Description
- Abstract:
- In recent years there have been significant progresses in the understanding of scattering amplitudes at both strong and weak coupling. There are new dualities discovered, new symmetries demystified and new hidden structures unearthed. And we will discuss these aspects of planar scattering amplitudes in N = 4 Super Yang-Mills theory in this dissertation.Firstly, we review the discovery and development of a new symmetry: the dual superconformal symmetry. Inspired by this we present our study of dual conformally invariant off-shell four-point Feynman diagrams. We classify all such diagramsthrough four loops and evaluate 10 new off-shell integrals in terms of Mellin-Barnes representations, also finding explicit expression for their infrared singularities.Secondly, we discuss about the recent progress on the calculation of Wilson loops at both strong and weak coupling. A remarkable feature of light-like polygon Wilson loops is their conjectured duality to MHV scattering amplitudes, which apparentlyholds at all orders in perturbation as well as non-perturbation theories. We demonstrate, by explicit calculation, the completely unanticipated fact that the duality continues to hold at two loops through order epsilon in dimensional regularization for both the four-particle amplitude and the (parity-even part of the) five-particle amplitude.Finally, we discuss about the structure of scattering amplitudes in N = 8 Super Gravity. We present and prove a new formula for the MHV scattering amplitude of n gravitons at tree level. Some of the more interesting features of this formula, which set itapart as being significantly different from many more familiar formulas, include the absence of any vestigial reference to a cyclic ordering of the gravitons and the fact that it simultaneously manifests both Sn-2 symmetry as well as large-z behavior. The formula is seemingly related to others by an enormous simplification providedby O(n) iterated Schouten identities, but our proof relies on a complex analysis argument rather than such a brute force manipulation. We find that the formula has a very simple link representation in twistor space, where cancellations that arenon-obvious in physical space become manifest.
- Notes:
- Thesis (Ph.D. -- Brown University (2011)
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Citation
Nguyen, Dung Van Tien,
"Aspects of Scattering Amplitudes: Symmetry and Duality"
(2011).
Physics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.7301/Z0BG2M7B
