Modularity in orbifold theory for vertex operator superalgebras

仿费米子顶点算子代数 $K(osp(1|2),k)$ 的轨形表示

Representations of the orbifold of parafermion vertex operator algebra $K(osp(1|2),k)$

针对任意正整数水平 $k$，论文研究 $K(osp(1|2),k)$ 的轨形理论，并完成其轨形不可约模的分类。

关于Whittaker型模的不可约性：扭模与非阿贝尔轨形

On irreducibility of modules of Whittaker type: twisted modules and nonabelian orbifolds

本文将Dong-Mason不可约性定理推广到顶点算子超代数的非阿贝尔轨形，证明了中心元扭模在满足一定非同构条件下的不可约性，并应用于多种顶点代数的Whittaker型模。

Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras II

We define and compute the continuous orbifold partition function and a generating function for all $n$-point correlation functions for the rank two free fermion vertex operator superalgebra on a genus two Riemann surface formed by self-sewing a torus. The partition function is proportional to an infinite dimensional determinant with entries arising from torus Szego kernel and the generating function is proportional to a finite determinant of genus two Szego kernels. These results follow from an explicit analysis of all torus $n$-point correlation functions for intertwiners of the irreducible m…

Self-Dual Vertex Operator Superalgebras of Large Minimal Weight

The new general upper bound mu <= [c/24] + 1 for the minimal weight mu of a self-dual vertex operator superalgebra of central charge c different from 47/2 is proven. For central charges c <= 48, further improved estimates are given and examples of with large minimal weight are discussed. We also study the case of vertex operator superalgebras with N=1 supersymmetry which was first considered by Witten in connection with three-dimensional quantum gravity. The upper bound mu^* <= (1/2)[c/12]+1/2 for the minimal superconformal weight is obtained for c different from 47/2. In addition, we show tha…

置换轨道和简单电流扩张

Permutation orbifolds and simple current extensions

本文在顶点算子（超）代数框架下研究置换轨道和简单电流扩张，通过张量范畴方法和简单电流扩张建立可解自同构群的诱导理论，并分类不可约扭模。

Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras I

We define the partition and $n$-point correlation functions for a vertex operator superalgebra on a genus two Riemann surface formed by sewing two tori together. For the free fermion vertex operator superalgebra we obtain a closed formula for the genus two continuous orbifold partition function in terms of an infinite dimensional determinant with entries arising from torus Szegö kernels. We prove that the partition function is holomorphic in the sewing parameters on a given suitable domain and describe its modular properties. Using the bosonized formalism, a new genus two Jacobi product identi…

On Exceptional Vertex Operator (Super) Algebras

We consider exceptional vertex operator algebras and vertex operator superalgebras with the property that particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendents of the vacuum. We show that the genus one partition function and characters for simple ordinary modules must satisfy modular linear differential equations. We show the rationality of the central charge and module lowest weights, modularity of solutions, the dimension of each graded space is a rational function of the central charge and that the lowest weight primaries generat…

有理c=1顶点算子代数与顶点算子超代数的分类

Classification of Rational $c=1$ Vertex Operator Algebras and Vertex Operator Superalgebras

该文严格分类了有理c=1顶点算子代数与顶点算子超代数，证实其为秩1整格格VO(S)A或其有限群自同构的orbifold，为后续完整CFT分类奠定基础。

紧李群对偶的直极限完备化中的代数对象与c=1顶点算子代数的分类

Algebra objects in direct limit completions of compact Lie group duals and the classification of $c=1$ vertex operator algebras

该研究通过直极限完备化的代数对象分类，结合A₅-轨道模型的强合理性假设，完成了中心电荷c=1的强合理顶点算子代数的完整分类。