标题： 开放弦的Regge轨迹及其场论极限 显示英文标题

标题： The Open String Regge Trajectory and Its Field Theory Limit

摘要： 我们研究开弦理论中主导Regge轨迹的性质，包括开弦平面一环修正。 带有SU(N) Chan-Paton因子，平面开弦多环图的求和描述了't Hooft极限N\to \infty 。 我们的动机是改进对有限\alpha 时开弦理论的理解，作为规范理论的模型。 D时空维度中的SU(N)规范理论通过要求开弦终止于一个N个Dp膜的堆栈上进行描述，其时空维度D=p+1。 大N主导轨迹\alpha (t)=1+\alpha ' t+\Sigma (t) 可以通过g^2阶从四开弦树图和平面环图的s\to -\infty 极限中提取，在固定t的情况下。 我们分析 t\to 0 的行为，结果为 \Sigma (t)\sim -Cg^2(-\alpha ' t)^{(D-4)/2}/(D-4). 这个结果精确地跟踪了 D>4 空间时间维数中规范理论的1循环 Reggeized 胶子。 特别是，对于 D\to 4，它在四维空间中再现了规范理论已知的红外发散，并且 Regge 轨迹表现为其 -\ln (-\alpha ^\prime t)。 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 >0 depends on D and the number of massless scalars. 因此，只要 4<D<8，在整个范围 -\infty <t<0 内，1圈修正相对于树图轨迹仍然很小。最后我们给出了所有负t的\Sigma (t) 的数值计算结果。 显示英文摘要

摘要： 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 multi-loop diagrams describes the 't Hooft limit N\to\infty. Our motivation is to improve the understanding of open string theory at finite \alpha' as a model of gauge 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 \alpha(t)=1+\alpha' t+\Sigma(t) can be extracted, through order g^2, from the s\to-\infty limit, at fixed t, of the four open string tree and 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 tracks the 1-loop Reggeized gluon of gauge theory in D>4 space-time dimensions. In particular, for D\to4 it reproduces the known infrared divergences of gauge theory in 4 dimensions with a Regge trajectory behaving as -\ln(-\alpha^\prime t). 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>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 the whole range -\infty<t<0. Finally we present the results of numerical calculations of \Sigma(t) for all negative t.