We obtain the perturbative expression for the Green function of the massless scalar field in a curved background being the tensor product of (d − 2)-dimensional Minkowski space-time and two-dimensional conical space. For d > 4 such a spacetime is considered as the simplest model for higher-dimensional cosmic string with (d − 3) flat extra dimensions. To the lowest perturbativetheory order on the angle deficit, one computes the renormalized vacuum mean values of ⟨ϕ2(x)⟩ren and ⟨TMN(x)⟩ren, valid for arbitrary dimensionality d > 3 and curvature coupling ξ. The old results for the vacuum mean values, corresponding to the infinitely thin straight cosmic string in four dimensions, are revised.
11.10.Gh Renormalization
11.25.-w Strings and branes
$^1$MSU, Faculty of Physics
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