SUSY vertex algebras and supercurves

Characters of topological N=2 vertex algebras are Jacobi forms on the moduli space of elliptic supercurves

We show that trace functions on modules of topological N=2 super vertex algebras give rise to conformal blocks on elliptic supercurves. We show that they satisfy a system of linear partial differential equations with respect to the modular parameters of the supercurves. Under some finiteness condition on the vertex algebra these differential equations can be interpreted as a connection on the vector bundle of conformal blocks. We show that this connection is equivariant with respect to a natural action of the Jacobi modular group on the modular parameters and the trace functions. In the append…

Superconformal Vertex Algebras and Jacobi Forms

We discuss the appearance of Jacobi automorphic forms in the theory of superconformal vertex algebras, explaining it by way of supercurves and formal geometry. We touch on related topics such as Ramanujan's differential equations for Eisenstein series.

SUSY Poisson顶点代数的代数operad

Algebraic operad of SUSY Poisson vertex algebra

本文延续此前SUSY顶点代数operad的研究，引入刻画SUSY Poisson顶点代数结构的SUSY coisson operad，证明其是经典Poisson顶点代数operad的自然SUSY类比，并给出滤过情形下的分次嵌入结果。

从SUSY因子化代数构造SUSY顶点代数的BV构造

BV construction of SUSY vertex algebras from SUSY factorization algebras

通过超黎曼曲面上的SUSY因子化代数，构造N=1超对称顶点代数，并证明SUSY版本的Costello-Gwilliam提取定理，应用于BV形式下的全纯sigma模型，得到自由bc-βγ系统及手征de Rham复形。

Superconformal structures of supersymmetric free fermion vertex algebras

In this paper, we define the shifted superconformal vector of supersymmetric charged free fermion vertex algebras, which is a 1-parameter deformation of the superconformal vector of the SUSY $bc$-$βγ$ system. Moreover, we find the corresponding shifted $N=2$ superconformal symmetry of SUSY charged free fermion vertex algebras, by using the $N_{K}=1$ SUSY vertex algebra formalism. Finally, in order to describe the shifted $N=2$ superconformal symmetry of the SUSY charged free fermion vertex algebra by $N=2$ superfields, we construct an $N_{K}=2$ SUSY version of the $bc$-$βγ$ system.

Li filtrations of SUSY vertex algebras

Any vertex algebra has a canonical decreasing filtration, called Li filtration, whose associated graded space has a natural structure of a vertex Poisson algebra. In this note, we introduce an analogous filtration for any SUSY vertex algebra, which was introduced by Heluani and Kac as a superfield formalism of a supersymmetric vertex algebra. We prove that the associated graded superspace of our filtration has a structure of SUSY vertex Poisson algebras. We also introduce and discuss related notions, such as Zhu's $C_2$-Poisson superalgebras, associated superschemes and singular supports, for …