New applications of on-shell methods in quantum field theory

Open Access
Engelund, Oluf Tang
Graduate Program:
Doctor of Philosophy
Document Type:
Date of Defense:
June 06, 2014
Committee Members:
  • Radu Roiban, Dissertation Advisor
  • Murat Gunaydin, Committee Member
  • Nigel David Higson, Committee Member
  • Jainendra Jain, Committee Member
  • Scattering Amplitudes
  • Integrability
This thesis incorporates 4 years of work: it gives a small introduction to the eld of scattering amplitudes and especially into the method of generalized unitarity then discuss 4 di erent projects all in the eld of scattering amplitudes. First we will look at a duality between correlation functions in a special lightlike limit and Wilson loops in N = 4 Super-Yang-Mills. The duality, originally suggested by Alday, Eden, Korchemsky, Maldacena and Sokatchev, was part of an e ort to put a rmer footing on the duality between scattering amplitudes and Wilson loops. The duality between correlation functions and Wilson loops does not have any regularization issues (like the other duality) as both have infrared divergences in the speci c limits considered. We show how the duality works vertex-by-vertex using just Feynman rules. The method is suciently general to allow for extensions of the original duality including operators not taking part in the special light-like limit, other types of operators as well as other theories than N = 4 Super-Yang-Mills. After that we look at how to use generalized unitarity for correlation functions with some examples from N = 4 Super-Yang-Mills. For computations one needs quantities known as form factors which have both asymptotic states like scattering amplitudes and local operators like correlation functions. We compute several form factors using modern methods from scattering amplitudes. Thirdly, we study how to use generalized unitarity for two-dimensional integrable systems. Two-dimensional systems have their own unique set of challenges but generalized unitarity can be adapted to them and we show how one can carry out tests of integrability which would otherwise be dicult. Finally, we look at the 3-dimensional theory known as ABJ(M). Its tree-level amplitudes can be incorporated into a single formula very reminiscent of a result in N = 4 Super-Yang-Mills. Since the result from N = 4 Super-Yang-Mills follow directly from a twistor string theory it is natural to guess that something similar could be true for ABJ(M). We construct a twistor string theory that after a certain set of projections give us the ABJ(M) formula.