Skip to main content
SpringerLink
Log in

Moduli Spaces of Calabi-Yau Compactifications

  • Chapter
M-Theory and Quantum Geometry

Part of the book series: NATO Science Series ((ASIC,volume 556))

Abstract

We review properties of Calabi-Yau compactifications of string theory, M-theory and F-theory.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. For a review of perturbative string theory see, for example,M. Green,J. Schwarz and E. Witten, “Superstring theory”, Vol. 1&2, Cambridge University Press, (1987);D. Lüst and S. Theisen, “Lectures on string theory”, Springer, (1989);J. Polchinski, “String Theory”,Vol.1&2,Cambridge University Press, (1998).

    Google Scholar 

  2. For a review see, for example, A.A. Tseytlin, in Superstrings ‘89, eds. M. Green, R. Iengo, S. Randjbar-Daemi, E. Sezgin and A. Strominger, World Scientific (1990). C. Callan and L. Thorlacius, in Particles, Strings and Supernovae, eds. A. Jevicki and C.-I. Tan World Scientific, (1989).

    Google Scholar 

  3. A. Schellekens and N. Warner, “Anomalies and modular invariance in string theory”, Phys. Lett. 177B (1986) 317.

    MathSciNet  ADS  Google Scholar 

  4. For a review see, for example, J. Schwarz, “Lectures on superstring and M-theory dualities”, hep-th/9607021;A. Sen, “Unification of string dualities”, hep-th/9609176;W. Lerche, “Introduction to Seiberg-Witten Theory and its Stringy Origin”, Nucl. Phys. Proc. Suppl. 55B (1997) 83, hep-th/9611190; P.K. Townsend, “Four Lectures on M-theory”, lectures given at the 1996 ICTP Summer School in High Energy Physics and Cosmology, Trieste, hep-th/9612121;S. Förste and J. Louis, “ Duality in String Theory”, in Gauge Theories, Applied Supersymmetry and Quantum Gravity II, ed. A. Sevrin, K.S. Stelle K. Thielemans and A. Van Proeyen, Imperial College Press, 1997, hep-th/9612192; C. Vafa, “Lectures on Strings and Dualities”, hep-th/9702201;A. Klemm, “On the Geometry behind N=2 Supersymmetric Effective Actions in Four Dimensions”, hep-th/9705131;E. Kiritsis, “Introduction to non-perturbative String Theory”, hep-th/9708130;W. Lerche, “Recent Developments in String Theory”, hep-th/9710246; P.K. Townsend, “M-theory from its Superalgebra”, hep-th/9712004;B. de Wit und J. Louis, “Supersymmetry and Dualities in Various Dimensions”, hep-th/9801132, lectures at the NATO Advanced Study Institute on “Strings, Branes and Duality”, Carg¨¨se, France, June 1997, published in the Proccedings.

    Google Scholar 

  5. For a review, see, for example, A. Giveon, M. Porrati and E. Rabinovici,“Target space duality in string theory”, Phys. Rept. 244 (1994) 77, hep-th/9401139.

    Google Scholar 

  6. For a review see, for example, J. Polchinski, “TASI lectures on D-branes”, hepth/9611050;C. Bachas, “(Half) a Lecture on D-branes”, in Gauge Theories, Applied Supersymmetry and Quantum Gravity II, ed. A. Sevrin, K.S. Stelle K. Thielemans and A. Van Proeyen, Imperial College Press, 1997, hep-th/9701019.

    Google Scholar 

  7. C.M. Hull and P.K. Townsend,“Unity of superstring dualities”,Nucl. Phys. B438 (1995) 109, hep-th/9410167;C.M. Hull,“String-string duality in ten-dimensions”, Phys. Lett. B357 (1995) 545, hep-th/9506194.

