Hmm .. interesting .. thanks for that, Steven.
For my understanding, it seems this may come back to what we know ie: quantum (discreteness) theory, works cleanly for discrete particles.
The concept of a 'Field', (ie: resulting from interactions between particles), which is covered by continuous symmetry groupings, can be incorporated into the quantum world (QFT), with all of the complexities and issues arising therein. I can see now, how this theory may be playing in that region. Continuous anything fitting into the quantum world, would seemingly require special handling, and thus may fit into its own category.
And within that given category, symmetry of behaviour exists (and the laws of physics remain unchanged).
(I just made all that up … I hope its along the right lines. Don't want to disrupt the thread too much .. so I'll let it drop and do some more reading on it.)
Cheers