Mathew Bullimore

Scattering amplitudes and Wilson loops in twistor space.

This paper reviews the recent progress in twistor approaches to Wilson loops, amplitudes and their duality for super-Yang?Mills. Wilson loops and amplitudes are derived from first principles using the twistor action for maximally supersymmetric Yang?Mills theory. We start by deriving the MHV rules for gauge theory amplitudes from the twistor action in an axial gauge in twistor space, and show that this gives rise to the original momentum space version given by Cachazo, Svr?ek and Witten. We then go on to obtain from these the construction of the momentum twistor space loop integrand using (planar) MHV rules and show how it arises as the expectation value of a holomorphic Wilson loop in twistor space. We explain the connection between the holomorphic Wilson loop and certain light-cone limits of correlation functions. We give a brief review of other ideas in connection with amplitudes in twistor space: twistor-strings, recursion in twistor space, the Grassmannian residue formula for leading singularities and amplitudes as polytopes. This paper is an invited review for a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ?Scattering amplitudes in gauge theories?.

MHV Diagrams in Momentum Twistor Space

We show that there are remarkable simplifications when the MHV diagram formalism for

The Coulomb Branch of 3d

\mathcal{N} = 4

{\mathcal{N}= 4}

super Yang-Mills is reformulated in momentum twistor space. The vertices are replaced by unity while each propagator becomes a dual superconformal ‘R-invariant’ whose arguments may be read off from the diagram, and include an arbitrarily chosen reference twistor. The momentum twistor MHV rules generate a formula for the full, all-loop planar integrand for the super Yang-Mills S-matrix that is manifestly dual superconformally invariant up to the choice of a reference twistor. We give a general proof of this reformulation and illustrate its use by computing the momentum twistor NMHV and N2MHV tree amplitudes and the integrands of the MHV and NMHV 1-loop and the MHV 2-loop planar amplitudes.

Theories

We propose a construction for the quantum-corrected Coulomb branch of a general 3d gauge theory with

Twistor-strings, Grassmannians and leading singularities

{\mathcal{N}=4}

Supersymmetric Casimir energy and the anomaly polynomial

N=4 supersymmetry, in terms of local coordinates associated with an abelianized theory. In a fixed complex structure, the holomorphic functions on the Coulomb branch are given by expectation values of chiral monopole operators. We construct the chiral ring of such operators, using equivariant integration over BPS moduli spaces. We also quantize the chiral ring, which corresponds to placing the 3d theory in a 2d Omega background. Then, by unifying all complex structures in a twistor space, we encode the full hyperkähler metric on the Coulomb branch. We verify our proposals in a multitude of examples, including SQCD and linear quiver gauge theories, whose Coulomb branches have alternative descriptions as solutions to Bogomolnyi and/or Nahm equations.

The Superconformal Index of the (2,0) Theory with Defects

We prove that in the limit when its insertion points become pairwise null-separated, the ratio of certain n-point correlation functions in