Abstract:
Coleman’s theorem states that continuous internal symmetries cannot be spontaneously broken in two-dimensional quantum field theories (QFTs). I will discuss under which conditions a similar result holds for two-dimensional defects in CFTs invariant under a continuous symmetry group. I will argue that spontaneous symmetry breaking is only possible for exotic RG flows, that do not terminate at a fixed point. I will present examples and describe a generic defect universality class, formerly found by Metlitski for boundaries in the O(N) model, where correlation functions decay logarithmically at large distances.
