Duality in compactified string theory

Ngee Pong Chang; Da Xi Li

doi:10.1103/PhysRevD.42.511

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Duality in compactified string theory

Ngee Pong Chang^* and Da Xi Li^†

Department of Physics, The City College of The City University of New York, New York, New York 10031

^*Electronic address: NPCCC@CUNYVM.Bitnet.
^†Electronic address: LI@CCNYSCI.Bitnet.

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Phys. Rev. D 42, 511 – Published 15 July, 1990

DOI: https://doi.org/10.1103/PhysRevD.42.511

Abstract

We reformulate compactified strings in order to manifest its duality under the transformation $R \to \frac{α^{'}}{R}$ . New degrees of freedom $y^{i}' s$ are introduced. The duality for the nonperturbative effects of orbifolds is also proved using the new formalism.

References (18)

M. B. Green, J. Schwarz, and E. Witten, Superstring Theory (Cambridge University Press, Cambridge, England, 1986) M. Kaku, Introduction to Superstrings (Springer, Berlin, 1988)
J. Schwarz, Phys. Rep. 89, 223 (1982) M. B. Green and J. Schwarz, Nucl. Phys. B198, 252 (1982)
K. Kikkawa and M. Yamasaki, Phys. Lett. 149B, 357 (1984) V. P. Nair, A. Shapere, A. Strominger, and F. Wilczek, Nucl. Phys. B287, 414 (1987) A. Shapere and F. Wilczek, ibid. B320, 669 (1989)
M. Dine, P. Huet, and N. Seiberg, Nucl. Phys. B322, 301 (1989)
S. Weinberg, University of Texas Report No. UTTG-17-87 (unpublished)
D. J. Gross, J. A. Harvey, E. Martinec, and R. Rohm, Nucl. Phys. B256, 253 (1985) ibid.B267, 75 (1986)
N. P. Chang and D. X. Li, City University of New York Report No. CCNY-HEP-90-5 (unpublished)
J. Lauer, J. Mas, and H. P. Nilles, Phys. Lett. B 226, 251 (1989)
L. Dixon, J. A. Harvey, C. Vafa, and E. Witten, Nucl. Phys. B261, 651 (1985) ibid.B274, 285 (1986)
N. P. Chang, D. X. Li, and J. Pérez-Mercader, Int. J. Mod. Phys. A 4, 287 (1989)
K. S. Narain, M. S. Sarmadi, and C. Vafa, Nucl. Phys. B279, 369 (1987)
S. Harmidi and C. Vafa, Nucl. Phys. B279, 465 (1987)
L. Dixon, D. Friedan, E. Martinec, and S. H. Shenker, Nucl. Phys. B282, 13 (1987)
I. Frenkel and V. Kac, Inv. Math. 62, 23 (1982) G. Segal, Commun. Math. Phys. 80, 301 (1982) P. Goddard and D. Olive, in Proceedings of the Conference on Vertex Operator in Mathematics and Physics, edited by J. Lepowsky (Springer, Berlin, 1984)
J. Lepowsky, Proc. Natl. Acad. Sci. 82, 8295 (1985) V. G. Kac and D. H. Peterson, in Anomalies, Geometry and Topology, proceedings of the Symposium, Argonne, Illinois, 1985, edited by W. A. Bardeen and A. R. White (World Scientific, Singapore, 1985)
M. Duff, Texas A&M University Report No. CTP-TAMU-53/89 (unpublished)
L. J. Dixon, Princeton University Report No. PUPT-1074/1987 (unpublished)
M. Bershadskii and A. Radul, Int. J. Mod. Phys. A 2, 165 (1987) J. J. Atick, L. Dixon, P. Griffin, and D. Nemeschansky, Nucl. Phys. B298, 1 (1988)

[c1] M. B. Green, J. Schwarz, and E. Witten, Superstring Theory (Cambridge University Press, Cambridge, England, 1986) M. Kaku, Introduction to Superstrings (Springer, Berlin, 1988)

[c2] J. Schwarz, Phys. Rep. 89, 223 (1982) M. B. Green and J. Schwarz, Nucl. Phys. B198, 252 (1982)

[c3] K. Kikkawa and M. Yamasaki, Phys. Lett. 149B, 357 (1984) V. P. Nair, A. Shapere, A. Strominger, and F. Wilczek, Nucl. Phys. B287, 414 (1987) A. Shapere and F. Wilczek, ibid. B320, 669 (1989)

[c4] M. Dine, P. Huet, and N. Seiberg, Nucl. Phys. B322, 301 (1989)

[c5] S. Weinberg, University of Texas Report No. UTTG-17-87 (unpublished)

[c6] D. J. Gross, J. A. Harvey, E. Martinec, and R. Rohm, Nucl. Phys. B256, 253 (1985) ibid.B267, 75 (1986)

[c7] N. P. Chang and D. X. Li, City University of New York Report No. CCNY-HEP-90-5 (unpublished)

[c8] J. Lauer, J. Mas, and H. P. Nilles, Phys. Lett. B 226, 251 (1989)

[c9] L. Dixon, J. A. Harvey, C. Vafa, and E. Witten, Nucl. Phys. B261, 651 (1985) ibid.B274, 285 (1986)

[c10] N. P. Chang, D. X. Li, and J. Pérez-Mercader, Int. J. Mod. Phys. A 4, 287 (1989)

[c11] K. S. Narain, M. S. Sarmadi, and C. Vafa, Nucl. Phys. B279, 369 (1987)

[c12] S. Harmidi and C. Vafa, Nucl. Phys. B279, 465 (1987)

[c13] L. Dixon, D. Friedan, E. Martinec, and S. H. Shenker, Nucl. Phys. B282, 13 (1987)

[c14] I. Frenkel and V. Kac, Inv. Math. 62, 23 (1982) G. Segal, Commun. Math. Phys. 80, 301 (1982) P. Goddard and D. Olive, in Proceedings of the Conference on Vertex Operator in Mathematics and Physics, edited by J. Lepowsky (Springer, Berlin, 1984)

[c15] J. Lepowsky, Proc. Natl. Acad. Sci. 82, 8295 (1985) V. G. Kac and D. H. Peterson, in Anomalies, Geometry and Topology, proceedings of the Symposium, Argonne, Illinois, 1985, edited by W. A. Bardeen and A. R. White (World Scientific, Singapore, 1985)

[c16] M. Duff, Texas A&M University Report No. CTP-TAMU-53/89 (unpublished)

[c17] L. J. Dixon, Princeton University Report No. PUPT-1074/1987 (unpublished)

[c18] M. Bershadskii and A. Radul, Int. J. Mod. Phys. A 2, 165 (1987) J. J. Atick, L. Dixon, P. Griffin, and D. Nemeschansky, Nucl. Phys. B298, 1 (1988)

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Duality in compactified string theory

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