Week 17.04.2023 – 23.04.2023

In this talk, I explore the set of line defects supported by 3D N=4 theories, and their significance in the context of generalised symmetries. I begin by discussing mirror symmetry of line defects using the example of Sp(k) SQCD and its two mirror theories. I then introduce rational Q-systems, a powerful technique borrowed from spin-chains/integrability, for evaluating twisted indices and studying line operator correlation functions. Finally, I highlight the role of line defects in realising mirror symmetry in the presence of non-trivial higher symmetries

When computing scattering amplitudes in dimensional regularization, one frequently encounters contributions whose integrands vanish in strictly four dimensions. While these "evanescent" integrals can be handled with dimensional shift identities at one-loop, a similar treatment at the next perturbative order is insufficient. In this talk, we introduce a novel systematic method to compute evanescent contributions. By employing the local subtraction method of Anastasiou and Sterman we show that evanescent Feynman integrals are controlled by regions of loop-momentum space associated to ultra-violet, soft or collinear divergences. These integrals are then reduced to either products of one-loop integrals or one-fold integrals thereof. Starting from known integrands, we use this technique to easily recompute the leading-color two-loop four- and five-gluon QCD amplitudes in the all-plus helicity configuration. Remarkably, we find that the finite remainder is given by contributions arising from only ultra-violet regions of momentum space, and that the collinear contributions cancel in a highly non-trivial way.