Skip to main content
SpringerLink
Log in

On the Worldsheet Derivation of Large N Dualities for the Superstring

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

Abstract

Large N topological string dualities have led to a class of proposed open/closed dualities for superstrings. In the topological string context, the worldsheet derivation of these dualities has already been given. In this paper we take the first step in deriving the full ten-dimensional superstring dualities by showing how the dualities arise on the superstring worldsheet at the level of F terms. As part of this derivation, we show for F-term computations that the hybrid formalism for the superstring is equivalent to a ĉ=5 topological string in ten-dimensional spacetime. Using the ĉ=5 description, we then show that the D brane boundary state for the ten-dimensional open superstring naturally emerges on the worldsheet of the closed superstring dual.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Gopakumar, R., Vafa, C.: On the gauge theory/geometry correspondence. Adv. Theor. Math. Phys. 3, 1415 (1999)

    MathSciNet  MATH  Google Scholar 

  2. Witten, E.: Chern-Simons gauge theory as a string theory. Prog. Math. 133, 637 (1995)

    MATH  Google Scholar 

  3. Ooguri, H., Vafa, C.: Worldsheet derivation of a large N duality. Nucl. Phys. B 641, 3 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  4. Witten, E.: Phases of = 2 theories in two dimensions. Nucl. Phys. B 403, 159 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bershadsky, M., Cecotti, S., Ooguri, H., Vafa, C.: Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes. Commun. Math. Phys. 165, 311 (1994)

    MathSciNet  MATH  Google Scholar 

  6. Vafa, C.: Superstrings and topological strings at large N. J. Math. Phys. 42, 2798 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cachazo, F., Fiol, B., Intriligator, K.A., Katz, S., Vafa, C.: A geometric unification of dualities. Nucl. Phys. B 628, 3 (2002)

    Article  MATH  Google Scholar 

  8. Dijkgraaf, R., Vafa, C.: A perturbative window into non-perturbative physics. http://arxiv.org/abs/hep-th/0208048, 2002

  9. Berkovits, N.: Covariant quantization of the Green-Schwarz superstring in a Calabi-Yau background. Nucl. Phys. B431, 258 (1994)

    Google Scholar 

  10. Berkovits, N., Vafa, C.: = 4 topological strings. Nucl. Phys. B433, 123 (1995)

    Google Scholar 

  11. Berkovits, N.: A New Description of the Superstring. http://arxiv.org/abs/hep-th/9604123, 1996

  12. Ooguri, H., Vafa, C.: The C-deformation of gluino and non-planar diagrams. Adv. Theor. Math. Phys. 7, 53–85 (2003)

    MathSciNet  Google Scholar 

  13. Ooguri, H., Vafa, C.: Gravity induced C-deformation. Adv. Theor. Math. Phys. 7, 405–417 (2004)

    MATH  Google Scholar 

  14. Dijkgraaf, R., Grisaru, M.T., Ooguri, H., Vafa, C., Zanon, D.: Planar gravitational corrections for supersymmetric gauge theories. JHEP 0404, 028 (2004)

    Google Scholar 

  15. Ooguri, H., Vafa, C.: Knot invariants and topological strings. Nucl. Phys. B 577, 419 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  16. Labastida, J.M., Marino, M.: Polynomial invariants for torus knots and topological strings. Commun. Math. Phys. 217, 423 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  17. Ramadevi, P., Sarkar, T.: On link invariants and topological string amplitudes. Nucl. Phys. B 600, 487 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  18. Labastida, J.M., Marino, M., Vafa, C.: Knots, links and branes at large N. JHEP 0011, 007 (2000)

    Google Scholar 

  19. Labastida, J.M., Marino, M.: A new point of view in the theory of knot and link invariants. http://arxiv.org/abs/math.qa/0104180, 2001

  20. Marino, M., Vafa, C.: Framed knots at large N. http://arxiv.org/abs/hep-th/0108064, 2001

  21. Klebanov, I.R., Strassler, M.J.: Supergravity and a confining gauge theory: Duality cascades and χ SB-resolution of naked singularities. JHEP 0008, 052 (2000)

    Google Scholar 

  22. Maldacena, J.M., Nunez, C.: Towards the large N limit of pure = 1 super Yang Mills. Phys. Rev. Lett. 86, 588 (2001)

    Article  MathSciNet  Google Scholar 

  23. Ooguri, H., Oz, Y., Yin, Z.: D-branes on Calabi-Yau spaces and their mirrors. Nucl. Phys. B 477, 407 (1996)

    Article  MATH  Google Scholar 

  24. Maldacena, J.M.: The large N limit of superconformal field theories and supergravity. Adv. Theor. Math. Phys. 2, 231 (1998)

    MATH  Google Scholar 

  25. Polchinski, J.: Dirichlet-branes and Ramond-Ramond charges. Phys. Rev. Lett. 75, 4724 (1995)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto de Física Teórica, Universidade Estadual Paulista, Rua Pamplona 145, São Paulo, SP, 01405-900, Brasil

    Nathan Berkovits

  2. California Institute of Technology 452-48, Pasadena, CA, 91125, USA

    Hirosi Ooguri

  3. Jefferson Physical Laboratory, Harvard University, Cambridge, MA, 02138, USA

    Cumrun Vafa

Authors
  1. Nathan Berkovits
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hirosi Ooguri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cumrun Vafa
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by M.R. Douglas

Acknowledgement. C.V. thanks the theory group at Caltech for hospitality of, when he was a Gordon Moore Distinguished Scholar. N.B., H.O., and C.V. thank the Simons Workshop on Mathematics and Physics and the YITP at Stony Brook for their hospitality during the completion of this work. H.O. also thanks KITP, Santa Barbara and N.B. thanks Caltech for their hospitality. The research of H.O. was supported in part by DOE grant DE-FG03-92-ER40701. The research of C.V. was supported in part by NSF grants PHY-9802709 and DMS-0074329. The research of N.B. was supported in part by FAPESP grant 99/12763-0, CNPq grant 300256/94-9 and Pronex grant 66.2002/ 1998-9.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Berkovits, N., Ooguri, H. & Vafa, C. On the Worldsheet Derivation of Large N Dualities for the Superstring. Commun. Math. Phys. 252, 259–274 (2004). https://doi.org/10.1007/s00220-004-1181-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00220-004-1181-9

Keywords

Search

Navigation