The rest of the conformal group is spontaneously broken.

This is because the conformal group decomposes into separate diffeomorphisms of the forward and back lightcones.

In mathematics, the conformal group is the group of transformations from a space to itself that preserve all angles within the space.

Several specific conformal groups are particularly important:

The conformal group of the sphere.

The ones of most interest in theoretical physics are the ones which extend the Poincaré group or the conformal group.

Together they came up with the idea of a conformal group of spacetime which involved an extension of the method of images.

The conformal group has the following representation:

In two dimensional spacetime, the transformations of the conformal group are the conformal transformations.

But recall that the conformal group on Minkowski spacetime is the symmetry group of the Maxwell equations.