Advertisement

Communications in Mathematical Physics

, Volume 271, Issue 1, pp 103–178 | Cite as

Supersymmetric Vertex Algebras

  • Reimundo HeluaniEmail author
  • Victor G. Kac
Article

Abstract

We define and study the structure of SUSY Lie conformal and vertex algebras. This leads to effective rules for computations with superfields.

Keywords

Central Charge Commutation Relation Central Extension Jacobi Identity Formal Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bar00.
    Barron, K.: N = 1 Neveu Schwarz vertex operator superalgebras over Grassmann algebras with odd formal variables. In: Representations and Quantizations: Proceedings of the International Conference on Representation Theory 1998, Berlin Heidelberg New York: China Higher Ed. Press and Springer Verlag, 2000, pp 9–36Google Scholar
  2. BD04.
    Beilinson, A., Drinfeld, V.: Chiral Algebras. AMS Colloquium Publications Vol. 51, Providence, RI: Amer. Math. Soc., 2004Google Scholar
  3. BDK01.
    Bakalov B., D’Andrea A. and Kac V.G. (2001). Theory of finite pseudoalgebras. Adv. Math. 162(1): 1–140 zbMATHCrossRefMathSciNetGoogle Scholar
  4. BK03.
    Bakalov B. and Kac V.G. (2003). Field algebras. Int. Math. Res. Not. 3: 123–159 CrossRefMathSciNetGoogle Scholar
  5. Bor86.
    Borcherds R. (1986). Vertex algebras, Kac-Moody algebras and the Monster. Proc. Nat. Acad. Sci. USA 83(10): 3068–3071 CrossRefMathSciNetADSGoogle Scholar
  6. BZHS06.
    Ben-Zvi, D., Heluani, R., Szczesny, M.: Supersymmetry of the chiral de Rham complex. http:// arxiv.org/list/math.QA/0601532, 2006Google Scholar
  7. Coh87.
    Cohn J.D. (1987). N  =  2 super-Riemann surfaces. Nucl. Phys. B284: 349–364 CrossRefADSGoogle Scholar
  8. DM99.
    Deligne, P., Morgan, J.W.: Notes on supersymmetry. In: Quantum fields and strings: A course for mathematicians, Vol. 1. Providence, RI:Amer. Math. Soc., 1999Google Scholar
  9. DRS90.
    Dolgikh S.N., Rosly A.A. and Schwarz A.S. (1990). Supermoduli spaces. Commun. Math. Phys. 135(1): 91–100 zbMATHCrossRefMathSciNetADSGoogle Scholar
  10. DSK05.
    De Sole, A., Kac, V.G.: Finite vs affine W-algebras. Japanese J. Math. (to appear), available at http://arxiv. math-ph/0511055, 2005Google Scholar
  11. FBZ01.
    Frenkel, E., Ben-Zvi, D.: Vertex algebras and algebraic curves. Mathematical surveys and monographs, Vol. 88, Providence, RI: Amer. Math. Soc. 2001Google Scholar
  12. FHL93.
    Frenkel I.B., Huang Y. and Lepowsky J. (1993). On axiomatic approaches to vertex operators algebras and modules. Mem. Amer. Math. Soc. 104: 494 MathSciNetGoogle Scholar
  13. FK02.
    Fattori D. and Kac V.G. (2002). Classification of finite simple Lie conformal superalgebras. J. Algebra 258(1): 23–59 zbMATHCrossRefMathSciNetGoogle Scholar
  14. FLM88.
    Frenkel, I., Lepowsky, J., Meurman, A.: Vertex operator algebras and the Monster. Pure and Applied Mathematics, Vol. 134. New York London: Academic Press Inc., 1988Google Scholar
  15. Hel06.
    Heluani, R.: SUSY vertex algebras and supercurves. Preprint, http://arxiv.org/list/math.QA/ 0603591, 2006Google Scholar
  16. Hua97.
    Huang, Y.Z.: Two dimensional conformal geometry and vertex operator algebras. Progress in Mathematics, Vol. 148. Boston, MA: Birkhäuser Boston Inc., 1997Google Scholar
  17. Kac77.
    Kac V.G. (1977). Lie superalgebras. Advances in Mathematics 26(1): 8–96 zbMATHCrossRefMathSciNetGoogle Scholar
  18. Kac96.
    Kac, V.G.: Vertex algebras for beginners. University Lecture series, Vol. 10. Providence, RI:Amer. Math. Soc., 1996, Second edition 1998Google Scholar
  19. KT85.
    Kac V.G. and Todorov I.T. (1985). Superconformal current algebras and their unitary representations. Commun. Math. Phys. 102(2): 337–347 CrossRefMathSciNetADSGoogle Scholar
  20. KvdL89.
    Kac, V.G., van de Leur, J.: On classification of superconformal algebras. In: Strings-88, Singapore: World Scientific, 1989, pp. 77–106Google Scholar
  21. LL05.
    Lian, B., Linshaw, A.: Chiral equivariant cohomology I. Preprint. http://arxiv.org/list/math.DG/0501084, 2005Google Scholar
  22. MSV99.
    Malikov A., Shechtman V. and Vaintrob A. (1999). Chiral de Rham complex. Commun. Math. Phys 204(2): 439–473 zbMATHCrossRefADSGoogle Scholar
  23. Oda89.
    Odake S. (1989). Extension of n = 2 superconformal algebra and Calabi-Yau compactification. Mod. Phys. Lett. A 4(6): 557–568 CrossRefMathSciNetADSGoogle Scholar
  24. SV95.
    Shatashvili S.L. and Vafa C. (1995). Superstrings and manifolds of exceptional holonomy. Selecta Mathematica 1(2): 347–381 zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of MathematicsMITCambridgeUSA

Personalised recommendations