High energy scattering and renormalization in the NS+ string and large N QCD

In this work we study a model of open strings and its low energy limit as a device to understand certain aspects of gauge theory. More specifically, we use the even G-parity sector of the Neveu-Schwarz model with the open strings endpoints attached to a stack of N coincident Dp-branes as our starting point. After various projections, the low energy limit of this string theory is pure Yang-Mills and the field theory limit of the sum of the planar open string diagrams becomes to the sum of the leading diagrams of ’t Hooft’s large N expansion of QCD.;The typical expression for the amplitude we study here, namely for the scattering of open string massless vector bosons, comes in an integral form that shows multiple (spurious) divergences in various corners of the integration region. However, we regularize all of these divergences by momentarily suspending total momentum conservation by an amount p, as first suggested by Goddard and by Neveu and Scherk [1, 2], and construct the appropriate counterterms.;We show that all the counterterms we need to introduce, after analytic continuation to p = 0, are all proportional to the tree amplitude which then amounts to a renormalization the string coupling constant.;Using this renormalized expression, we also study its high-energy behavior. We obtain the one-loop ( O (g2)) correction to the open string Regge trajectory α(t) also as a function of the spacetime dimensionality of the Dp-branes. We also study the field theory limit of the new trajectory which amounts to analyzing the small t behavior of α(t). We obtain the exact same answer given by conventional calculations in dimensionally regularized gauge theory which puts the gluon on a Regge trajectory of order g2. We think that this is a useful insight that open string theory provides into the understanding of gauge theory. Additionally we study the behavior of the new trajectory α(t) for t away from zero which is relevant for open string physics.;Finally we work out the high-energy regime at fixed scattering angle (hard scattering) for the renormalized amplitude through one-loop. We obtain the well known exponential falloff expected for stringy amplitudes, but we also provide the complete factor that multiplies this exponential in terms of the kinematical invariants. By studying the s >> t limit of this novel expression, which involves taking various approximations in the integral representation found for the amplitude, we recover the Regge limit at high t as is indeed expected.