GALLONI, DANIELE,STEFANO (2015) Supersymmetric Field Theories, Scattering Amplitudes and the Grassmannian. Doctoral thesis, Durham University.
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In this thesis we carry out a detailed investigation of a class of four-dimensional N=1 gauge theories, known as Bipartite Field Theories (BFTs), and their utility in integrable systems and scattering amplitudes in 4-dimensional N=4 Super-Yang-Mills (SYM). We present powerful combinatorial tools for analyzing the moduli spaces of BFTs, and find an interesting connection with the matching and matroid polytopes, which play a central role in the understanding of the Grassmannian.
We use the tools from BFTs to construct (0+1)-dimensional cluster integrable systems, and propose a way of obtaining (1+1)- and (2+1)-dimensional integrable field theories.
Using the matching and matroid polytopes of BFTs, we analyze the singularity structure of planar and non-planar on-shell diagrams, which are central to modern developments of scattering amplitudes in N=4 SYM. In so doing, we uncover a new way of obtaining the positroid stratication of the Grassmannian.
We use tools from BFTs to understand the boundary structure of the amplituhedron, a recently found geometric object whose volume calculates the integrand of scattering amplitudes in planar N=4 SYM theory. We provide the most comprehensive study of the geometry of the amplituhedron to date.
We also present a detailed study of non-planar on-shell diagrams, constructing the on-shell form using two new, independent methods: a non-planar boundary measurement valid for arbitrary non-planar graphs, and a proposal for a combinatorial method to determine the on-shell form directly from the graph.
|Item Type:||Thesis (Doctoral)|
|Award:||Doctor of Philosophy|
|Faculty and Department:||Faculty of Science > Physics, Department of|
|Copyright:||Copyright of this thesis is held by the author|
|Deposited On:||04 Jun 2015 10:40|