Description
- Abstract:
- The main subject of this thesis is scattering amplitudes in N=4 super-Yang-Mills theory (SYM) and N=8 super-gravity theory (SUGRA). We study several aspects of the scattering amplitudes of these two theories using modern techniques. After the introductory chapter, we apply these methods to study the scattering amplitudes both in N=4 SYM and N=8 SUGRA. We first study two dual formulations of N=4 SYM, namely the Arkani-Hamed et al Grassmannian formulation and Witten's twistor string theory. We present a new, explicit formula for all tree-level amplitudes in N=4 SYM. The formula is written as a certain contour integral of the connected prescription of Witten's twistor string, expressed in link variables. A very simple and interesting deformation of the integrand gives directly the Grassmannian integrand proposed together with the explicit contour of integration.Then we calculate for the first time the five-point three-loop amplitudes of N=4 SYM using the leading singularity method. Using the method of obstructions we numerically evaluate two previously unfixed coefficients which appear in the three-loop BDS ansatz. After the study of N=4 SYM, we turn our journey to N=8 SUGRA by first presenting and proving a new formula for MHV scattering amplitude in SUGRA. Some of interesting features of the formula set it apart as being significantly different from many more familiar formulas. We then present an algorithm for writing down explicit formulas for all tree amplitudes in N=8 SUGRA, obtained from solving the supersymmetric on-shell recursion relations. The formula is patterned after one recently obtained for all tree amplitudes in N=4 SYM which involves nested sums of dual superconformal invariants. We find that all graviton amplitudes can be written in terms of exactly the same structure of nested sums with two modifications. To illustrate the procedure we give explicit closed-form formulas for all NMHV, NNMHV and NNNMV gravity superamplitudes. The obtained results are further simplified by applying bonus relations between gravity amplitudes, which arise from the soft behavior of tree-level gravity amplitude.
- Notes:
- Thesis (Ph.D. -- Brown University (2011)
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Citation
Wen, Congkao,
"Scattering amplitudes in N=4 SYM and N=8 SUGRA"
(2011).
Physics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.7301/Z0KS6PTK
