Kick-off event: AI and the future of mathematics and physics - 21.10.2026
In light of recent developments, the incoming kick-off event at the Institut Henri Poincaré will take the form of a debate gathering mathematicians and theoretical physicists around the role of AI in the practice of research. Registration: indico.math.cnrs.fr/event/17376/.
Spontaneous symmetry breaking on surface defects
byGabriel Cuomo
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.