Skip to main content
SpringerLink
Log in
Book cover

Strings, Branes and Dualities pp 319–356Cite as

Notes on Matrix and Micro Strings

  • Chapter

  • 359 Accesses

Part of the book series: NATO ASI Series ((ASIC,volume 520))

Abstract

In spite of considerable recent progress, M-theory is as yet a theory without a fundamental formulation. It is usually specified by means of a number of fundamental properties that we know it should posses. Among the most important of these characteristics is that the degrees of freedom and interactions of M-theory should provide a (mathematically consistent) representation of the maximally extended supersymmetry algebra of eleven dimensional supergravity [1]

$$\{ {Q_\alpha },{Q_\beta }\} = {({\Gamma ^m})_{\alpha \beta }}{P_m} + {({\Gamma ^{mn}})_{\alpha \beta }}Z_{mn}^{(2)} + {({\Gamma ^{{m_1} \ldots {m_5}}})_{\alpha \beta }}Z_{^{{m_1} \ldots {m_5}}}^{(5)}$$
(1.1)

Here P m denotes the eleven dimensional momentum, and Z (2) and Z (5) represent the two- and five-index central charges corresponding to the two types of extended objects present in M-theory, respectively the membrane and the fivebrane. Upon compactification, these extended objects give rise to a rich spectrum of particles, with many quantized charges corresponding to the various possible wrapping numbers and internal Kaluza-Klein momenta.

This is a preview of subscription content, 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   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. Townsend, “P-brane democracy,” in Particles, Strings and Cosmology, eds. J. Bagger e.a. (World Scientific 1996), hep-th/9507048.

    Google Scholar 

  2. E. Witten, “String Theory Dynamics in Various Dimensions,” Nucl. Phys. B443 (1995) 85–126, hep-th/9503124.

    Article  MathSciNet  ADS  Google Scholar 

  3. J. Polchinski, “Dirichlet Branes and Ramond Ramond Charges,” hep-th/951001.

    Google Scholar 

  4. R. Dijkgraaf, E. Verlinde and H. Verlinde, “BPS Spectrum of the Five-Brane and Black Hole Entropy,” Nucl. Phys. B486 (1997) 77–88, hep-th/9603126; “BPS Quantization of the Five-Brane,” Nucl. Phys. B486 (1997) 89–113, hep-th/9604055.

    Article  MathSciNet  ADS  Google Scholar 

  5. E. Witten, “Bound States of Strings and p-Branes,” Nucl. Phys. B460 (1996) 335–350, hep-th/9510135.

    Article  MathSciNet  ADS  Google Scholar 

  6. U.H. Danielsson, G. Ferretti, and B. Sundborg, “D-particle Dynamics and Bound States,” Int. J. Mod. Phys. A11 (1996) 5463–5478, hep-th/9603081; D. Kabat and P. Pouliot, “A Comment on Zerobrane Quantum Mechanics,” Phys. Rev. Lett. 77 (1996) 1004–1007, hep-th/9603127.

    MathSciNet  ADS  Google Scholar 

  7. M._R. Douglas, D. Kabat, P. Pouliot, and S. H. Shenker, “D-branes and Short Distances in String Theory,” Nucl. Phys. B485 (1997) 85–127, hep-th/9608024.

    Article  MathSciNet  ADS  Google Scholar 

  8. C. Hull and P. Townsend, “Unity of Superstring Dualities,” Nucl. Phys. B 438 (1995) 109.

    Article  MathSciNet  ADS  Google Scholar 

  9. T. Banks, W. Fischler, S. H. Shenker, and L. Susskind, “M Theory as a Matrix Model: A Conjecture,” hep-th/9610043.

    Google Scholar 

  10. L. Motl, “Proposals on Non-perturbative Superstring Interactions,” hep-th/9701025.

    Google Scholar 

  11. T. Banks and N. Seiberg, “Strings from Matrices,” hep-th/9702187.

    Google Scholar 

  12. R. Dijkgraaf, E. Verlinde, and H. Verlinde, “Matrix String Theory,” hep-th/9703030.

    Google Scholar 

  13. R. Dijkgraaf, E. Verlinde, and H. Verlinde, “5D Black Holes and Matrix Strings,” hep-th/9704018.

    Google Scholar 

  14. N. Seiberg, “Matrix Description of M-theory on T 5 and T 5/Z 2,” hep-th/9705221

    Google Scholar 

  15. J. Hoppe, “Quantum Theory of a Relativistic Surface,” Ph.D. Thesis, MIT (1982). B. de Wit, J. Hoppe and H. Nicolai, “On the Quantum Mechanics of Supermembranes,” Nucl. Phys. B305 (1988) 545–581.

