Lonti Autumn 2021 Series: Lecture 1. Live Tutorial. Please register at https://lonti.weebly.com/registration.html to receive joining instructions for this live session which will be held via Zoom. Four examples of an anomaly are presented, two from quantum mechanics and two from quantum field theory. The first example is a charged bead on a wire in the presence of a magnetic field. This example of a 't Hooft anomaly is related to the theta angle in Yang-Mills theory. The remaining three examples present scale and conformal anomalies. We will scatter a plane wave off an attractive delta function in two dimensions. We also look at a massless scalar field, both in two dimensions without a boundary and in three dimensions with one.

Lonti Autumn 2021 Series: Lecture 1. Release of Recorded Lecture. Available here: https://youtu.be/hiUnq_5iiPM. Four examples of an anomaly are presented, two from quantum mechanics and two from quantum field theory. The first example is a charged bead on a wire in the presence of a magnetic field. This example of a 't Hooft anomaly is related to the theta angle in Yang-Mills theory. The remaining three examples present scale and conformal anomalies. We will scatter a plane wave off an attractive delta function in two dimensions. We also look at a massless scalar field, both in two dimensions without a boundary and in three dimensions with one.

The infrared fixed point of graphene under the renormalization group flow is a relatively under studied yet important example of a boundary conformal field theory with a number of remarkable properties. It has a close relationship with three dimensional QED. It maps to itself under electric-magnetic duality. Moreover, it along with its supersymmetric cousins all possess an exactly marginal coupling -- the charge of the electron -- which allows for straightforward perturbative calculations in the weak coupling limit. I will review past work on this model and also discuss my own contributions, which focus on understanding the boundary contributions to the anomalous trace of the stress tensor and their role in helping to understand the structure of boundary conformal field theory.

The infrared fixed point of graphene under the renormalization group flow is a relatively under studied yet important example of a boundary conformal field theory with a number of remarkable properties. It has a close relationship with three dimensional QED. It maps to itself under electric-magnetic duality. Moreover, it along with its supersymmetric cousins all possess an exactly marginal coupling -- the charge of the electron -- which allows for straightforward perturbative calculations in the weak coupling limit. I will review past work on this model and also discuss my own contributions, which focus on understanding the boundary contributions to the anomalous trace of the stress tensor and their role in helping to understand the structure of boundary conformal field theory.

I discuss some aspects of boundary conformal field theories (bCFTs) with an emphasis on space-time dimensions greater than two. I will demonstrate that free bCFTs have a universal way of satisfying crossing symmetry constraints. I will introduce a simple class of interacting bCFTs where the interaction is restricted to the boundary. Finally, I will discuss relationships between boundary trace anomalies and boundary limits of stress-tensor correlation functions. (Tea and biscuits + wine at the end!)