Multi–Gluon Scattering in Open Superstring Theory

Abstract We discuss the amplitudes describing N -gluon scattering in type I superstring theory, on a disk world-sheet. After reviewing the general structure of amplitudes and the complications created by the presence of a large number of vertices at the boundary, we focus on the most promising case of maximally helicity violating (MHV) configurations because in this case, the zero Regge slope limit (α′ → 0) is particularly simple. We obtain the full-fledged MHV disk amplitudes for N = 4, 5 and N = 6 gluons, expressed in terms of one, two and six functions of kinematic invariants, respectively. These functions represent certain boundary integrals generalized Euler integrals which for N ≥ 6 correspond to multiple hypergeometric series (generalized Kampé de Fériet functions). Their α′expansions lead to Euler-Zagier sums. For arbitrary N , we show that the leading string corrections to the Yang-Mills amplitude, of order O(α′2), originate from the well-known α′2TrF 4 effective interactions of four gauge field strength tensors. By using iteration based on the soft gluon limit, we derive a simple formula valid to that order for arbitrary N . We argue that such a procedure can be extended to all orders in α′. If nature gracefully picked a sufficiently low string mass scale, our results would be important for studying string effects in multi-jet production at the Large Hadron Collider (LHC).