The N=4 SYM Integrable Super Spin Chain
The N=4 SYM Integrable Super Spin Chain
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N=4 SYM 可集成超级旋转链
DOI：
10.1016/j.nuclphysb.2003.08.015
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
M. Staudacher
中科院分区：
文献类型：
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作者：
N. Beisert;M. Staudacher
最近建立了N =4超杨-米尔斯理论的单环平面膨胀产生器，在某些限制情况下，可以用各种可积量子自旋链的哈密顿量来识别。特别是Minahan和Zarembo建立了对标量算子的限制导致可积向量so(6)链，而最近在QCD中的工作表明，对主要包含协变导数的扭转算子的限制，产生了具有非紧化自旋对称sl(2)的某些可积海森堡XXX链。在此，我们统一并推广了这些见解，并论证了N =4的完全单环平面膨胀发生器可以用一个可积的su（2,2|4）超自旋链来描述。我们还给出了相关Bethe ansatz方程的各种形式，其解与N =4规范理论中所有单环平面异常维的完备集一一对应。我们最后推测了这些可积结构的非微扰扩展，这似乎涉及到守恒电荷的非局部变形。
Recently it was established that the one-loop planar dilatation generator of N =4 super-Yang–Mills theory may be identified, in some restricted cases, with the Hamiltonians of various integrable quantum spin chains. In particular Minahan and Zarembo established that the restriction to scalar operators leads to an integrable vector so (6) chain, while recent work in QCD suggested that restricting to twist operators, containing mostly covariant derivatives, yields certain integrable Heisenberg XXX chains with non-compact spin symmetry sl (2) . Here we unify and generalize these insights and argue that the complete one-loop planar dilatation generator of N =4 is described by an integrable su (2,2|4) super spin chain. We also write down various forms of the associated Bethe ansatz equations, whose solutions are in one-to-one correspondence with the complete set of all one-loop planar anomalous dimensions in the N =4 gauge theory. We finally speculate on the non-perturbative extension of these integrable structures, which appears to involve non-local deformations of the conserved charges.