We will motivate and introduce the study of conformal defects in superconformal field theories (SCFTs). We will show how symmetries constrain the anomaly coefficients of BPS defects. In the case of N=(2,2) surface defects in four-dimensional N=2 SCFTs these anomaly coefficients can be computed by studying a protected sub-sector captured by a two-dimensional chiral algebra. [please email a.held@imperial.ac.uk for zoom link or password]

We study symmetry constraints on BPS surface defects in four-dimensional superconformal field theories, showing how supersymmetry imposes relations on anomaly coefficients. Turning to dynamics, we analyze a protected subsector of N=(2,2) surface defects that is captured by a two-dimensional chiral algebra. We discuss how to compute observables of interacting defects from the chiral algebra, including the aforementioned anomaly coefficients.

In this talk we will discuss the bootstrap program applied to four-dimensional N=2 superconformal field theories, with focus on analytical results. After a brief review of the protected subsector captured by a two-dimensional chiral algebra, we will show how analytic bounds on anomaly coefficients are obtained and constrain the space of allowed SCFTs. Finally we will comment the implications for the numerical bootstrap program.