Generalized dynamical spin chain and 4-loop integrability in N=6 superconformal Chern–Simons theory
Generalized dynamical spin chain and 4-loop integrability in N=6 superconformal Chern–Simons theory
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DOI：
10.1016/j.nuclphysb.2009.10.011
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发表时间：
2009-04
期刊：
影响因子：
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通讯作者：
D. Bak;Hyunsoo Min;S. Rey
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文献类型：
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作者：
D. Bak;Hyunsoo Min;S. Rey
我们重新审视中心扩展psu的酉表示（2| 2）激发超代数。我们发现，最普遍的是“赝动量”，而不是晶格动量，对角化自旋链哈密顿量，并导致广义动力学自旋链。所有已知的结果都指向N=4的超杨-米尔斯理论的格点动量对角化。在不同的相互作用结构下，我们问N=6超共形Chern-Simons理论是否提供了一个赝动量对角化的例子。对于SO（6）扇区，我们研究了伸缩算子中的最大洗牌项和次最大洗牌项，并与psu（2）的结果进行了比较|2）超代数与可积性。在两个循环，我们重新推导最大洗牌项（3-网站），并找到完美的协议与已知的结果。在四个循环中，我们首先发现不存在下一个最大的洗牌项（4-站点），与基于可积性的预测一致。接下来，我们提取最大洗牌项（5-站点），用于检查伪动量对角化的可能性的最相关项。奇怪的是，我们发现这个结果与基于晶格动量的可积性预言一致，如在N=4的超杨-米尔斯理论中。我们的结果的一致性是完全确保了可重正化检查多达六个循环。
We revisit unitary representation of centrally extended psu(2|2) excitation superalgebra. We find most generally that ‘pseudo-momentum’, not lattice momentum, diagonalizes spin chain Hamiltonian and leads to generalized dynamic spin chain. All known results point to lattice momentum diagonalization for N=4 super-Yang–Mills theory. Having different interacting structure, we ask if N=6 superconformal Chern–Simons theory provides an example of pseudo-momentum diagonalization. For SO(6) sector, we study maximal shuffling and next-to-maximal shuffling terms in the dilatation operator and compare them with results expected from psu(2|2) superalgebra and integrability. At two loops, we rederive maximal shuffling term (3-site) and find perfect agreement with known results. At four loops, we first find absence of next-to-maximal shuffling term (4-site), in agreement with prediction based on integrability. We next extract maximal shuffling term (5-site), the most relevant term for checking the possibility of pseudo-momentum diagonalization. Curiously, we find that result agrees with integrability prediction based on lattice momentum, as in N=4 super-Yang–Mills theory. Consistency of our results is fully ensured by checks of renormalizability up to six loops.