Two-loop AdS5 × S5 superstring: testing asymptotic Bethe ansatz and finite size corrections
Two-loop AdS5 × S5 superstring: testing asymptotic Bethe ansatz and finite size corrections
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二环 AdS5 × S5 超弦：测试渐近 Bethe ansatz 和有限尺寸修正
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
A. Tseytlin
中科院分区：
文献类型：
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作者：
S. Giombi;R. Ricci;R. Roiban;A. Tseytlin
在大J和=固定的标度极限下，我们继续研究了在AdS5和S5中具有自旋S和角动量J的折叠弦的能量的双圈弦修正。我们计算了两回路阶f2(ℓ)的广义尺度函数，对于ℓ的小值和大值，都与基于渐近Bethe ansatz的预测相匹配。特别地，在小ℓ展开式中，我们得到了加泰罗尼亚常数项在f2(ℓ)中依赖于ℓ的系数的精确积分形式。此外，通过恢复多圈费曼图的某个子类，我们得到了其前导ln ℓ部分的精确表达式，它对展开式中的任何阶都有效。在大ℓ下，弦能量具有类似于BMN的展开，前几个领先系数有望受到保护，即在弱耦合和强耦合时是相同的。我们为弦理论中的两圈和规范理论中的单圈(1/J中子-子导)项的这种非重整化提供了一个新的例子。我们还给出了f2(ℓ)在大ℓ下展开的极大超越项的一个简单的代数公式。在论文的第二部分，我们通过形式化地压缩在快速旋转的长弦附近展开的弦作用中的空间世界薄片方向，开始了对弦能量的双圈有限尺寸修正的研究。我们观察到主要的有限尺寸修正是来自至少包含一个无质量传播子的项的‘Casimir’类型。我们详细考虑了单圈有序(再现了主要的Landau-Lifshitz模型预测)，然后重点讨论了双圈对项的贡献(对于J=0)。我们发现，在用于丢弃功率分歧的某个正则化方案中，项的双环系数似乎为零。
We continue the investigation of two-loop string corrections to the energy of a folded string with a spin S in AdS5 and an angular momentum J in S5, in the scaling limit of large J and S with = fixed. We compute the generalized scaling function at two-loop order f2(ℓ) both for small and large values of ℓ matching the predictions based on the asymptotic Bethe ansatz. In particular, in the small ℓ expansion, we derive an exact integral form for the ℓ-dependent coefficient of Catalan's constant term in f2(ℓ). Also, by resumming a certain subclass of multi-loop Feynman diagrams we obtain an exact expression for the leading ln ℓ part of which is valid to any order in the expansion. At large ℓ the string energy has a BMN-like expansion and the first few leading coefficients are expected to be protected, i.e. to be the same at weak and 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 f2(ℓ) expanded at large ℓ. 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 term (for J = 0). We find that in a certain regularization scheme used to discard power divergences the two-loop coefficient of the term appears to vanish.
扭曲二算子的五环反常维数
影响因子：
2.8
作者：
Lukowski T
通讯作者：
Lukowski T