Yukawa couplings in heterotic compactification

Communications in Mathematical Physics

Volumn 297, Issue 1, 2010, Pages 95-127

  Anderson, Lara B ^a,e   Gray, James ^b   Grayson, Dan ^c   He, Yang Hui ^b,d   Lukas, André ^b  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b UNIVERSITY OF OXFORD   (United Kingdom)

^c UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^d MERTON COLLEGE   (United Kingdom)

^e INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77952407953     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-010-1033-8     Document Type: Article

References (41)

1. Greene B. R., Kirklin K. H., Miron P. J., Ross G. G.: 27**3 Yukawa Couplings For A Three Generation Superstring Model. Phys. Lett. B 192, 111 (1987).
2. Candelas P.: Yukawa Couplings Between (2, 1) Forms. Nucl. Phys. B 298, 458 (1988).
3. Candelas P., Kalara S.: Yukawa couplings for a three generation superstring compactification. Nucl. Phys. B 298, 357 (1988).
4. McOrist J., Melnikov I. V.: Summing the Instantons in Half-Twisted Linear Sigma Models. JHEP 0902, 026 (2009).
5. Donagi, R., Reinbacher, R., Yau, S. T.: Yukawa couplings on quintic threefolds. http://arxiv. org/abs/hep-th/0605203v1, 2006.
6. Donagi R., He Y. H., Ovrut B. A., Reinbacher R.: The particle spectrum of heterotic compactifications. JHEP 0412, 054 (2004).
7. Berglund P., Parkes L., Hubsch T.: The Complete Matter Sector In A Three Generation Compactification. Commun. Math. Phys. 148, 57 (1992).
8. Green, M. B., Schwarz, J. H., Witten, E.: Superstring Theory. Vol. 2: Loop Amplitudes, Anomalies And Phenomenology. Cambridge: Cambridge Univ. Pr., 1987.
9. Gabella M., He Y. H., Lukas A.: An Abundance of Heterotic Vacua. JHEP 0812, 027 (2008).
10. Anderson L. B., He Y. H., Lukas A.: Heterotic compactification, an algorithmic approach. JHEP 0707, 049 (2007).
11. Candelas P., Dale A. M., Lutken C. A., Schimmrigk R.: Complete Intersection Calabi-Yau Manifolds. Nucl. Phys. B 298, 493 (1988).
12. Okonek C., Schneider M., Spindler H.: Vector Bundles on Complex Projective Spaces. Birkhäuser Verlag, Basel (1988).
13. Anderson L. B., He Y. H., Lukas A.: Monad Bundles in Heterotic String Compactifications. JHEP 0807, 104 (2008).
14. Anderson, L. B.: Heterotic and M-theory Compactifications for String Phenomenology. Oxford University DPhil Thesis, 2008, http://arxiv. org/abs/0808. 3621v1[hep-th], 2008.
15. Anderson, L. B., He, Y. H., Lukas, A.: Vector bundle stability in heterotic monad models. In preparation.
16. Donaldson, S. K.: Some numerical results in complex differential geometry. http://arxiv. org/abs/math/0512625v1[math. DG], 2005. Douglas, M. R., Karp, R. L., Lukic, S., Reinbacher, R.: Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic. JHEP 0712, 083 (2007); Douglas, M. R., Karp, R. L., Lukic, S., Reinbacher, R.: Numerical Calabi-Yau metrics. J. Math. Phys. 49, 032302 (2008). Braun, V., Brelidze, T., Douglas, M. R., Ovrut, B. A.: Calabi-Yau Metrics for Quotients and Complete Intersections. JHEP 0805, 080 (2008).
17. Blumenhagen R., Moster S., Weigand T.: Heterotic GUT and standard model vacua from simply connected Calabi-Yau manifolds. Nucl. Phys. B 751, 186 (2006).
18. Blumenhagen R., Honecker G., Weigand T.: Loop-corrected compactifications of the heterotic string with line bundles. JHEP 0506, 020 (2005).
19. Distler J., Greene B. R.: Aspects of (2, 0) String Compactifications. Nucl. Phys. B 304, 1 (1988).
20. Lukas A., Ovrut B. A., Waldram D.: On the four-dimensional effective action of strongly coupled heterotic string theory. Nucl. Phys. B 532, 43 (1998).
21. Lukas A., Ovrut B. A., Stelle K. S., Waldram D.: The universe as a domain wall. Phys. Rev. D 59, 086001 (1999).
22. Hubsch T.: Calabi-Yau manifolds: A Bestiary for physicists. World Scientific, Singapore (1992).
