Cerenkov radiation from moving straight strings

Abstract

We study Cerenkov radiation from moving straight strings which slide with respect to each other in such a way that the projected intersection point moves faster than light. To calculate this effect we develop classical perturbation theory for the system of Nambu-Goto strings interacting with the dilaton, two-form, and gravity fields. In the first order, one encounters divergent self-action terms which are eliminated by classical renormalization of the string tension. Cerenkov radiation arises in the second order. It is generated by an effective source which contains contributions localized on the string world sheets and bulk contributions quadratic in the first-order fields. In the ultrarelativistic limit radiation exhibits angular peaking on the Cerenkov cone in the forward direction of the fast string in the rest frame of another. The radiation spectrum then extends up to high frequencies proportional to the square of the Lorentz factor of the relative velocity. Gravitational radiation is absent since the $1+2$ space-time transverse to the straight string does not allow for gravitons. A rough estimate of the Cerenkov radiation in the cosmological cosmic strings network is presented.