Relativity Seminar (past)

Abstract: In this talk, I will discuss the proportionality between tree amplitudes and the ultraviolet divergences in their one-loop corrections in Yang-Mills and (N < 4) Super Yang-Mills theories in four-dimensions. From the point of view of local perturbative quantum field theory, i.e. Feynman diagrams, this proportionality is straightforward: ultraviolet divergences at loop-level are absorbed into coefficients of local operators/interaction vertices in the original tree-amplitude. Ultraviolet divergences in loop amplitudes are also calculable through on-shell methods. These methods ensure manifest gauge-invariance, even at loop-level (no ghosts), at the expense of manifest locality. From an on-shell perspective, the proportionality between the ultraviolet divergences the tree amplitudes is thus not guaranteed. I describe systematic structures which ensure proportionality, and their possible connections to other recent developments in the field.

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.