# Do Boundary Conditions depend on spin connections for gauge fields?

In the article arXiv:1206.5642, which talks about gauge fields in conical spacetime, I came across the statement in footnote 4 that the boundary conditions on the gauge field depend on the spin connections on the cone. How to see this? Is it true for any curved spacetime?

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Which article? –  Qmechanic Jan 21 '13 at 19:09
See footnote 4 of 1206.5642. –  user1349 Jan 21 '13 at 19:31
I read that footnote as referring to a boundary condition on the scalar field $\phi$, not on the gauge field $A$. Presumably it means that $\phi$ has to have appropriate periodicity in the $\psi$ angular variable in the conical coordinates. My guess is that since the field is non minimally coupled (eq 7), solutions for $\phi$ depend on the curvature, and consequently on the spin connection. A minimally coupled scalar field would't have the curvature term, and since the other derivatives are ordinary partials, no connection would be involved. –  twistor59 Jan 21 '13 at 20:52