DUALITY COVARIANT SOLUTIONS IN EXTENDED FIELD THEORIES
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Double ﬁeld theory and exceptional ﬁeld theory are formulations of supergravity that make certain dualities manifest symmetries of the action. To achieve this, the geometry is extended by including dual coordinates corresponding to winding modes of the fundamental objects. This geometrically uniﬁes the spacetime metric and the gauge ﬁelds (and their local symmetries) in a generalized geometry. Solutions to these extended ﬁeld theories take the simple form of waves and monopoles in the extended space. From a supergravity point of view they appear as 1/2 BPS objects such as the string, the membrane and the ﬁvebrane in ordinary spacetime. In this thesis double ﬁeld theory and exceptional ﬁeld theory are introduced, solutions to their equations of motion are constructed and their properties are analyzed. Further it is established how isometries in the extended space give rise to duality relations between the supergravity solutions. Extensions to these core ideas include studying Goldstone modes, probing singularities at the core of solutions and localizing them in winding space. The relation of exceptional ﬁeld theory to F-theory is also covered providing an action for the latter and incorporating the duality between M-theory and F-theory.
AuthorsRudolph, Felix J
- Theses