted in a very complicated way; they fall under the mathematical classification of "manifold".The specific manner in which some of the  properties of elementary particles. There are many possible manifolds and the aim of the proposed research is to pin down the manifold which corresponds to our known world.