Princeton University High Energy Theory Seminar

Abstract: Conformal field theories that exhibit spontaneous breaking of conformal symmetry (a moduli space of vacua) are expectedly rare in the landscape of CFTs. Intuitively, this is because a delicate conspiracy is needed to fine-tune to zero the potential of the dilaton. Yet, it is difficult to phrase this intuition in abstract CFT language, and we do not know a sharp criterion that establishes which CFTs, as abstractly defined by their conformal bootstrap data, admit moduli spaces of vacua. In this talk, I will discuss some results and limitations of two different approaches to address this issue: a bootstrap equation for two-point functions in the broken vacuum, and the large charge expansion.