The critical O(N) models are one of the most thoroughly studied classes of conformal field theories (CFTs) in three dimensions. Indeed, there exists a variety of approximation methods applicable to them, such as epsilon expansion, large N expansion or conformal bootstrap. It is then of interest to study the 3-dimensional O(N) models with interfaces (co-dimension 1 defects), as well as on spaces with boundaries. In particular, we are interested in “extraordinary” critical interfaces and boundaries which break the O(N) symmetry to O(N −1). Such models were studied recently with a D-dimensional bulk and surface defects quadratic in the fields. In this talk, we will adopt a different approach and study defects that are always of co-dimension 1. More precisely, I will present the renormalization group analysis for a quartic O(N) model in 4 − ε dimensions with cubic interactions on an interface. For sufficiently large N, we find stable IR fixed points with purely imaginary cubic couplings. I will also review the special case N = 1 corresponding to a boundary Yang-Lee model.
This video was produced by the University of Münster, as part of the workshop Stochastic Analysis meets QFT – critical theory.
