AI 中文总结
本文构造了基本经典李超代数相关N=1超对称仿射顶点代数的Wakimoto型自由场实现，其同态单射性依赖于水平，在κ=0处出现普通仿射情形无对应物的退化。
AI 中文摘要
我们构造了与基本经典李超代数相关联的N=1超对称（SUSY）仿射顶点代数的Wakimoto型自由场实现。利用超场形式论，我们得到了Wakimoto实现的超对称类似物，其涉及βγ-bc系统与玻色子-费米子系统（或超对称海森堡顶点代数）。我们还为这些自由场实现构造了筛选算子。超对称情形的一个显著特征是，与普通Wakimoto实现不同，自由场同态的单射性依赖于水平（level）。我们证明，对于非退化的κ，该同态是单射的；而当κ=0时，它不具有单射性。因此，超对称Wakimoto实现在κ=0处表现出一种退化现象，这在普通仿射情形中没有直接对应物。
英文摘要
We construct Wakimoto-type free field realizations of $N=1$ SUSY affine vertex algebras associated with basic classical Lie superalgebras. Using the superfield formalism, we obtain a SUSY analogue of the Wakimoto realization in terms of $βγ$--$bc$ systems and boson--fermion systems (or SUSY Heisenberg vertex algebras). We also construct screening operators for the free field realizations. A distinctive feature of the SUSY setting is that, unlike the ordinary Wakimoto realization, the injectivity of the free field homomorphism depends on the level. We prove that the homomorphism is injective for nondegenerate $κ$, whereas at $κ=0$ it fails to be injective. Thus, the SUSY Wakimoto realization exhibits a degeneration at $κ=0$ that has no direct counterpart in the ordinary affine case.
Comments24 pages