    Article  MathSciNet  ADS  Google Scholar 

  8. E. Witten, “String theory dynamics in various dimensions”, Nucl. Phys. B443 (1995) 85, hep-th/9503124.

    Article  MathSciNet  ADS  Google Scholar 

  9. J. Schwarz, “An SL(2,Z) multiplet of type-IIB superstrings”, Phys. Lett. B360 (1995) 13, hep-th/9508143.

    ADS  Google Scholar 

  10. E. Witten, “Bound states of strings and p-branes”,Nucl. Phys. B460 (1996) 335, hep-th/9510135.

    Article  MathSciNet  ADS  Google Scholar 

  11. C. Vafa, “Evidence for F theory”, Nucl. Phys. B469 (1996) 403, hep-th/9602022.

    Article  MathSciNet  ADS  Google Scholar 

  12. B.R. Greene, A. Shapere, C. Vafa and S.-T. Yau, “Stringy cosmic strings and noncompact Calabi-Yau Manifolds”, Nucl. Phys. B337 (1990) 1.

    Article  MathSciNet  ADS  Google Scholar 

  13. P. Berglung and P. Mayr, “Heterotic String/F-theory Duality from Mirror Symmetry”, Adv. Theor. Math. Phys. 2 (1999) 1307, hep-th/9811217.

    Google Scholar 

  14. D.R. Morrison and C. Vafa, “Compactifications of F-theory on Calabi-Yau three-folds - I”,Nucl. Phys. B473 (1996) 74, hep-th/9602111; “Compactifications of F-theory on Calabi-Yau threefolds - II”, Nucl. Phys. B476 (1996) 437, hepth/9603161.

    Google Scholar 

  15. P.K. Townsend, “The eleven-th dimensional supermembrane revisited”, Phys. Lett. B350 (1995) 184, hep-th/9501068, “D-branes from M-branes”,Phys. Lett. B373 (1996) 68, hep-th/9512062.

    Google Scholar 

  16. P. Hotava and E. Witten, “Heterotic and type-I string dynamics from eleven-dimensions”, Nucl. Phys. B460 (1996), 506, hep-th/9510209; “Eleven-dimensional supergravity and a manifold with boundary”,Nucl. Phys. B475 (1996)94, hepth/9603142.

    Google Scholar 

  17. T. Banks, W. Fischler, S.H. Shenker and L. Susskind, “M Theory As A Matrix Model: A Conjecture”, Phys. Rev. D55 (1997) 5112, hep-th/9610043.

    MathSciNet  ADS  Google Scholar 

  18. M. Claudson and M.B. Halpern, “Supersymmetric ground state wave functions”, Nucl. Phys. B250 (1985) 689;R. Flume, “On quantum mechanics with extended supersymmetry and nonabelian gauge constraints”, Ann. Phys. 164 (1985) 189;M. Baake, P. Reinicke, and V. Rittenberg, “Fierz identities for real Clifford algebras and the number of supercharges”, J. Math. Phys. 26 (1985) 1070.

    Google Scholar 

  19. E.A. Bergshoeff, E. Sezgin and P.K. Townsend, “Supermembranes and eleven-dimensional supergravity”, Phys. Lett. B189 (1987) 75; “Properties of the eleven-dimensional supermembrane theory”, Ann. Phys. 185 (1988) 330.

    Google Scholar 

  20. B. de Wit, J. Hoppe and H. Nicolai, “On the quantum mechanics of supermembranes”, Nucl. Phys. B305 (1988) 545.

    Article  ADS  Google Scholar 

  21. For a review, see, for example, R. Dijkgraaf, E. Verlinde and H. Verlinde, “Notes on Matrix and Micro Strings”, hep-th/9709107;N. Seiberg, “Why is the Matrix Model correct?”, hep-th/9710009;A. Bilai, “M(atrix) Theory: a Pedagogical Introduction”,hep-th/9710136; T Banks, “Matrix Theory”, hep-th/9710231;D. Bigatti and L. Susskind, “Review of Matrix Theory”, hep-th/9712072.

    Google Scholar 

  22. K.S. Narain,“New heterotic string theories in uncompactified dimensions <10”, Phys. Lett. 169B (1986) 41; K.S. Narain, M.H. Samadi and E. Witten, “A note on toroidal compactification of heterotic string theory”, Nucl. Phys. B279 (1987) 369.

