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arXiv 0907.4118hep-th
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在SL的敷料阶段（2）Bethe Anastomy

On the dressing phase in the SL(2) Bethe Ansatz

M. Kruczenski, A. Tirziu

备注：
23 pages, 1 figure, LaTeX. V2: References added
发表信息：
Phys.Rev.D80:086002,2009
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摘要：

本文研究了N=4超Yang-Mills理论SL（2）扇区的全圈Bethe Answer方程中决定修整相位的函数chi（x1，x2，g）.首先，我们考虑chi（x1，x2，g）在x1，x2的逆幂中的展开的系数c_{r,s}（g）。我们得到一个表达式，在一个单一的积分有效的所有值的耦合g。该表达式是这样的，小和大的耦合膨胀可以简单地计算与预期的结果一致。这证明了，到目前为止，证明了相位的两种展开的等价性。强耦合展开只是渐近的，但我们找到了一个精确的表达式，可以看出，随着g的指数下降的剩余值。之后，我们考虑函数chi（x1，x2，g）本身，并使用相同的方法，将其扩展为小耦合和大耦合。对于偶数和奇数n，所有小的和大的耦合系数chi^（n）（x1，x2）都可以用有限和的形式给出，或者用生成函数在某些极点的留数的形式给出。

英文摘要：

In this paper we study the function chi(x1,x2,g) that determines the dressing phase that appears in the all-loop Bethe Ansatz equations for the SL(2) sector of N=4 super Yang-Mills theory. First, we consider the coefficients c_{r,s}(g) of the expansion of chi(x1,x2,g) in inverse powers of x1, x2. We obtain an expression in terms of a single integral valid for all values of the coupling g. The expression is such that the small and large coupling expansion can be simply computed in agreement with the expected results. This proves the, up to now conjectured, equivalence of both expansions of the phase. The strong coupling expansion is only asymptotic but we find an exact expression for the value of the residue which can be seen to decrease exponentially with g. After that, we consider the function chi(x1,x2,g) itself and, using the same method, expand it for small and large coupling. All small and large coupling coefficients chi^(n)(x1,x2), for even and odd n, are explicitly given in terms of finite sums or, alternatively, in terms of the residues of generating functions at certain poles.

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