23. Hartshorne, R.: Algebraic Geometry, Springer. GTM 52, Springer-Verlag, 1977; Griffith, P., Harris, J., Principles of algebraic geometry. New York: Wiley-Interscience, 1978.
24. Grayson, D., Stillman, M.: Macaulay 2, a software system for research in algebraic geometry. Available at http://www. math. uiuc. edu/Macaulay2/.
25. Greuel, G.-M., Pfister, G., Schönemann, H.: Singular: a computer algebra system for polynomial computations. Centre for Computer Algebra, University of Kaiserslautern (2001). Available at http://www. singular. uni-kl. de/.
26. Gray, J., He, Y. H., Ilderton, A., Lukas, A.: "STRINGVACUA: A Mathematica Package for Studying Vacuum Configurations in String Phenomenology." Comput. Phys. Commun. 180, 107-119 (2009); arXiv: 0801. 1508 [hep-th]. Gray, J., He, Y. H., Ilderton, A., Lukas, A.: "A new method for finding vacua in string phenomenology," JHEP 0707 (2007) 023; Gray, J., He, Y. H., Lukas, A.: "Algorithmic algebraic geometry and flux vacua." JHEP 0609 (2006) 031; The Stringvacua Mathematica package is available at: http://www-thphys. physics. ox. ac. uk/projects/Stringvacua/.
27. Braun, V., He, Y. H., Ovrut, B. A., Pantev, T.: "A heterotic standard model." Phys. Lett. B 618, 252 (2005); "The exact MSSM spectrum from string theory." JHEP 0605, 043 (2006).
28. Donagi R., He Y. H., Ovrut B. A., Reinbacher R.: Moduli dependent spectra of heterotic compactifications. Phys. Lett. B 598, 279 (2004).
29. Bouchard V., Donagi R.: An SU(5) heterotic standard model. Phys. Lett. B 633, 783 (2006).
30. Buchberger, B.: "An Algorithm for Finding the Bases Elements of the Residue Class Ring Modulo a Zero Dimensional Polynomial Ideal" (German), Phd thesis, Univ. of Innsbruck (Austria), 1965; B. Buchberger, "An Algorithmical Criterion for the Solvability of Algebraic Systems of Equations" (German), Aequationes Mathematicae 4(3), 374-383, 1970; English translation can be found in: Buchberger, B., Winkler, F., eds.: "Gröbner Bases and Applications." Volume 251 of the L. M. S. series, Cambridge: Cambridge University Press, 1998; Proc. of the International Conference "33 Years of Gröbner bases"; See B. Buchberger, "Gröbner Bases: A Short Introduction for Systems Theorists." p1-19 Lecture Notes in Computer Science, Computer Aided Systems Theory - EUROCAST 2001, Berlin-Heidelberg: Springer, 2001, pp. 1-19.
31. Gray, J.: A Simple Introduction to Grobner Basis Methods in String Phenomenology. http://arxiv. org/abs/0901. 1662v1[hep-th], 2009.
32. Anderson L. B., Gray J., Lukas A., Ovrut B.: The Edge Of Supersymmetry: Stability Walls in Heterotic Theory. Phys. Lett B 677, 190-194 (2009).
33. Anderson L. B., Gray J., Lukas A., Ovrut B.: Stability Walls in Heterotic Theories. JHEP 0909, 026 (2009).
34. Avramov, L. L., Grayson, D. R.: Resolutions and cohomology over complete intersections, In: Computations in algebraic geometry with Macaulay 2, Algorithms Comput. Math., Vol. 8, Berlin: Springer, 2002, pp. 131-178.
35. Boardman J. M.: The principle of signs. Enseignement Math. (2) 12, 191-194 (1966).
36. Bourbaki, N.: Éléments de mathématique. Algèbre. Chapitre 10. Algèbre homologique, Berlin: Springer-Verlag, 2007, (Reprint of the 1980 original [Paris: Masson]).
37. Cartan H., Eilenberg S.: Homological algebra. Princeton University Press, Princeton, N. J. (1956).
38. Godement, R.: Topologie algébrique et théorie des faisceaux, Actualit'es Sci. Ind. No. 1252. Publ. Math. Univ. Strasbourg. No. 13, Paris: Hermann, 1964.
39. Grayson D. R.: Adams operations on higher K-theory. K-Theory 6(2), 97-111 (1992).
40. Swan R. G.: Cup products in sheaf cohomology, pure injectives, and a substitute for projective resolutions. J. Pure Appl. Algebra 144(2), 169-211 (1999).
41. Weibel, C. A.: An introduction to homological algebra. Cambridge Studies in Advanced Mathematics, Vol. 38, Cambridge: Cambridge University Press, 1994.