    Google Scholar 

  23. For a review, see P. Aspinwall, “K3 surfaces and string duality”,hep-th/9611137.

    Google Scholar 

  24. N. Seiberg, “Observations on the moduli space of superconforrnal field theories”, Nucl. Phys. B303 (1988) 286;P.S. Aspinwall and D.R. Morrison, “String theory on K3 surfaces”, in Mirror Symmetry II, eds. B. Greene and S.-T. Yau, International Press, Cambridge, 1997, hep-th/9404151.

    Google Scholar 

  25. M.J. Duff and J.X. Lü, `Black and super p-branes in diverse dimensions“, Nucl. Phys. B416 (1994) 301;M.J. Duff and R. Minasian, ”Putting string/string duality to the test“, Nucl. Phys. B436 (1995) 261, hep-th/9406198.

    Google Scholar 

  26. A. Sen, “String-string duality conjecture in six dimensions and charged solitonic strings”, Nucl. Phys. B450 (1995) 103, hep-th/9504027.

    Article  ADS  Google Scholar 

  27. J.A. Harvey and A. Strominger, “The heterotic string is a soliton”, Nucl. Phys. B449 (1995) 456, hep-th/9504047.

    MathSciNet  Google Scholar 

  28. C. Vafa and E. Witten, “Dual string pairs with N =1 and N = 2 supersymmetry in four-dimensions”, Nucl. Phys. Proc. Suppl. 46 (1996) 225, hep-th/9507050.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. A. Sen, “F-theory and orientifolds”, hep-th/9605150.

    Google Scholar 

  30. P.S. Aspinwall and D.R. Morrison, “Point-like Instantons on K3 Orbifolds”, Nucl. Phys. B503 (1997) 533, hep-th/9705104.

    Article  MathSciNet  ADS  Google Scholar 

  31. M.B. Green, J. Schwarz and P. C. West, “Anomaly-free chiral theories in six dimensions”, Nucl. Phys. B254 (1985) 327;J. Erler, “Anomaly cancellation in six dimensions”, J. Math. Phys. 35 (1994) 1819, hep-th/9304104;J. Schwarz, “Anomaly-free supersymmetric models in six dimensions”, Phys. Lett. B371 (1996) 223, hep-th/9512053.

    Google Scholar 

  32. M. Berkooz, R. Leigh, J. Polchinski, J. Schwarz, N. Seiberg and E. Witten, “Anomalies,Dualities, and Topology of D = 6, N = 1 superstring vacua”, Nucl. Phys. B475 (1996) 115, hep-th/9605184.

    Article  MathSciNet  ADS  Google Scholar 

  33. S. Ferrara, R. Minasian and A. Sagnotti, “Low-Energy Analysis of M and F Theories on Calabi-Yau Threefolds”, Nucl. Phys. B474 (1996) 323, hep-th/9604097.

    Google Scholar 

  34. C.G. Callan, J.A. Harvey and A. Strominger, “World-sheet approach to heterotic instantons and solitons”, Nucl. Phys. B359 (1991) 611; “World brane actions for string solitons”, Nucl. Phys. B367 (1991) 60; “Supersymmetric string solitons”, hep-th/9112030.

    Google Scholar 

  35. E. Witten, “Small instantons in string theory. ”, Nucl. Phys. B460 (1996) 541, hep-th/9511030.

    Article  MathSciNet  ADS  Google Scholar 

  36. N. Seiberg and E. Witten, “Comments on string dynamics in six dimensions”, Nucl. Phys. B471 (1996) 121, hep-th/9603003.

    Article  MathSciNet  ADS  Google Scholar 

  37. I. Antoniadis, S. Ferrara and T.R. Taylor, “N = 2 Heterotic Superstring and its Dual Theory in Five Dimensions”, Nucl. Phys. B460 (1996) 489, hep-th/9511108.

    Article  MathSciNet  ADS  Google Scholar 

  38. E. Witten, “Phase Transitions In M-Theory And F-Theory”, Nucl. Phys. B471 (1996) 195, hep-th/9603150.

    Article  MathSciNet  ADS  Google Scholar 

  39. B. de Wit, V. Kaplunovsky, J. Louis and D. Lüst, “Perturbative Couplings of Vector Multiplets in N = 2 Heterotic String Vacua”, Nucl. Phys. B451 (1995) 53, hep-th/9504006.

