量子艾里结构与矩阵模型：超流方法
Quantum Airy Structures and Matrix Models: a supercurrent approach
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中文总结 AI 辅助
该研究建立外源模型的超流公式，统一四类扇区并推导NS-NS与R-R微分约束的相似变换，为Kontsevich模型的超对称扩展提供Ward恒等式候选系统。
中文摘要 AI 辅助
我们针对外源模型建立了$\boldsymbol{\textit{N}=1}$超Virasoro约束的超流公式，通过独立赋予玻色子和费米子单值性，统一了NS-NS、NS-R、R-NS和R-R四个扇区。对每个扇区，超Miwa变换将投影后的超能量动量张量表示为谱变量中的微分算子；伸缩子偏移在NS-NS和R-NS扇区产生超量子艾里结构，而R-R和NS-R扇区则需要额外的奇坐标。我们的主要结果是一个将NS-NS和R-R微分约束关联起来的精确相似变换，该互作用预因子结合了玻色子行列式、三次艾里权重，以及由Neveu-Schwarz和Ramond费米子传播子之差定义的格拉斯曼指数核。这些结果为Kontsevich模型的超对称扩展建立了一个具体的Ward恒等式候选系统，明确了其潜在矩阵模型实现所需的测度和费米子核的精确代数与解析性质。
英文摘要
We develop a super-current formulation of $\mathcal{N}=1$ super-Virasoro constraints for external-source models. By assigning bosonic and fermionic monodromies independently, we unify the NS-NS, NS-R, R-NS, and R-R sectors. For each, a super-Miwa transformation represents the projected super energy-momentum tensor as a differential operator in spectral variables. Dilaton shifts yield Super Quantum Airy Structures in the NS-NS and R-NS sectors, whereas the R-R and NS-R sectors require an additional odd coordinate. Our principal result is an exact similarity transformation relating the NS-NS and R-R differential constraints. The intertwining prefactor combines a bosonic determinant, a cubic Airy weight, and a Grassmann exponential kernel defined by the difference of Neveu--Schwarz and Ramond fermionic propagators. These results establish a concrete candidate system of Ward identities for a supersymmetric extension of the Kontsevich model, delineating the precise algebraic and analytic properties of the measure and fermionic kernel required for its potential matrix-model realization.
