Holographic conformal order in supergravity

Abstract We explore the embedding of the phenomenological holographic models describing thermal relativistic ordered conformal phases in R 2 , 1 in SUGRA/String theory. The dual black branes in a Poincare patch of asymptotically A d S 4 have “hair” — a condensate of the order parameter for the broken symmetry. In a gravitational dual the order parameter for a spontaneous symmetry breaking is represented by a bulk scalar field with a nontrivial potential. To construct the ordered conformal phases perturbatively we introduce a phenomenological deformation parameter in the scalar potential. We find that while the ordered phases exist for different values of the deformation parameter, they disappear before the deformation is removed, in one case once the potential is precisely as in the top-down holography. While the holographic models with the conformal ordered phases considered here are in the String theory swampland, it remains an open question whether the presence of conformal ordered phases is a genuine swampland principle.