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 Neveu-Schwarz model with the open strings 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 of sum of the planar open string diagrams corresponds to the sum of the leading diagrams of large N QCD. The initial expression for the amplitude is given in an integral form and diverges in various corners of the integration region as usual. However, we regularized all these divergences by suspending total momentum conservation by an amount p, as first suggested by Goddard and by Neveu and Scherk [2, 3]. Using this regulator, we construct a completely finite expression for the one looop amplitude of open string massless vectors which become the “gluons” of large N QCD in the low energy limit. We show that all the counterterms we need to introduce, after analytic continuation to p = 0, are proportional to the tree amplitude which then simply amounts to a renormalization the open string coupling constant. Using this renormalized expression, we also study its high-energy behavior. The open string Regge trajectory a(t) through one loop is obtained also as a function of the dimensionality of the Dp-branes. We also study the field theory limit of a(t) which is simply the small t behavior and we obtain the exact same answer that conventional calculations in gauge theory provide. We think that this is a useful insight that open string theory provides into the understanding of gauge theory. We also 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. By studing the limit where s is much larger than t of this expression, which involves taking various approximations to the integral representation found for the amplitude, we recover the Regge limit at high t as is indeed expected. (en)