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arXiv 0712.2479hep-th
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双圈自旋超弦:大扭曲SYM算符维数的强耦合修正

Spinning superstrings at two loops: strong-coupling corrections to dimensions of large-twist SYM operators

R. Roiban, A. A. Tseytlin

摘要:

我们考虑AdS_5 × S^5中的折叠自旋弦(AdS_5中有一个自旋分量S,S^5中有一个自旋分量J),它对应于N=4 SYM理论sl(2)扇区中的Tr(D^S Z^J)算符,在特殊标度极限下,弦质量M ~ \sqrt λ \ln S和J都被发送到无穷远,且它们的比值固定.在参数\el = J/M中展开,我们计算了2-loop弦西格玛模型对弦能量的修正,并表明它与Alday和Maldacena在arxiv:0708.0672中提出的表达式一致。我们认为,为了建立弱耦合规范理论结果的插值,对数\el^2 \ln^n \el项的重新计算是必要的。在这个过程中,我们建立了一个计算多自旋弦组态能量的高圈修正的一般框架。特别地,我们发现除了弦能量中的直接2-圈项之外,由于经典解的参数与固定自旋(即SO(2,4)x SO(6)对称性的电荷)之间的关系的有限"重整化“,还有来自较低圈阶的贡献。

英文摘要:

We consider folded spinning strings in AdS_5xS^5 (with one spin component S in AdS_5 and J in S^5) corresponding to the Tr(D^S Z^J) operators in the sl(2) sector of the N=4 SYM theory in the special scaling limit in which both the string mass M ~ \sqrt λ\ln S and J are sent to infinity with their ratio fixed. Expanding in the parameter \el= J/M we compute the 2-loop string sigma model correction to the string energy and show that it agrees with the expression proposed by Alday and Maldacena in arxiv:0708.0672. We suggest that a resummation of the logarithmic \el^2 \ln^n \el terms is necessary in order to establish an interpolation to the weakly coupled gauge theory results. In the process, we set up a general framework for the calculation of higher loop corrections to the energy of multi-spin string configurations. In particular, we find that in addition to the direct 2-loop term in the string energy there is a contribution from lower loop order due to a finite ``renormalization'' of the relation between the parameters of the classical solution and the fixed spins, i.e. the charges of the SO(2,4) x SO(6) symmetry.

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