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Geometric Properties of W-Algebras and the Toda model

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Abstract

The W-algebra minimal models on hyperelliptic Riemann surfaces are constructed. Using a proposal by Polyakov, we reduce the partition function of the Toda field theory on the hyperelliptic surface to a product of partition functions: one of a “free field” theory on the sphere with inserted Toda vertex operators and one of a free scalar field theory with antiperiodic boundary conditions with inserted twist fields.

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REFERENCES

  1. E. Martinec, “Quantum field theory: a guide for mathematicians,” in: Theta Functions (Proc. Symp. Pure Math., Vol. 49, Part 1, L. Ehrenpreis and R. C. Gunning, eds.), Amer. Math. Soc., Providence, R. I. (1989), p. 391.

    Google Scholar 

  2. J. Polchinski, Superstring Theory, Cambridge Univ. Press, Cambridge (1998); M. B. Green, J. H. Schwarz, and E. Witten, Superstring Theory, Vols. 1 and 2, Cambridge Univ. Press, Cambridge (1987).

    Google Scholar 

  3. M. A. Olshanetsky and A. M. Perelomov, Phys. Rep., 71, 313 (1981); I. M. Krichever, Russ. Math. Surveys, 32, 185 (1977).

    Google Scholar 

  4. N. Seiberg and E. Witten, Nucl. Phys. B, 426, 19 (1994); “Erratum,” 430, 485 (1994).

    Google Scholar 

  5. A. Marshakov, Seiberg–Witten Theory and Integrable Systems, World Scientific, Singapore (1999).

    Google Scholar 

  6. V. G. Kac, Infinite Dimensional Lie Algebras, Cambridge Univ. Press, Cambridge (1990); P. Goddard and D. Olive, Internat. J. Mod. Phys. A, 1, 303 (1986).

    Google Scholar 

  7. P. Bouwknegt and K. Schoutens, Phys. Rep., 223, 184 (1993).

    Google Scholar 

  8. A. B. Zamolodchikov, Theor. Math. Phys., 65, 1205 (1985); V. Fateev and A. B. Zamolodchikov, Nucl. Phys. B, 280, 644 (1987).

    Google Scholar 

  9. A. M. Polyakov, “Lectures presented at Landau Institute,” unpublished (1982); L. Takhtajan, “Semi-classical Liouville theory, complex geometry of moduli space, and uniformization of Riemann surface,” in: New Symmetry Principles in Quantum Field Theory (J. Frohlich et al., eds.), Plenum, New York (1992).

  10. Al. B. Zamolodchikov, Nucl. Phys. B, 285, 481 (1987); V. Knizhnik, Comm. Math. Phys., 112, 567 (1987); L. Dixon, D. Friedan, E. Martinec, and S. Shenker, Nucl. Phys. B, 282, 13 (1987); C. Crnkovic, G. Sotkov, and M. Stanishkov, Phys. Lett. B, 220, 397 (1989); S. A. Apikyan and C. J. Efthimiou, Phys. Lett. B, 359, 313 (1995).

    Google Scholar 

  11. V. S. Dotsenko and V. A. Fateev, Nucl. Phys. B, 240, 312 (1984); 251, 691 (1985).

    Google Scholar 

  12. S. A. Apikyan and Al. B. Zamolodchikov, JETP, 65, 19 (1987).

    Google Scholar 

  13. A. Belavin, A. Polyakov, and A. Zamolodchikov, Nucl. Phys. B, 241, 333 (1984).

    Google Scholar 

  14. M. Goulian and M. Li, Phys. Rev. Lett., 66, 2051 (1991); A. B. Zamolodchikov and Al. B. Zamolodchikov, Nucl. Phys. B, 477, 577 (1996); H. Dorn and H. Otto, Phys. Lett. B, 291, 39 (1992); Nucl. Phys. B, 429, 375 (1994); S. A. Apikyan and C. Efthimiou, JETP Letters, 74, 569 (2001); hep-th/0106272 (2001).

    Google Scholar 

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Authors and Affiliations

  1. Theoretical Physics Department, Yerevan State University, Yerevan, Armenia

    S. A. Apikyan

  2. Department of Mathematics, State University of New York, Stony Brook, New York, USA

    M. H. Barsamian

  3. Department of Physics, University of Central Florida, Orlando, Florida, USA

    C. J. Efthimiou

Authors
  1. S. A. Apikyan
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  2. M. H. Barsamian
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  3. C. J. Efthimiou
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Apikyan, S.A., Barsamian, M.H. & Efthimiou, C.J. Geometric Properties of W-Algebras and the Toda model. Theoretical and Mathematical Physics 138, 151–162 (2004). https://doi.org/10.1023/B:TAMP.0000014848.19523.a0

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  • DOI: https://doi.org/10.1023/B:TAMP.0000014848.19523.a0

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