Stringy profiles of gauge field tadpoles near orbifold singularities: I. heterotic string calculations

Closed string theories on orbifolds contain both untwisted and twistedstates. The latter are normally assumed to live exactly at the orbifold fixedpoints. We perform a calculation of a gauge field tadpole amplitude and showthat off-shell both the twisted and untwisted states give rise to non-trivialmomentum profiles over the orbifold C^3/Z_3. These profiles take the form ofGaussian distributions integrated over the fundamental domain of the modularparameter of the torus. The propagators of the internal coordinate fields onthe torus world sheet determine the width of the Gaussian profiles. Thesepropagators are determined up to a single normal ordering constant which mustbe bounded below to allow the existence of the coordinate space representationof these Gaussians. Apart from the expected massless states, massive and eventachyonic string excitations contribute to the profiles in some anomalous U(1)models. However, when a tadpole is integrated over the internal dimensions,these tachyonic contributions cancel in a non-trivial manner.Comment: 1+20 pages LaTe