N=4 SYM自旋链的迭代结构
Iterative Structure of the N=4 SYM Spin Chain
摘要：
我们发展了在非紧psu（1，1）中寻找N=4 SYM膨胀生成元的环路修正的代数方法|2）部门。该扇区给出psu（1，1）的t Hooft耦合依赖于常数的表示|2）乘以psu（1| 1）^2.首先，独立于表示，我们给出了这个李代数的生成元的依赖性的全阶代数分析。如果辅助生成元h满足与李代数生成元的简单交换关系，则该方法解决了对称性约束。将其应用于PSU（1，1| 2）扇形导致了平面三圈膨胀生成元在首阶对称生成元和h方面的迭代解，该迭代解通过了一组完整的谱检验。我们还认为，这种代数分析也可以适用于非平面理论。
英文摘要：
We develop algebraic methods for finding loop corrections to the N=4 SYM dilatation generator, within the noncompact psu(1,1|2) sector. This sector gives a 't Hooft coupling lambda-dependent representation of psu(1,1|2) times psu(1|1)^2. At first working independently of the representation, we present an all-order algebraic ansatz for the lambda-dependence of this Lie algebra's generators. The ansatz solves the symmetry constraints if an auxiliary generator, h, satisfies certain simple commutation relations with the Lie algebra generators. Applying this to the psu(1,1|2) sector leads to an iterative solution for the planar three-loop dilatation generator in terms of leading order symmetry generators and h, which passes a thorough set of spectral tests. We argue also that this algebraic ansatz may be applicable to the nonplanar theory as well.
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