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

The effect of ξR 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 r₀, are constructed. In two and four dimensions, the nonzero ξ term modifies the behavior within a region centered about the string, whose radius is proportional to r₀; 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 ξ do not appear.