On the EFT of Conformal Symmetry Breaking

Abstract

Conformal symmetry can be spontaneously broken due to the presence of a defect or other background, which gives a symmetry-breaking vacuum expectation value (VEV) to some scalar operators. We study the effective field theory of fluctuations around these backgrounds, showing that it organizes as an expansion in powers of the inverse of the VEV, and computing some of the leading corrections. We focus on the case of space-like defects in a four-dimensional Lorentzian theory relevant to the pseudo-conformal universe scenario, although the conclusions extend to other kinds of defects and to the breaking of conformal symmetry to Poincar\'e symmetry.