态场对应与共形超代数
State-Field Correspondences and Conformal Super-Algebras
摘要: 给出了共形超代数的概念并研究它与态场对应之间的关系;推广了有关Laurent-幂级数局部性的概念并给出它的具体实例。特别,用张量积的方法构造了Loop-态场对应,并研究了其局部性质。
Abstract: In the present paper, the concept of a conformal super-algebra is introduced and its relationship with a state-field correspondence is given. The locality is defined for any two Laurent-series with well-defined coefficients and some examples are discussed. In particular, the Loop state-field cor-respondence is constructed and some properties are obtained.
文章引用:翟敏序, 王宪栋. 态场对应与共形超代数[J]. 理论数学, 2019, 9(8): 857-863. https://doi.org/10.12677/PM.2019.98112

参考文献

[1] Borcherds, R.E. (1986) Vertex Algebras, Kac-Moody Algebras and the Monster. Proceedings of the National Academy of Sciences of the United States of America, 83, 3068-3071. [Google Scholar] [CrossRef] [PubMed]
[2] Dong, C. and Lepowsky, J. (1993) Generalized Vertex Algebras and Relative Vertex Operators. Progress in Mathematics, Vol. 112, Birkhauser, Boston. [Google Scholar] [CrossRef
[3] Lepowsky, J. and Li, H.-S. (2004) In-troduction to Vertex Operator Algebras and Their Representations. Progress in Mathematics, Vol. 227, Birkhauser, Boston. [Google Scholar] [CrossRef
[4] Frenkel, I.B., Lepowsky, J. and Meurman, A. (1988) Vertex Operator Algebras and the Monster. Pure and Applied Mathematics, Vol. 134, Academic Press, Boston. [Google Scholar] [CrossRef
[5] Frenkel, I.B. and Zhu, Y. (1992) Vertex Operator Algebras Associated to Representations of Affine and Virasoro Algebras. Duke Mathematical Journal, 66, 123-168. [Google Scholar] [CrossRef
[6] Dong, C. and Lin, X. (2014) Unitary Vertex Operator Al-gebras. Journal of Algebra, 397, 252-277. [Google Scholar] [CrossRef
[7] Bakalov, B. and Kac, V.G. (2003) Field Algebras. International Mathematics Research Notices, 3, 123-159. [Google Scholar] [CrossRef
[8] De Sole, A. and Kac, V.G. (2005) Freely Generated Vertex Algebras and Non-Linear Lie Conformal Algebras. Communications in Mathematical Physics, 254, 659-694. [Google Scholar] [CrossRef
[9] De Sole, A. and Kac, V.G. (2009) Lie Conformal Algebra Cohomology and the Variational Complex. Communications in Mathematical Physics, 292, 667-719. [Google Scholar] [CrossRef
[10] Kac, V.G. (1998) Vertex Algebras for Beginners. University Lecture Series 10, 2nd Edition, American Mathematical Society, Providence. [Google Scholar] [CrossRef