Open string Regge trajectory and its field theory limit

We study the properties of the leading Regge trajectory in open string theory including the open string planar one-loop corrections. With SU(N) Chan-Paton factors, the sum over planar open string multiloop diagrams describes the 't Hooft limit N→ with Ngs2 fixed. Our motivation is to improve the understanding of open string theory at finite α^′ as a model of gauge field theories. SU(N) gauge theories in D space-time dimensions are described by requiring open strings to end on a stack of N Dp-branes of space-time dimension D=p+1. The large N leading trajectory α(t)= 1+α^′t+Σ(t) can be extracted, through order g2, from the s→- limit, at fixed t, of the four open string tree and planar loop diagrams. We analyze the t→0 behavior with the result that Σ(t)∼-Cg2(-α^′t)(D^-4)2/(D-4). This result precisely tracks the 1-loop Reggeized gluon of gauge theory in D>4 space-time dimensions. In particular, for D→4 it reproduces the known infrared divergences of gauge theory in 4 dimensions with a Regge trajectory behaving as -ln(-α^′t). We also study Σ(t) in the limit t→- and show that, when D<8, it behaves as α ^′t/(ln(-α^′t))γ, where γ>0 depends on D and the number of massless scalars. Thus, as long as 4<D<8, the 1-loop correction stays small relative to the tree trajectory for -α^′t arbitrarily large. Finally we present the results of numerical calculations of Σ(t) for all negative t.