Abstract
A new mechanism for the cancellation of gauge residue symmetries in the framework of heterotic superstring compactification theories is revealed. The model preserves all the string features and fits naturally in the consistent topological structure of the homogeneousCP 4 Calabi-Yau manifold.
Similar content being viewed by others
References
Gross, J., Harvey, J. A., Martinec, E., Rohm, R.: Phys. Rev. Lett.54, 502 (1985); Nucl. Phys.B256, 253 (1985);B267, 75 (1986); Narain, K. S.: Phys. Lett.B169 (1986); Narain, K. S. Sarmadi, ?. ?., Witten, E.: Nucl. Phys.B279, 369 (1987); Dixon, L., Harvey, J. A., Vafa, C., Witten, E.: Nucl. Phys.B274, 285 (1986);B261, 651 (1985); Strominger, A., Witten, E.: Commun. Math. Phys.101, 341 (1985)
Ibanez, L. E., Nilles, H. P., Quevedo, F.: Phys. LettB187, 25 (1989); Phys. Lett.B192, 332 (1987)
Kawai, H., Lewellen, C., Tye, H.: Nucl. Phys.B288, 1 (1987); Lerche, W., Lust, D., Schellekens, N.: Phys. Lett.B181, 71 (1986); Nucl. Phys.B287, 667 (1987)
Borel, A.: Topology of Lie Group and Characteristic Classes. Am. Math. Bull. 397–432 (1955). For a general overview of differential geometry see S. Kobayashi: Differential Geometry of Complex Vector Bundles. Princeton, NJ: Princeton Univ. Press, 1987. Kobayashi and Nomizu: Foundations of Differential Geometry, Vol. 2. New York: Intersciences Publishers 1963–1969
An extensive discussion about the heterotic superstring compactification is given in Unified String Theories, Gross and Green (ed.). Singapore: World Scientific, 1985, pp. 294, 357, 400–438, 635. For a deep mathematical approach to this topic see Candelas, E.: Lecture on Complex Manifolds, pp. 1–88. Superstring 88, Singapore: World Scientific, Trieste 87 Spring School on Superstrings, Gaune, A., Green, Grisaru (ed.). See also Symposium on Anomalies, Geometry, and Topology, eds. Bardeen and White, Argonne, 1985, also Calabi, L.: Rend. Math. e Appl. Vol. 11 (1952) pp. 1–5
Cartan, E.: Notions d'Algebre Differentielles: Application Aux Groupes de Lie. (Collogue de Topologie sur les Espaces Fibrés) Bruxelles (1950), Paris-Liege (1951) pp. 15–27. Cartan, E.: La Transpression dans un Groupe de Lie et dans an Espace Fibré Principal; ibid. (Collogue de Topologie sur les Espaces Fibrés) Bruxelles (1950), Paris-Liege (1951) pp. 57–71
For a specific discussion see R. Bott, W. Tu: Differential Forms in Algebraic Topology, Berlin, Heidelberg, New York: Springer, 1982, pp. 8, 266. A general connection between homogeneous spaces and characteristic class may be found in Cartan, E.: Sur les invariants integraux de certains Espaces Homogènes Clos et les Proprietés topologiques de ces espaces 7, Annal. Societe Polonaise Math., Vol.8 (1929) pp. 181–225; Cartan, E.: Oeuvres Completes, Part I, Vol. 3, Paris: Gallimard-Gauthier Villars, 1952, pp. 1081–1125. See also the good paper of Borel, A. and Hirzebruch, F. on characteristic classes of homogeneous space (1956)
Cartan, E.: La Transgression dans un Groupe de Lie et dans un Space Fibré Principal. Colloque de Topologie sur les espace fibrés. Paris (1951)
Witten, E.: Commun. Math. Phys.100, 197 (1985); S. Panier: Algebraic Topology, New York: McGraw Hill, 1966. See also Chap. 3 of Bott & Tu: Differential Forms in Algebraic Topology
Borel, A.: Sur la Torsion des Groupes de Lie, J. Math. Pures Appl., (1955), and Torsion in Lie Groups, Proc. Natl. Acad. Sciences USA40, 586–588 (1954)
For an introduction to the theory of Universal Coefficients see Spanier, E.: Algebraic Topology. New York: McGraw Hill, 1966, pp. 222–338
Kodiaira, K.: Complex Manifolds and Deformation of Complex Structures, in particular, Chap. 5, Berlin, Heidelberg, New York: Springer 1986
Baadhio, R. A.: On the Chern-Weil Homomorphism in HomogeneousM 55 with a TrivialU(1) Bundle and 2-form Curvature. CRSR/Newman Lab Report, December 1989
Baadhio R. A.: On the E8, E7 and E6 Topological obstructions structure. CRSR/Newman Lab, March 90
Witten, E.: Physics and Geometry, in Proceedings of the 1986 Congress of Mathematicians. Berkeley, and New issues in Manifold ofSU(N) Holonomy, Nucl. Phys.B268, 79–112 (1986) and references therein
Okonek, C.: Vectors Bundles on Complex Projective Spaces. Birkhauser, 1980; Schneider, M.: Sem. Bourbaki 530, Nov. 1978, no. 18-19-20, page 80
Author information
Authors and Affiliations
Additional information
Communicated by S.-T. Yau
Rights and permissions
About this article
Cite this article
Baadhio, R.A. Heterotic superstring gauge residue trivialization via homogeneousCP 4 topology change. Commun.Math. Phys. 136, 251–264 (1991). https://doi.org/10.1007/BF02100024
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02100024