    Article  ADS  Google Scholar 

  40. For recent reviews on special geometry, see, for example, B. de Wit and A. van Proeyen, “Special geometry and symplectic transformations”, Nucl. Phys. B (Proc. Suppl.) 45B,C (1996) 196, hep-th/9510186;A. van Proeyen, “Vector multiplets in N = 2 supersymrnetry and its associated moduli spaces”, hep-th/9512139.

    Google Scholar 

  41. S. Ferrara and A. Van Proeyen, “A Theorem on N = 2 Special Kähler Product Manifolds” Class. Quant. Gray. 6 (1989) 243.

    Article  MathSciNet  ADS  Google Scholar 

  42. S. Kachru and C. Vafa, “Exact results for N = 2 compactifications of heterotic strings”, Nucl. Phys. B450 (1995) 69, hep-th/9505105;S. Ferrara, J.A. Harvey, A. Strominger and C. Vafa, “Second-quantized mirror symmetry”, Phys. Lett. B361 (1995) 59, hep-th/9505162.

    Google Scholar 

  43. P. Candelas and X. de la Ossa, “Moduli space of Calabi-Yau manifolds”, Nucl. Phys. B355 (1991), 455; A. Strominger, “Special Geometry”, Commun. Math. Phys. 133 (1990) 163.

    Google Scholar 

  44. P. Candelas, X. de la Ossa, P. Green and L. Parkes, Nucl. Phys. B359 (1991) 21; P. Candelas, X. De la Ossa, A. Font, S. Katz and D. Morrison, Nucl. Phys. B416 (1994) 481, hep-th/9308083;P. Candelas, A. Font, S. Katz and D. Morrison, Nucl. Phys. B429 (1994) 626, hep-th/9403187.

    Google Scholar 

  45. J.A. Harvey and G. Moore, Nucl. Phys. B463 (1996) 315, hep-th/9510182.

    Article  MathSciNet  ADS  Google Scholar 

  46. S. Ferrara and S. Sabharwal, “Quaternionic Manifolds for Type II Superstrings Vacua of Calabi-Yau Spaces” Class. Quant. Gray. 6 (1989) L77, Nucl. Phys. B332 (1990) 317;M. Bodner, A.C. Cadavid and S. Ferrara, Class. Quant. Gray. 8 (1991) 789.

    Google Scholar 

  47. L. Dixon, “Some Worldsheet Properties of Superstring Compactifications, on Orbifolds and Otherwise”,in Superstrings, Unified Theories, and Cosmology ed. G. Furlan et al., World Scientific (1988);P. Candelas, M. Lynker and R. Schimmrigk, “Calabi-Yau manifolds in weighted P(4) ”, Nucl. Phys. B341 (1990) 383;B. Greene and R. Plesser, “Duality in Calabi-Yau Moduli Space”, Nucl. Phys. B338 (1990) 15.

    Google Scholar 

  48. For a review, see, for example, S. Hosono, A. Klemm and S. Theisen, “Lectures on mirror symmetry”, hep-th/9403096;B. Greene, “String Theory on Calabi-Yau Manifolds”, hep-th/9702155.

    Google Scholar 

  49. S. Cecotti, S. Ferrara and L. Girardello, “Geometry of type-II superstrings and the moduli of superconformal field theories”, Int. J. Mod. Phys. A4 (1989), 2475.

    MathSciNet  ADS  Google Scholar 

  50. E. Kiritsis and C. Kounnas, “Infrared regularization of superstring theory and the one loop calculation of coupling constants”, Nucl. Phys. B442 (1995) 472, hepth/9501020;A. Strominger “Loop Corrections to the Universal Hypermultiplet” Phys. Lett. B421 (1998) 139, hep-th/9706195;I. Antoniadis, S. Ferrara, R. Minasian and K.S. Narain, “R4 couplings in M and type II theories on Calabi-Yau spaces”, Nucl. Phys. B507 (1997) 571, hepth/9707013.

