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arXiv 0906.4294hep-th
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AdS_5 × S^5中的量子弦:Konishi算符维数的强耦合修正

Quantum strings in AdS_5 x S^5: strong-coupling corrections to dimension of Konishi operator

R. Roiban, A. A. Tseytlin

摘要:

我们考虑对AdS_5 × S^5中最轻质量弦模的能量引入强耦合修正,它应该是N=4 SYM理论中Konishi算符多重态的对偶成员。这决定了小西算子反常维数强耦合展开的一般结构。我们使用1圈的结果,几个半经典弦状态,以提取信息的领先系数在此展开。我们的预测是Delta= 2 lambda^{1/4} + b_0 + b_1 lambda^{-1/4} + b_3 lambda^{-3/4} +.,其中b_0和b_1是有理数,而b_3是包含zeta(3)的超越数。我们证明了b_0= Delta_0 - 4(其中Delta_0是Konishi多重态中相应规范理论算符的正则维数)和b_1=1。我们的结论是敏感的几个假设,暗示了对应的平空间表达式,如何将半经典量子化的结果转化为准确的量子弦谱的预测。

英文摘要:

We consider leading strong coupling corrections to the energy of the lightest massive string modes in AdS_5 x S^5, which should be dual to members of the Konishi operator multiplet in N=4 SYM theory. This determines the general structure of the strong-coupling expansion of the anomalous dimension of the Konishi operator. We use 1-loop results for several semiclassical string states to extract information about the leading coefficients in this expansion. Our prediction is Delta= 2 lambda^{1/4} + b_0 + b_1 lambda^{-1/4} + b_3 lambda^{-3/4} +..., where b_0 and b_1 are rational while b_3 is transcendental containing zeta(3). Explicitly, we argue that b_0= Delta_0 - 4 (where Delta_0 is the canonical dimension of the corresponding gauge-theory operator in the Konishi multiplet) and b_1=1. Our conclusions are sensitive to few assumptions, implied by a correspondence with flat-space expressions, on how to translate semiclassical quantization results into predictions for the exact quantum string spectrum.

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