What the authors did is build a unified setup for classical gravity and electromagnetism as the solution of one action, under specific assumptions (Weyl geometry, etc...). Usually we consider gravity as the curvature of spacetime, and electromagnetic forces as the curvature of the electromagnetic field. The authors built something elegant where you can get both in one go.

What this work doesn't do is as important as what it does given the "ambitious" title. The authors' work is interesting, but a casual interpretation of the title would really mislead people into thinking they solved the unification problem.

This work doesn't address other forces or the general particularities of the standard model and how they would also bundle. The second thing it doesn't answer is how to quantize any of these fields (gravity is notoriously difficult to quantize for many reasons).

I wonder if mass could also be represented as a distortion of space-time. Like if charge is the divergence, mass could be the curl?

And I'm in way over my head here, but if charge is the compression of space time in a classical theory, what keeps it in place, instead of diffusing/spreading out? Seems like space-time is very stiff (i.e. speed of light is pretty high). Something to do with the non-linearity built into this new theory? Space time "yields" after a certain point?

Fun stuff to think about anyway!

[0] https://iopscience.iop.org/article/10.1088/1742-6596/2987/1/...

[1] https://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect