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开弦Regge轨线及其场论极限

The Open String Regge Trajectory and Its Field Theory Limit

Francisco Rojas, Charles B. Thorn

备注：
19 pages, 5 figures
发表信息：
Phys.Rev.D84:026006,2011
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摘要：

研究了开弦论中包含开弦平面单圈修正的首Regge轨线的性质。利用SU（N）Chan-Paton因子，平面开弦多圈图上的和描述了t Hooft极限NPDMATHABMN \infty.我们的动机是提高对有限α '处开弦理论作为规范理论模型的理解。D时空维的SU（N）规范理论是通过要求开弦终止于一堆N个D = p +1的DP-膜来描述的。通过阶数g^2，可以从四个开弦树和平面回路图的s \to-\infty极限中提取出大N导轨线α（t）= 1 + α't + α't（t）.我们分析了t \to 0的行为，结果是：（t）\sim-Cg ^2（-α't）^{（D-4）/2}/（D-4）.这个结果精确地跟踪了D> 4维时空中规范理论的1圈Reggeized胶子。特别地，对于D \to 4，它再现了4维规范理论的已知红外发散，其Regge轨迹表现为-\ln（-α ^\prime t）。我们还研究了极限t \to-\infty中的σ（t），并证明了当D <8时，σ（t）表现为α ^\prime t/（\ln（-α ^\prime t））^γ，其中γ> 0依赖于D和无质量标量的个数.因此，只要4 <D <8，1-回路校正相对于整个范围的树轨迹保持较小-\infty <t <0。最后给出了对所有负的t，τ（t）的数值计算结果.

英文摘要：

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 α' 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 α(t)=1+α' t+Σ(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 Σ(t)\sim-Cg^2(-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\to4 it reproduces the known infrared divergences of gauge theory in 4 dimensions with a Regge trajectory behaving as -\ln(-α^\prime t). We also study Σ(t) in the limit t\to-\infty and show that, when D<8, it behaves as α^\prime t/(\ln(-α^\prime 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 the whole range -\infty<t<0. Finally we present the results of numerical calculations of Σ(t) for all negative t.

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