    Google Scholar 

  51. H. Günther, C. Herrmann and J. Louis, “Quantum Corrections in the Hypermultiplet Moduli Space”, hep-th/9901137.

    Google Scholar 

  52. H. Ooguri and C. Vafa, Phys. Rev. Lett. 77 (1996) 3296, hep-th/9608079.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  53. H. Günther, C. Herrmann and J. Louis, in preperation.

    Google Scholar 

  54. A. Klemm, W. Lerche and P. Mayr, “K3 fibrations and heterotic type-II string duality”, Phys. Lett. B357 (1995) 313, hep-th/9506112.

    MathSciNet  ADS  Google Scholar 

  55. V. Kaplunovsky, J. Louis and S. Theisen, “Aspects of duality in N = 2 string vacua”, Phys. Lett. B357 (1995) 71, hep-th/9506110;I. Antoniadis, E. Gava, K.S. Narain and T.R. Taylor, “N = 2 type-II - het-erotic duality and higher derivative F-terms”, Nucl. Phys. B455 (1995) 109, hepth/9507115;G. Aldazabal, A. Font, L.E. Ibañez and F. Quevedo, “Chains of N = 2, D = 4 heterotic type-II duals”, Nucl. Phys. B461 (1996) 85, hep-th/9510093;G. Lopes Cardoso, G. Curio, D. Lüst, T. Mohaupt and S.-J. Rey, “BPS spectra and non-perturbative couplings in N = 2,4 supersymmetric string theories”, Nucl. Phys. B464 (1996) 18, hep-th/9512129;P. Candelas and A. Font, “Duality Between the Webs of Heterotic and Type II Vacua, hep-th/9603170;P. Berglund, S. Katz, A. Klemm and P. Mayr, ”New Higgs transitions between dual N = 2 string models“, Nucl. Phys. B483 (1997) 209, hep-th/9605154;M. Bershadsky, K. Intriligator, S. Kachru, D.R. Morrison, V. Sadov and C. Vafa, ”Geometric singularities and enhanced gauge symmetries“, Nucl. Phys. B481 (1996) 215, hep-th/9605200;J. Louis, J. Sonnenschein, S. Theisen and S. Yankielowicz, ”Nonperturbative properties of heterotic string vacua“, Nucl. Phys. B480 (1996) 185, hep-th/9606049; B. de Wit, G. Lopes Cardoso, D. Lüst, T. Mohaupt and S.-J. Rey, ”Higher order gravitational couplings and modular forms in N = 2, D = 4 heterotic string corn-pactifications“, Nucl. Phys. B481 (1996) 353hep-th/9607184; for a review see, J. Louis and K. Förger, ”Holomorphic couplings in string theory“, Nucl. Phys. (Proc. Suppl.) 55B (1997) 33, hep-th/9611184.

    Google Scholar 

  56. P.S. Aspinwall and J. Louis, “On the ubiquity of K3 fibrations in string duality”, Phys. Lett. B369 (1996) 233, hep-th/9510234.

    MathSciNet  ADS  Google Scholar 

  57. P.S. Aspinwall and M. Gross, Phys. Lett. B382 (1996) 81, hep-th/9602118.

    MathSciNet  ADS  Google Scholar 

  58. J. Louis, J. Sonnenschein, S. Theisen and S. Yankielowicz, “Non-perturbative Properties of Heterotic String Vacua compactified on K3 x T2 ”, Nucl. Phys. B451 (1995) 53, hep-th/9606049.

    Google Scholar 

  59. M. Bershadsky, K. Intriligator, S. Kachru, D.R. Morrison, V. Sadov and C. Vafa, “Geometric singularities and enhanced gauge symmetries”, hep-th/9605200.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Martin—Luther—Universität Halle-Wittenberg, FB Physik, D-06099, Halle, Germany

    Jan Louis

Authors
  1. Jan Louis
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Science Institute, University of Iceland, Iceland

    Lárus Thorlacius  & Thordur Jonsson  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Louis, J. (2000). Moduli Spaces of Calabi-Yau Compactifications. In: Thorlacius, L., Jonsson, T. (eds) M-Theory and Quantum Geometry. NATO Science Series, vol 556. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4303-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-4303-5_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-6475-7

  • Online ISBN: 978-94-011-4303-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation