##plugins.themes.bootstrap3.article.sidebar##
##plugins.themes.bootstrap3.article.main##
Abstract
The duality between E8xE8 heteritic string on manifold K3xT2 and Type IIA string compactified on a Calabi-Yau manifold induces a correspondence between vector bundles on K3xT2 and Calabi-Yau manifolds. Vector bundles over compact base space K3xT2 form the set of isomorphism classes, which is a semi-ring under the operation of Whitney sum and tensor product. The construction of semi-ring V ect X of isomorphism classes of complex vector bundles over X leads to the ring KX = K(V ect X), called Grothendieck group. As K3 has no isometries and no non-trivial one-cycles, so vector bundle winding modes arise from the T2 compactification. Since we have focused on supergravity in d = 11, there exist solutions in d = 10 for which space-time is Minkowski space and extra dimensions are K3xT2. The complete set of soliton solutions of supergravity theory is characterized by RR charges, identified by K-theory. Toric presentation of Calabi-Yau through Batyrev's toric approximation enables us to connect transitions between Calabi-Yau manifolds, classified by enhanced symmetry group, with K-theory classification.
Keywords:
There are no keywords for this language.
##plugins.themes.bootstrap3.article.details##
How to Cite
Obikhod, T. (2016). K-theory and phase transitions at high energies. Proceedings of the International Geometry Center, 9(1). https://doi.org/10.15673/tmgc.v9i1.87
Issue
Section
Papers
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution (CC-BY) 4.0 License that allows others to share the work with an acknowledgment of the work’s authorship and initial publication in this journal.
Provided they are the owners of the copyright to their work, authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal’s published version of the work (e.g., post it to an institutional repository, in a journal or publish it in a book), with an acknowledgment of its initial publication in this journal.
Authors are permitted and encouraged to post their work online (e.g., in institutional repositories, disciplinary repositories, or on their website) prior to and during the submission process.
References
1. Duff, Michael; Howe, Paul; Inami, Takeo; Stelle, Kellogg: Superstrings in D=10 from supermembranes in D=11. Nuclear Physics B191 (1), 70-74 (1987).
2. Arkani-Hamed N., Dimopoulos S., Dvali G.: The Hierarchy problem and new dimensions at a millimeter. Physics Letters B429 (3-4), 263-272 (1998), arXiv:hep-ph/9803315; Arkani-Hamed N., Dimopoulos S., Dvali G.: Phenomenology, astrophysics and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity. Physical Review D59 (8), 086004 (1999), arXiv:hep-ph/9807344; Randall, L., Sundrum, R.: Large Mass Hierarchy from a Small Extra Dimension. Physical Review Letters 83 (17), 3370-3373 (1999), arXiv:hep-ph/9905221;
3. Giddings, S. B., Thomas, S. D.: High-energy colliders as black hole factories: The End of short distance physics. Phys. Rev. D65 (5), 056010 (2002), arXiv:hep-ph/0106219; Dimopoulos, S., Landsberg, G. L.: Black Holes at the Large Hadron Collider. Phys. Rev. Lett. 87 (16), 161602 (2001), arXiv:hep-ph/0106295; Johnson, George: Physicists Strive to Build A Black Hole. The New York Times. Retrieved 2010-05-12; The case for mini black holes. CERN courier. November 2004.
4. Kachru Shamit, Vafa Cumrun: Exact Results for N=2 Compactifications of Heterotic Strings. Nucl. Phys. B450, 69-89 (1995).
5. Candelas Philip; Font Anamaria: Duality Between the Webs of Heterotic and Type II Vacua, arXiv: hep-th/9603170.
6. Klemm A., Lerche W., and Mayr P.: K3.Fibrations and Heterotic-Type II String Duality. Phys.Lett. B357, 313-322 (1995), hep-th/9506112.
7. Witten E.: String Theory Dynamics in Various Dimensions. Nucl.Phys. B443, 85-126 (1995), hep-th/9503124; Hull C. and Townsend P. K.: Enhanced Gauge Symmetries in Superstring Theory. Nucl.Phys. B451, 525-546 (1995), hep-th/9505073; Schwarz J.: The power of M theory. Phys. Lett. B367, 97-103 (1996), hep-th/9510086; Vafa C.: Evidence for F-theory. Nucl. Phys. B469, 403-418 (1996), hep-th/9602022; Morrison D. R. and Vafa C.: Compactifications of F-theory on Calabi-Yau threefolds I,II, hep-th/9602114, hep-th/9603161.
8. Batyrev V. V.: Variations of the Mixed Hodge Structure of Affine Hypersurfaces in Algebraic Tori. Duke Math. J. 69, 349-409 (1993).
9. Malyuta Yu. and Obikhod T.: Compactifications of F-Theory on Calabi-Yau Fourfolds, arXiv:hep-th/9803241.
10. Bershadsky Michael; Sadov Vladimir: F Theory on K3xK3 and Instantons on 7-branes. Nucl.Phys. B510, 232-246 (1998).
11. K. Wirthmuller: Vector Bundles and K-Theory 2011/2012.
12. Hartshorne, Robin: Algebraic Geometry.- Berlin, New York: Springer-Verlag, (1977), 496p.
13. Aspinwall Paul S.: D-Branes on Calabi-Yau Manifolds, arXiv:hep-th/0403166.
14. Sharpe Eric R.: D-Branes, Derived Categories, and Grothendieck Groups. Nucl.Phys. B561, 433-450 (1999).
15. Harvey J. and Moore G.: On the algebras of BPS states. Comm. Math. Phys. 197, 489-519 (1998), hep-th/9609017; Hori K. and Oz Y.: F-theory, T-duality on K3 surfaces and N = 2 supersymmetric gauge theories in four dimensions. Nucl. Phys. B501, 97-108 (1997), hep-th/9702173.
16. Braun A.: Elliptic K3s, T 4/Z2 and Enriques involutions. Bonn - May 19th, 2009, http://hep.itp.tuwien.ac.at/ abraun/bonn.pdf.
17. Becker Katrin: Torsional heterotic geometries. ""14th Itzykson Meeting"" IPHT, Saclay, June 19, 2009.
18. The World in Eleven Dimensions: Supergravity, Supermembranes and M-theory. Edited by. M.J. Duff. University of Michigan, (1999), 513p.
2. Arkani-Hamed N., Dimopoulos S., Dvali G.: The Hierarchy problem and new dimensions at a millimeter. Physics Letters B429 (3-4), 263-272 (1998), arXiv:hep-ph/9803315; Arkani-Hamed N., Dimopoulos S., Dvali G.: Phenomenology, astrophysics and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity. Physical Review D59 (8), 086004 (1999), arXiv:hep-ph/9807344; Randall, L., Sundrum, R.: Large Mass Hierarchy from a Small Extra Dimension. Physical Review Letters 83 (17), 3370-3373 (1999), arXiv:hep-ph/9905221;
3. Giddings, S. B., Thomas, S. D.: High-energy colliders as black hole factories: The End of short distance physics. Phys. Rev. D65 (5), 056010 (2002), arXiv:hep-ph/0106219; Dimopoulos, S., Landsberg, G. L.: Black Holes at the Large Hadron Collider. Phys. Rev. Lett. 87 (16), 161602 (2001), arXiv:hep-ph/0106295; Johnson, George: Physicists Strive to Build A Black Hole. The New York Times. Retrieved 2010-05-12; The case for mini black holes. CERN courier. November 2004.
4. Kachru Shamit, Vafa Cumrun: Exact Results for N=2 Compactifications of Heterotic Strings. Nucl. Phys. B450, 69-89 (1995).
5. Candelas Philip; Font Anamaria: Duality Between the Webs of Heterotic and Type II Vacua, arXiv: hep-th/9603170.
6. Klemm A., Lerche W., and Mayr P.: K3.Fibrations and Heterotic-Type II String Duality. Phys.Lett. B357, 313-322 (1995), hep-th/9506112.
7. Witten E.: String Theory Dynamics in Various Dimensions. Nucl.Phys. B443, 85-126 (1995), hep-th/9503124; Hull C. and Townsend P. K.: Enhanced Gauge Symmetries in Superstring Theory. Nucl.Phys. B451, 525-546 (1995), hep-th/9505073; Schwarz J.: The power of M theory. Phys. Lett. B367, 97-103 (1996), hep-th/9510086; Vafa C.: Evidence for F-theory. Nucl. Phys. B469, 403-418 (1996), hep-th/9602022; Morrison D. R. and Vafa C.: Compactifications of F-theory on Calabi-Yau threefolds I,II, hep-th/9602114, hep-th/9603161.
8. Batyrev V. V.: Variations of the Mixed Hodge Structure of Affine Hypersurfaces in Algebraic Tori. Duke Math. J. 69, 349-409 (1993).
9. Malyuta Yu. and Obikhod T.: Compactifications of F-Theory on Calabi-Yau Fourfolds, arXiv:hep-th/9803241.
10. Bershadsky Michael; Sadov Vladimir: F Theory on K3xK3 and Instantons on 7-branes. Nucl.Phys. B510, 232-246 (1998).
11. K. Wirthmuller: Vector Bundles and K-Theory 2011/2012.
12. Hartshorne, Robin: Algebraic Geometry.- Berlin, New York: Springer-Verlag, (1977), 496p.
13. Aspinwall Paul S.: D-Branes on Calabi-Yau Manifolds, arXiv:hep-th/0403166.
14. Sharpe Eric R.: D-Branes, Derived Categories, and Grothendieck Groups. Nucl.Phys. B561, 433-450 (1999).
15. Harvey J. and Moore G.: On the algebras of BPS states. Comm. Math. Phys. 197, 489-519 (1998), hep-th/9609017; Hori K. and Oz Y.: F-theory, T-duality on K3 surfaces and N = 2 supersymmetric gauge theories in four dimensions. Nucl. Phys. B501, 97-108 (1997), hep-th/9702173.
16. Braun A.: Elliptic K3s, T 4/Z2 and Enriques involutions. Bonn - May 19th, 2009, http://hep.itp.tuwien.ac.at/ abraun/bonn.pdf.
17. Becker Katrin: Torsional heterotic geometries. ""14th Itzykson Meeting"" IPHT, Saclay, June 19, 2009.
18. The World in Eleven Dimensions: Supergravity, Supermembranes and M-theory. Edited by. M.J. Duff. University of Michigan, (1999), 513p.