    Google Scholar 

  16. M. Rozali, “Matrix Theory and U-Duality in Seven Dimensions,” hep-th/9702136.

    Google Scholar 

  17. M. Berkooz, M. Rozali, and N. Seiberg, “Matrix Description of M theory on T 4 and T 5,” hep-th/9704089.

    Google Scholar 

  18. W. Fishier, E. Halyo, A. Rajaraman, and L. Susskind, “The Incredible Shrinking Torus,” hep-th/9703102.

    Google Scholar 

  19. J.M. Maldacena and L. Susskind, “D-branes and Fat Black Holes,” Nucl. Phys. B475 (1996) 679, hep-th/9604042.

    Article  MathSciNet  ADS  Google Scholar 

  20. T. Banks, N. Seiberg, and S. Shenker, “Branes from Matrices,” hep-th/9612157.

    Google Scholar 

  21. H. Verlinde, “The Stringy Fivebrane,” talk at Strings’ 96, Santa Barbara, June 1996.

    Google Scholar 

  22. A. Strominger, C. Vafa, “Microscopic Origin of the Bekenstein-Hawking Entropy,” hep-th/9601029.

    Google Scholar 

  23. J. Maldacena, “Statistical Entropy of Near Extremal Five-branes,” hep-th/9605016.

    Google Scholar 

  24. For a recent account of these developments see J. Maldacena and A. Strominger, “Universal Low-Energy Dynamics for Rotating Black Holes” hep-th/9702015, and references therein.

    Google Scholar 

  25. E. Witten, “Some Comments on String Dynamics,” hep-th/9510135

    Google Scholar 

  26. A. Strominger, “Open P-Branes,” hep-th/9512059; P. Townsend, “D-branes from M-branes,” hep-th/9512062.

    Google Scholar 

  27. A. Losev, G. Moore, S. L. Shatashvili, “M & m’s,” hep-th/9707250; N. Seiberg and S. Sethi “Comments on Neveu-Schwarz Five-Branes,” hep-th/9708085

    Google Scholar 

  28. P. Pasti, D. Sorokin, and M. Tonin, “Covariant Action for a D=11 Five-Brane with the Chiral Field,” Phys.Lett. B398 (1997) 41–46, hep-th/9701037; M. Aganagic, J. Park, C. Popescu, J. Schwarz “World-Volume Action of the M Theory Five-Brane,” Nucl.Phys. B496 (1997) 191–214, hep-th/9701166; J. Schwarz, “Remarks on the M5-Brane,” talk at Strings’ 97, hep-th/9707119.

    MathSciNet  ADS  Google Scholar 

  29. D. Sorokin, P. Townsend, “M-theory superalgebra from the M-5-brane,” hep-th/9708003

    Google Scholar 

  30. E. Witten, “Five-Brane Effective Action In M-Theory” hep-th/9610234

    Google Scholar 

  31. R. Dijkgraaf, G, Moore, E. Verlinde, and H. Verlinde, “Elliptic Genera of Symmetric Products and Second Quantized Strings,” Commun. Math. Phys. hep-th/9608096.

    Google Scholar 

  32. S. Mandelstam, “Lorentz Properties of the Three-String Vertex,” Nucl. Phys. B83 (1974) 413–439; “Interacting-String Picture of the Fermionic String,” Prog. Theor. Phys. Suppl. 86 (1986) 163–170.

    Article  ADS  Google Scholar 

  33. S-J. Rey, “Heterotic M(atrix) Strings and Their Interactions,” hep-th/9704158.

    Google Scholar 

  34. G. Arutyunov and S. Frolov, “Virasoro amplitude from the S N R 24 orbifold sigma model,” hep-th/9708129.

    Google Scholar 

  35. T. Wynter, “Gauge fields and interactions in matrix string theory,” hep-th/9709029

    Google Scholar 

  36. K. Becker and M. Becker, “A Two Loop Test of M(atrix) Theory, hep-th/9705091. K. Becker, M. Becker, J. Polchinski, and A. Tseytlin, “Higher Order Scattering in M(atrix) Theory,” hep-th/9706072.

