AI 中文总结
研究四维庞加莱超引力中引力常数κ的流，通过超共形表述导出流算子，虽 BRST 规范固定带来问题，但借助维克定理有望解决，克服了部分障碍，还与尼科莱映射直接壳上构造作比较。
AI 中文摘要
超对称场论中的量子关联函数可通过尼科莱映射编码。无穷小逆映射通过‘流方程’给出它们对耦合常数变化的响应。我们通过其超共形表述研究四维庞加莱超引力中引力常数κ的流。通过将完整的超共形壳外作用表示为超变分，我们在有效 vierbein 理论中导出一个‘流算子’，其指数化产生超引力全阶（逆）尼科莱映射的规范不变部分。然而，BRST 规范固定给这个泛函微分流算子增加了一个乘法项，破坏了其推导性质，危及它与尼科莱映射的联系。不过我们认为并给出一个例子，在自由有效理论中借助维克定理，这种乘法流贡献可能可重写为推导性的。至少在朗道规范中，超引力流方程在κ = 0 处是正则的，允许围绕闵可夫斯基几何进行微扰展开。我们克服了早期构建庞加莱超引力尼科莱映射尝试中遇到的三个障碍中的两个。最后，我们将其与κ的主导阶尼科莱映射的直接壳上构造进行比较。
英文摘要
Quantum correlation functions in supersymmetric field theories can be encoded in the Nicolai map. The infinitesimal inverse map provides their response to a change in a coupling constant through a "flow equation". We investigate the flow in the gravitational constant $κ$ for four-dimensional Poincaré supergravity via its superconformal formulation. By expressing the full superconformal off-shell action as a supervariation we derive a "flow operator" in the effective vierbein theory, whose exponentiation yields the gauge-invariant part of an all-order (inverse) Nicolai map for supergravity. Alas, the BRST gauge fixing adds to this functional differential flow operator a multiplicative term, which ruins its derivational property and therefore jeopardizes its connection with the Nicolai map. We argue and present an example, however, that such multiplicative flow contributions might be rewritable as derivational ones with the help of Wick's theorem in the free effective theory where the Nicolai-transformed correlators are ultimately evaluated. At least in the Landau gauge, the supergravity flow equation is shown to be regular at $κ=0$, allowing for a perturbative expansion around Minkowski geometry. Therewith, we have overcome two of the three obstacles met in an earlier attempt towards a Nicolai map for Poincaré supergravity. Finally, we compare with the direct on-shell construction of a Nicolai map to leading order in $κ$.
Comments1+16 pages; v2: gauge fixing detailed for the on-shell method, 6 references added, matches published version
