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QED has U(1) symmetry. The transformation is a function of x (psi -> psi*theta(x)). How does this depend on the spacetime? Do interactions therefore differ between curved space and flat space? Is this what leads on to QFT on curved spacetime research?

My second question:

If we believe that the curvature of spacetime in our universe is positive, why do string theorists like to play around with the Ads/CFT correspondance? Ads is a space with negative curvature is it not? If so, then surely any correspondance between string theory and gauge theory, whilst interesting, is ultimatley incorrect based on the fact that the string theory has been set up in an unphysical space?

Any illumination here would be appreciated.

Sox