Effects of curvature couplings for quantum fields on cosmic-string space-times

The effect of $\xi R$ curvature coupling terms in the equation of motion of a massless scalar field are considered on a cosmic-string background. Realistic two- and four-dimensional models of a string, where the space-time curvature is spread over a region of nonzero size $r_0$, are constructed. In two and four dimensions, the nonzero $\xi$ term modifies the behavior within a region centered about the string, whose radius is proportional to $r_0$; however, the constant of proportionality may be exponentially large. For the standard idealized string (a conical space-time) which has no intrinsic length scale, the effects of nonzero $\xi$ do not appear.