论文标题
尼古拉地图的超对称性大扰动
Supersymmetric large-order perturbation with the Nicolai map
论文作者
论文摘要
在严格的超对称量子理论中，尼古拉图允许通过保持（自由）功能积分度量，但使磁场遭受特定的非局部和非线性变换，可以打开耦合常数（从零到有限值）。尼古拉转化的场配置的递归扰动构造将其表示为耦合中的功率序列，其系数功能在$ n $中为特定树图的总和。对于量子力学的示例，这些树图的大小（在某个功能规范下）由$（n {+} 1）$ st the场尺寸的功率估算，它们的数字像$ n^{ - 3/2} \ times4.967^{\ n} $一样生长。这种渐近行为转化为尼古拉图的形式扰动扩张的有限收敛半径，该尼古拉图建立了其非扰动存在。量子相关因子的Feynman图数量的已知阶乘增长是通过像往常的自由田芯收缩的组合来重现的。我们预计我们的结果将扩展到更高的维度，包括超级阳米尔斯理论。
In rigidly supersymmetric quantum theories, the Nicolai map allows one to turn on a coupling constant (from zero to a finite value) by keeping the (free) functional integration measure but subjecting the fields to a particular nonlocal and nonlinear transformation. A recursive perturbative construction of the Nicolai-transformed field configuration expresses it as a power series in the coupling, with its coefficient function at order $n$ being a sum of particular tree diagrams. For a quantum-mechanical example, the size of these tree diagrams (under a certain functional norm) is estimated by the $(n{+}1)$st power of the field size, and their number grows like $n^{-3/2}\times4.967^{\;n}$. Such an asymptotic behavior translates to a finite convergence radius for the formal perturbative expansion of the Nicolai map, which establishes its non-perturbative existence. The known factorial growth of the number of Feynman diagrams for quantum correlators is reproduced by the combinatorics of free-field Wick contractions as usual. We expect our results to extend to higher dimensions, including super Yang-Mills theory.
