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arXiv 1001.4018hep-thmath-phmath.MP
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AdS_5 × S^5自旋折叠弦能量单圈修正的精确计算

Exact computation of one-loop correction to energy of spinning folded string in AdS_5 x S^5

M. Beccaria, G. V. Dunne, V. Forini, M. Pawellek, A. A. Tseytlin

摘要:

我们考虑了在AdS_5 × S^5的AdS_3部分中折叠自旋弦解能量的单圈修正。经典的弦解是用椭圆函数表示的,因此对于自旋的一般值,相应的涨落行列式的显式计算似乎是一个非平凡的问题。我们展示了如何使用弦配分函数的静态规范表达式(我们证明了它等价于共形规范函数)和观察到所有相应的二阶涨落算子都可以放入标准(单能隙)Lamé形式来精确求解。我们系统地推导了弦能量表达式的小自旋展开式和大自旋展开式,并评述了它们的一些应用。

英文摘要:

We consider the 1-loop correction to the energy of folded spinning string solution in the AdS_3 part of AdS_5 x S^5. The classical string solution is expressed in terms of elliptic functions so an explicit computation of the corresponding fluctuation determinants for generic values of the spin appears to be a non-trivial problem. We show how it can be solved exactly by using the static gauge expression for the string partition function (which we demonstrate to be equivalent to the conformal gauge one) and observing that all the corresponding second order fluctuation operators can be put into the standard (single-gap) Lamé form. We systematically derive the small spin and large spin expansions of the resulting expression for the string energy and comment on some of their applications.

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