Modern Methods for Scattering Amplitudes (Dr G Travaglini)
This project aims at constructing scattering amplitudes of elementary particles using recent ideas inspired by twistor string theory. Major progress in this field has been achieved over the past few years, leading to a reformulation and reorganisation of gauge theories and gravity, as well as to new, powerful techniques to compute scattering amplitudes - also in phenomenologically relevant theories, such as Quantum Chromodynamics. The three most important methods that emerged from these developments and which completely replace standard textbook methods (Feynman rules) are: MHV diagrams, on-shell recursion relations and generalized unitarity. Starting from the study of the symmetries of quantum field theories, the student will investigate these new techniques in detail and apply them to many concrete examples in supersymmetric and non-supersymmetric theories.
Wilson Loops and Gauge Theory/String Theory duality (Dr A Brandhuber)
In 1996 Juan Maldacena proposed a duality between (super)strings moving on Anti-de-Sitter (AdS) spacetimes and certain supersymmetric gauge. In this project the student will be introduced to the main aspects of this duality and study various examples to understand the dictionary between physical quantities on the two sides of this duality. The phases of gauge theories can be characterized by the potential V(r) between electric/magnetic charges and the student will analyse, from the dual string theory point of view, how the Coulomb law (1/r potential) between electric charges and confinement (linear potential) between quarks arise by studying Wilson loop operators. Furthermore, the recently discovered duality between lightlike polygonal Wilson loops and scattering amplitudes at weak and strong coupling will be explored.
Generalized Geometryin M-Theory (Dr DS Berman)
This project will explore the ways in which through generalising the notions of geometry one may make manifest the hidden symmetries of string and M-theory and combine the local symmetries of p-form potentials with the diffeomorphisms of general relativity.