Week 01.05.2023 – 07.05.2023

These three lectures will aim to provide a pedagogical introduction to the dynamics of N=2 supersymmetric gauge theory and the work of Seiberg and Witten. We will assume only basic knowledge of supersymmetry.

Please visit https://lonti.weebly.com/spring-2023-series.html for more information.

The Thirring Model is a covariant quantum field theory of interacting fermions, sharing many features in common with effective theories of two-dimensional electronic systems with linear dispersion such as graphene. For a small number of flavors and sufficiently strong interactions the ground state may be disrupted by condensation of particle-hole pairs leading to a quantum critical point. With no small dimensionless parameters in play in this regime the Thirring model is plausibly the simplest theory of fermions requiring a numerical solution. I will review what is currently known focussing on recent simulations employing Domain Wall Fermions (a formulation drawn from state-of-the-art QCD simulation), to faithfully capture the underlying symmetries at the critical point, focussing on the symmetry-breaking transition, the critical flavor number, and the anomalous scaling of the propagating fermion.

The twisted holography program (1812.09257) describes a duality that is conjectured to be a topologically twisted version of the familiar AdS_5/CFT_4 correspondence. In the bulk this involves the topological B-model on \mathbb{C}^3. Including the D-branes on which the dual CFT lives, there is a backreaction that deforms the bulk geometry.
Recently, twisted holography has made contact with the celestial holography program (2201.02595) which led to the first concrete 4d/2d dual pair in asymptotically flat spacetime (2208.14233). I will try to discuss the role of branes and backreactions in this context and potentially some extensions that my supervisor David Skinner and me have worked out (to appear).