Twenty-Fourth Meeting of the North British Mathematical Physics Seminar

The talk deals with periodic arrays of BPS monopoles: either singly-periodic (monopole chains), or doubly-periodic (monopole sheets or walls). In the first half, we see how partial information about the geometry of the 2-monopole-chain moduli space --- an "ALG" gravitational instanton --- relates to the scattering of monopole chains. In the second half, I shall review monopole walls, and relate them to recent work on monopole bags.

Exact S-matrices play a fundamental role in integrable 1+1 dimensional relativistic QFTs. This is also true in AdS_5/CFT_4. Indeed, an all-loops S-matrix has been proposed which leads to all-loops asymptotic Bethe ansatz equations and to exact finite-size results. In the recently-discovered AdS_4/CFT_3 correspondence, an exact S-matrix is again expected to play a fundamental role. This talk reviews a proposal for this S-matrix and some checks on its validity. (Based on joint work with Changrim Ahn.)

It has been shown that the CSW rules for gluon scattering amplitudes can be accounted for by canonically transformed Yang-Mills lagrangian. We extend the method to N=1 and N=4 SYM to generate the corresponding rules for supersymmetric theories. Vertices are found to agree with the formula for MHV super-amplitudes.