arXiv 1010.45942010-10hep-th

双圈AdS_5 × S^5超弦：渐近Bethe检验和有限尺寸修正

Two-loop AdS_5 x S^5 superstring: testing asymptotic Bethe ansatz and finite size corrections

S. Giombi, R. Ricci, R. Roiban, A. A. Tseytlin

备注：: 50 pages, 4 figures v2: typos corrected, references added
发表信息：: J.Phys.A44:045402,2011
DOI：: 10.1088/1751-8113/44/4/045402

摘要：

在大J和S的标度极限中，我们继续研究了双圈弦对具有AdS_5中自旋S和S^5中角动量J的折叠弦能量的修正，其中ell=pi J/（λ ^（1/2）ln S）=固定。我们计算的广义尺度函数在两个循环的顺序f_2（ell）的小和大的ell值匹配的预测的基础上的渐近Bethe的anastomosis。特别地，在小单元展开中，我们导出了f_2（ell）中Catalan常数项的单元依赖系数的精确积分形式。通过对多圈Feynman图的一个子类的图解，我们得到了f（λ ^（1/2），ell）的首部分（ln ell）的精确表达式，它对α '~ 1/λ ^（1/2）展开式中的任何阶都是有效的.在大的井的弦能量有BMN样的扩展和前几个领先的系数预计是相同的弱耦合和强耦合。我们提供了一个新的例子，这是在弦论中的两个循环和在规范理论中的一个循环（1/J中的子子领导）产生的长期的非重整化。我们还导出了f_2（ell）中最大超越性项在大ell上展开的一个简单的代数公式。在本文的第二部分中，我们开始研究2-loop有限尺寸的弦能量的修正，形式上紧化的空间世界片方向的字符串行动扩展附近的长快速旋转的字符串。我们观察到，领先的有限尺寸的修正是“卡西米尔”类型的条款包含至少一个无质量传播。我们详细考虑单回路阶数（再现领先的Landau-Lifshitz模型预测），然后专注于双回路对（1/ln S）项的贡献（对于J=0）。我们发现，在一定的正则化计划用于丢弃功率发散的双循环系数（1/ln S）项似乎消失。

英文摘要：

We continue the investigation of two-loop string corrections to the energy of a folded string with a spin S in AdS_5 and an angular momentum J in S^5, in the scaling limit of large J and S with ell=pi J/(lambda^(1/2) ln S)=fixed. We compute the generalized scaling function at two-loop order f_2(ell) both for small and large values of ell matching the predictions based on the asymptotic Bethe ansatz. In particular, in the small ell expansion, we derive an exact integral form for the ell-dependent coefficient of the Catalan's constant term in f_2(ell). Also, by resumming a certain subclass of multi-loop Feynman diagrams we obtain an exact expression for the leading (ln ell) part of f(lambda^(1/2), ell) which is valid to any order in the alpha'~1/lambda^(1/2) expansion. At large ell the string energy has a BMN-like expansion and the first few leading coefficients are expected to be the same at weak and at strong coupling. We provide a new example of this non-renormalization for the term which is generated at two loops in string theory and at one-loop in gauge theory (sub-sub-leading in 1/J). We also derive a simple algebraic formula for the term of maximal transcendentality in f_2(ell) expanded at large ell. In the second part of the paper we initiate the study of 2-loop finite size corrections to the string energy by formally compactifying the spatial world-sheet direction in the string action expanded near long fast-spinning string. We observe that the leading finite-size corrections are of "Casimir" type coming from terms containing at least one massless propagator. We consider in detail the one-loop order (reproducing the leading Landau-Lifshitz model prediction) and then focus on the two-loop contributions to the (1/ln S) term (for J=0). We find that in a certain regularization scheme used to discard power divergences the two-loop coefficient of the (1/ln S) term appears to vanish.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文