Maximal supersymmetry and geometry

Research Project, 2012 – 2014

The purpose of the project is to study how a high degree of supersymmetry, such as is present in string theory, can be used for an efficient formulation of physical models and for extracting concrete results about their quantum-mechanical behaviour. The method I intend to use is the formulation of maximally (and some non-maximally) supersymmetric gauge and gravity theories using pure spinor superfields. The appropriate language is the Batalin-Vilkovisky (BV) formalism, which provides a natural cohomological interpretation of the degrees of freedom. This is known for super-Yang-Mills theory in ten dimensions, for supergravity in eleven dimensions and other models. I will turn to the problem that ten years ago became the starting point for the formalism: the question of higher derivative terms. While we then managed to extract one correction to super-Yang-Mills theory at the level of the equations of motion, it is now becoming clear that the BV formalism and master equation will treat the deformations much more economically, and it is maybe even realistic to ask questions about non-abelian Born-Infeld theory. Another issue is the conceptual basis for gravitational models. The action for eleven-dimensional supergravity is polynomial, contrary to expectations. The price which is payed is loss of manifest background invariance. I will examine if it can be recovered and how the action gives rise to geometry. Also other problems in this and other areas will be studied.

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