We construct Nicolai maps for supersymmetric Yang–Mills theory in four and ten spacetime dimensions in the light-cone gauge, where the elimination of non-propagating degrees of freedom causes nonlocal and four-fermi interactions in the Lagrangian. The presence of the latter used to be an obstruction to the Nicolai map, which has recently been overcome at the price of quantum corrections to the map. No gauge-fixing or ghost terms arise in this formulation, since only physical transverse degrees of freedom occur. We present an explicit form of the Nicolai map to second order in the gauge coupling. In four dimensions, a ‘chiral’ choice of the map leaves one of the two transverse gauge-field modes invariant, which forces the classical part of the map (on the other mode) to become a polynomial (quadratic in the gauge coupling, cubic in the gauge field)! In the power series expansion for the ten-dimensional map however, cancellations at each order in the coupling are systematic but incomplete, still leaving an infinite power series for the Nicolai map (on all eight transverse modes). Nevertheless, the existence of a polynomial variant is conceivable, also for the maximal N=4 theory in four dimensions.

中文翻译：

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Nicolai 在光锥上的超级 Yang-Mills 映射


我们在光锥测厚仪中为超对称 Yang-Mills 理论构建了四维和十维的 Nicolai 映射，其中非传播自由度的消除导致拉格朗日中的非局部和四费米相互作用。后者的存在曾经是 Nicolai 地图的障碍，最近以对地图进行量子校正的代价克服了这个问题。此公式中没有出现标距固定项或重影项，因为只出现物理横向自由度。我们提出了规范耦合中二阶的 Nicolai 映射的显式形式。在四个维度中，映射的“手性”选择使两个横向规范场模式之一保持不变，这迫使映射的经典部分（在另一个模式上）成为多项式（在规范耦合中为二次，在规范字段中为三次）！然而，在十维映射的幂级数展开中，耦合中每个阶次的抵消是系统性的但不完全的，仍然为 Nicolai 映射留下一个无限的幂级数（在所有八个横向模式上）。尽管如此，多项式变体的存在是可以想象的，对于四维的最大 N=4 理论也是如此。