Conformal Connections in Physics

Question

For my diploma thesis in Mathematics I investigate conformal connections (as an example of Cartan connections). All in all the thesis should deal with geometric aspects (associated bundles, (pseudo)-Riemannian manifolds, G-structures,...).

I just started my thoughts, where the concrete working assumption is not yet fixed. Besides I have a lot of freedom in writing my thesis; this is why I am looking for interesting fields to work.

Now, I'm interested in some physical applications. I think one of the fields most using this geometric object is general relativity. Is there a good reference (text book or paper)? Are there good references for applications in other fields, i.e. QFT?

Further I'm interested in the following question: Are there any attempts to write the Yang-Mills equations in terms of conformal connections? If not: Is it ever useful to write down the YM equations in this language?

This post imported from StackExchange Physics at 2016-05-05 11:28 (UTC), posted by SE-user Richard

Comments

If I understand what you mean by "conformal connection" correctly, then no, no gauge theory may be written in terms of it because gauge theories lack the solder forms that Cartan connections come with. (That is, the principal bundle of gauge connections is not tied to the geometry of spacetime itsef as is the case with Cartan connections)

This post imported from StackExchange Physics at 2016-05-05 11:28 (UTC), posted by SE-user ACuriousMind

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If you are studying conformal structures, the physics counterpart are the conformal field theories, which can be defined on conformal manifolds (while a general QFT requires metric structure). Much of the work done in physics is for conformally flat manifolds, but there definitely are some works on curved setting as well.

This post imported from StackExchange Physics at 2016-05-05 11:28 (UTC), posted by SE-user Peter Kravchuk