I am looking for examples of the physical systems with both conformal symmetry and Goldston bosons. The systems can be in any physical context, like QCD phases, Condensed Matter (Graphene, etc), or SUSY gauge theories.
Naively, in 1+1D gapless system, we can more easily have conformal symmetry. But to have a spontaneous symmetry breaking with Goldston bosons, and together with a (perhaps emergent) conformal symmetry seem to be somehow more challenging.
In 2+1D and higher dimensional system, we may find harder to have conformal symmetry. Are there such examples of conformal symmetry with Goldston bosons.?