    Google Scholar 

  37. V. Knizhnik, Sov. Phys. Usp. 32 (1989) 945.

    Article  MathSciNet  ADS  Google Scholar 

  38. W. Taylor, “D-brane Field Theory on Compact Spaces,” hep-th/9611042.

    Google Scholar 

  39. O.J. Ganor, S. Ramgoolam, and W. Taylor, “Branes, Fluxes and Duality in M(atrix)-Theory,” hep-th/9611202.

    Google Scholar 

  40. D. Kutasov, “Orbifold and Solitons,” hep-th/9512145.

    Google Scholar 

  41. M. Douglas, J. Polchinski, and A. Strominger, “Probing Five-Dimensional Black Holes with D-Branes,” hep-th/9703031.

    Google Scholar 

  42. M. Berkooz and M. Douglas, “Fivebranes in M(atrix) Theory,” hep-th/9610236.

    Google Scholar 

  43. O. Aharony, M. Berkooz, S. Kachru, N. Seiberg, and E. Silverstein, “Matrix Description of Interacting Theories in Six Dimensions,” hep-th/9707079

    Google Scholar 

  44. E. Witten, “On the Conformai Field Theory of the Higgs Branch,” hep-th/9707093

    Google Scholar 

  45. D. Diaconescu and N. Seiberg, “The Coulomb Branch of (4,4) Supersymmetric Field Theories in Two Dimensions,” hep-th/9707158

    Google Scholar 

  46. P. Aspinwal, “Enhanced Gauge Symmetries and K3 Surfaces,” Phys. Lett. B357 (1995) 329, hep-th/9507012.

    ADS  Google Scholar 

  47. C. Callan, J. Harvey and A. Strominger, “World-Sheet Approach to Heterotic Solitons and Instantons,” Nucl. Phys. 359 (1991) 611; I. Antoniadis, C. Bachas, J. Ellis and D. Nanopoulos, “Cosmological String Theories and Discrete Inflation,” Phys. Lett. B211 (1988) 393; Nucl. Phys. B328 (1989) 117; S.-J. Rey, “Confining Phase of Superstrings and Axionic Strings,” Phys. Rev. D43 (1991) 439.

    Article  MathSciNet  ADS  Google Scholar 

  48. M. Li and E. Martinec, “Matrix Black Holes,” hep-th/9703211; talk at Strings’ 97, hep-th/9709114.

    Google Scholar 

  49. J._A. Harvey and A. Strominger, “The Heterotic String is a Soliton,” Nucl. Phys. B 449 (1995) 535–552; Nucl. Phys. B458 (1996) 456–473, hep-th/9504047. S. Cherkis and J.H. Schwarz, “Wrapping the M Theory Five-Brane on K3,” hep-th/9703062.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  50. R. Dijkgraaf, E. Verlinde, and H. Verlinde, “Counting Dyons in N=4 String Theory,” Nucl. Phys. B484 (1997) 543, hep-th/9607026

    Article  MathSciNet  ADS  Google Scholar 

  51. T. Kawai, “N = 2 Heterotic String Threshold Correction, K3 Surface and Generalized Kac-Moody Superalgebra,” hep-th/9512046.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Amsterdam, 1018 TV, Amsterdam, The Netherlands

    R. Dijkgraaf

  2. TH-Division, CERN, CH-1211 Geneva 23, Institute for Theoretical Physics, University of Utrecht, 3508 TA, Utrecht, The Netherlands

    E. Verlinde

  3. Institute for Theoretical Physics, University of Amsterdam, 1018 XE, Amsterdam, The Netherlands

    H. Verlinde

Authors
  1. R. Dijkgraaf
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Verlinde
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Verlinde
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. CNRS and Université Pierre et Marie Curie (Paris VI), Paris, France

    Laurent Baulieu  & Marco Picco  & 

  2. University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

    Philippe Di Francesco

  3. Rutgers University, Piscataway, NJ, USA

    Michael Douglas

  4. Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France

    Michael Douglas

  5. Université Pierre et Marie Curie (Paris VI), and École Normale Supérieure, Paris, France

    Vladimir Kazakov

  6. Université Pierre et Marie Curie (Paris VI), Paris, France

    Paul Windey

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Dijkgraaf, R., Verlinde, E., Verlinde, H. (1999). Notes on Matrix and Micro Strings. In: Baulieu, L., Di Francesco, P., Douglas, M., Kazakov, V., Picco, M., Windey, P. (eds) Strings, Branes and Dualities. NATO ASI Series, vol 520. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4730-9_12

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-4730-9_12

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5989-3

  • Online ISBN: 978-94-011-4730-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation