Skip to main content
SpringerLink
Log in

Non-unitary minimal models, Bailey's Lemma and N=1,2 Superconformal algebras

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

Using the Bailey flow construction, we derive character identities for the N=1 superconformal models SM(p′,2p+p′) and SM(p′,3p′−2p), and the N=2 superconformal model with central charge c=3 from the nonunitary minimal models M(p,p′). A new Ramond sector character formula for representations of N=2 superconformal algebras with central element c=3 is given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Agarwal, A.K., Andrews, G.E., Bressoud, D.M.: The Bailey lattice. J. Ind. Math. Soc. 51, 57–73 (1987)

    Google Scholar 

  2. Andrews, G.E.: Multiple series Rogers-Ramanujan type identities. Pac. J. Math. 114(2), 267–283 (1984)

    Google Scholar 

  3. Bailey, W.N.: Identities of Rogers-Ramanujan type. Proc. London Math. Soc.( 2(50), 1–10 (1949)

    Google Scholar 

  4. Berkovich, A., McCoy, B.M., Schilling, A.: N=2 Supersymmetry and Bailey pairs. Physica A 228, 33–62 (1996)

    Article  Google Scholar 

  5. Berkovich, A., McCoy, B.M.: Continued fraction and fermionic representations for characters of M(p,p') minimal models, Lett. Math. Phys. 37, 49–66 (1996)

    Article  Google Scholar 

  6. Berkovich, A., McCoy, B.M., Schilling, A.: Rogers-Schur-Ramanujan type identities for the M(p,p') minimal models of conformal field theory. Commun. Math. Phys. 191, 325–395 (1998)

    Article  Google Scholar 

  7. Berkovich, A., McCoy, B.M., Schilling, A., Warnaar, S.O.: Bailey flows and Bose-Fermi identities for coset models (A1(1)) N × (A1(1))N'/(A1(1))N+N'. Nucl. Phys. B 499, 621–649 (1997)

    Article  Google Scholar 

  8. Deka, L.: PhD thesis, in preparation

  9. Dobrev, V.K.: Structure of Verma modules and characters of irreducible highest weight modules over N=2 superconformal algebras. In: Clausthal 1986, Proceedings,Differential Geometric Methods in Theoretical Physics, H.D. Doebner, J.D. Hennig (eds.), Singapore: World Scientific, 1987, pp. 289–307

  10. Dobrev, V.K.: Characters of the irreducible highest weight modules over the Virasoro and super-Virasoro algebras. Rend. Circ. Mat. Palermo 14, 25–42 (1987)

    Google Scholar 

  11. Dobrev, V.K.: Characters of the unitarizable highest weight modules over the N=2 superconformal algebras. Phys. Lett. B 186, 43–51 (1987)

    Article  Google Scholar 

  12. Dörrzapf, M.: The embedding structure of unitary N=2 minimal models. Nucl. Phys. B 529, 639–655 (1998)

    Article  Google Scholar 

  13. Eholzer, W., Gaberdiel, M.R.: Unitarity of rational N=2 superconformal theories. Commun. Math. Phys. 186, 61–85 (1997)

    Google Scholar 

  14. Foda, O., Quano, Y.H.: Polynomial identities of the Rogers-Ramanujan type. Int. J. Mod. Phys. A 10, 2291–2315 (1995)

    Article  Google Scholar 

  15. Foda, O., Quano, Y.H.: Virasoro charater identities from the Andrews-Bailey construction. Int. J. Mod. Phys. A 12, 1651–1675 (1996)

    Google Scholar 

  16. Foda, O., Welsh, T.A.: On the combinatorics of Forrester-Baxter models. In: Physical combinatorics (Kyoto, 1999), Progr. Math. 191, Boston, MA: Birkhuser Boston, 2000, pp. 49–103

  17. Goddard, P., Kent, A., Olive, D.: Unitary representations of the Virasoro and super-Virasoro algebras. Comm. Math. Phys. 103 no. 1, 105–119 (1986)

    Google Scholar 

  18. Klemm, H.: Embedding diagrams of the N=2 superconformal Algebra under spectral flow. Int. J. Mod. Phys. A19, 5263 (2004)

  19. Klemm, H.: Private communication

  20. Kiritsis, E.B.: Character formulae and the structure of the representations of the N=1, N=2 superconformal algebras. Int. J. Mod. Phys. A 3, 1871–1906 (1988)

    Article  Google Scholar 

  21. Matsuo, Y.: Character formula of C < 1 unitary representation of N=2 superconformal algebra. Prog. Theor. Phys. 77, 793–797 (1987)

    Google Scholar 

  22. Paule, P.: On identities of the Rogers–Ramanujan type. J. Math. Anal. Appl. 107, 255–284 (1985)

    Article  Google Scholar 

  23. Ravanini, F., Yang, S.-K.: Modular invariance in N=2 superconformal field theories. Phys. Lett. B 195, 202–208 (1987)

    Article  Google Scholar 

  24. Schwimmer, A., Seiberg, N.: Comments on the N=2,N=3,N=4 superconformal algebras in two dimensions. Phys. Lett. B 184, 191–196 (1987)

    Article  Google Scholar 

  25. Slater, L.J.: A new proof of Rogers's transformation of infinite series. Proc. London Math. Soc. (2) 53, 460–475 (1951)

    Google Scholar 

  26. Welsh, T.A.: Fermionic expressions for the minimal model Virasoro characters. In: Memoirs of the American Mathematical Society vd.F15, Providence, RI: Amer. Math. Soc., (2005)

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, One Shields Ave, Davis, CA, 95616-8633, U.S.A

    Lipika Deka & Anne Schilling

Authors
  1. Lipika Deka
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anne Schilling
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lipika Deka.

Additional information

Communicated by L. Takhtajan

Supported in part by NSF grant DMS-0200774.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Deka, L., Schilling, A. Non-unitary minimal models, Bailey's Lemma and N=1,2 Superconformal algebras. Commun. Math. Phys. 260, 711–725 (2005). https://doi.org/10.1007/s00220-005-1432-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00220-005-1432-4

Keywords

Search

Navigation