I think I get it. Very tall order.
A) Is there any research or theories in dealing with representing art.
Probably. But the chances are big that they would be rather convoluted if you could find them. (Unless you are asking about general semiotics).
You obviously cannot represent art with art without at least vaguely pointing to a particular style/school. I would actually suggest you reconsider that: too much neutrality is toothless. Your audience might well have no problem that a Mondrian is a general representation of all art. Or the Vitruvian man. Or Michelangelos hands.
I have seen Mondrians iconic painting...
... represented pretty well on a nerd merit badge:
If this is impossible, then you are left with meta:
...and then you are right back at awful clipart. In addition, the visuals of palettes, brushes and easels contains connotations that are more kindergarden/evening classes/autie Margies watercolour course in Greece.
Of course, it can be done well. But I believe strongly that you are better off doing something like the Mondrian example above. It expects an understanding, familiarity or a tiny learning curve. It does not talk down to people. The association is very quickly learned. It is not so bland as to be meaningless; it is not (shudder) Word clipart. And it will just feel that bit more professional.