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We study the properties of the leading Regge trajectory in open string theoryincluding the open string planar one-loop corrections. With SU(N) Chan-Patonfactors, the sum over planar open string multi-loop diagrams describes the 'tHooft limit N\to\infty. Our motivation is to improve the understanding of openstring theory at finite \alpha' as a model of gauge theories. SU(N) gaugetheories in D space-time dimensions are described by requiring open strings toend on a stack of N Dp-branes of space-time dimension D=p+1. The large Nleading trajectory \alpha(t)=1+\alpha' t+\Sigma(t) can be extracted, throughorder g^2, from the s\to-\infty limit, at fixed t, of the four open string treeand planar loop diagrams. We analyze the t\to0 behavior with the result that\Sigma(t)\sim-Cg^2(-\alpha' t)^{(D-4)/2}/(D-4). This result precisely tracksthe 1-loop Reggeized gluon of gauge theory in D>4 space-time dimensions. Inparticular, for D\to4 it reproduces the known infrared divergences of gaugetheory in 4 dimensions with a Regge trajectory behaving as -\ln(-\alpha^\primet). We also study \Sigma(t) in the limit t\to-\infty and show that, when D<8,it behaves as \alpha^\prime t/(\ln(-\alpha^\prime t))^{\gamma}, where \gamma>0depends on D and the number of massless scalars. Thus, as long as 4<D<8, the1-loop correction stays small relative to the tree trajectory for the wholerange -\infty<t<0. Finally we present the results of numerical calculations of\Sigma(t) for all negative t.

The Open String Regge Trajectory and Its Field Theory Limit