Past Relativity Seminar
Abstract: In this talk, I will discuss the peeling behaviour of the Weyl tensor near null infinity for asymptotically flat higher dimensional spacetimes. The result is qualitatively different from the peeling property in 4d. Also, I will discuss the rewriting of the Bondi energy flux in terms of "Newman-Penrose" Weyl components.
Abstract:
Motivated by the correlation functions-Wilson loop correspondence in
maximally supersymmetric Yang-Mills theory, we will investigate a
conjecture of Alday, Buchbinder, and Tseytlin regarding correlators of
null polygonal Wilson loops with local operators in general position.
By translating the problem to twistor space, we can show that such
correlators arise by taking null limits of correlation functions in the
gauge theory, thereby providing a proof for the conjecture.
Additionally, twistor methods allow us to derive a recursive formula for
computing these correlators, akin to the BCFW recursion for scattering
amplitudes.
The WZW functional for a map from a surface to a Lie group has a role in the theory of harmonic maps, and it also arises as the determinant of a d-bar operator on the surface, as the action functional for a 2-dimensional quantum field theory, as the partition function of 3-dimensional Chern-Simons theory on a manifold with boundary, and as the norm-squared of a state-vector. It is intimately related to the quantization of the symplectic manifold of flat bundles on the surface, a fascinating test-case for different approaches to geometric quantization. It is also interesting as an example of interpolation between commutative and noncommutative geometry. I shall try to give an overview of the area, focussing on the aspects which are still not well understood.