Skip to main content

From Quiver Diagrams to Particle Physics

  • Conference paper
European Congress of Mathematics

Part of the book series: Progress in Mathematics ((PM,volume 202))

  • 1155 Accesses

Abstract

Recent scenarios of phenomenologically realistic string compactifications involve the existence of gauge sectors localized on D-branes at singular points of Calabi¡ªYau threefolds. The spectrum and interactions in these gauge sectors are determined by the local geometry of the singularity, and can be encoded in quiver diagrams. We discuss the physical models arising for the simplest case of orbifold singularities, and generalize to non-orbifold singularities and orientifold singularities (a generalization naturally arising in string theory). Finally we show that relatively simple singularities lead to gauge sectors surprisingly close to the standard model of elementary particles.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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. C. Beasley, B. R. Greene, C. I. Lazaroiu, M. R. PlesserD3-branes on partial resolutions of abelian quotient singularities of Calabi-Yau threefoldsNucl.Phys. B566 (2000) 599–6.

    Google Scholar 

  2. J. D. Blum, K. IntriligatorNew phases of string theory and 6-D RG fixed points via branes at orbifold singularitiesNucl. Phys. B506 (1997) 199–22; J. Park, A. M. Uranga, A Note on superconformal N=2 theories and orientifoldsNucl. Phys. B542 (1999) 139–15.

    Google Scholar 

  3. K. Dasgupta, S. MukhiBrane constructions conifolds and M theoryNucl. Phys. B551 (1999) 204–22.

    Google Scholar 

  4. M. R. Douglas, B. R. Greene, D. R. MorrisonOrbifold resolution by D-branesNucl. Phys. B506 (1997) 84–10.

    MathSciNet  Google Scholar 

  5. M. R. Douglas, G. MooreD-branes quivers and ALE instantons hep-th/9603167.

    Google Scholar 

  6. B. Feng, A. Hanany, Y.-H. HeD-brane gauge theories from toric singularities and tonic duality,hep-th/0003085.

    Google Scholar 

  7. E. G. Gimon, J. PolchinskiConsistency conditions for orientifolds and d manifoldsPhys. Rev. D54 (1996) 1667; E. G. Gimon, C. V. JohnsonK3 orientifoldsNucl.Phys. B477 (1996) 715; A. Dabholkar, J. ParkStrings on orientifoldsNucl. Phys. B477 (1996) 701.

    MathSciNet  Google Scholar 

  8. L. E. Ibüñez, R. Rabadün, A. M. UrangaAnomalous U(1)’s in type I and type IIB D =4N=1 string vacua, Nucl. Phys. B542 (1999) 112–13.

    Google Scholar 

  9. C. V. Johnson, R. C. MyersAspects of type IIB theory on ALE spacesPhys. Rev. D55 (1997) 6382.

    Google Scholar 

  10. I. R. Klebanov, E. WittenSuperconformal field theory on three-branes at a CalabiYau singularityNucl. Phys. B536 (1998) 199–21.

    Google Scholar 

  11. P. B. KronheimerThe construction of ALE spaces as hyper-Kähler quotientsJ. Diff. Geom. 29 (1989) 665.

    MathSciNet  MATH  Google Scholar 

  12. A. Lawrence, N. Nekrasov, C. VafaOn conformal field theories in four-dimensionsNucl. Phys. B533 (1998) 199–20.

    MathSciNet  Google Scholar 

  13. R. G. Leigh, M. RozaliBrave boxes anomalies,bending and tadpolesPhys. Rev. D59 (1999) 026004.

    MathSciNet  Google Scholar 

  14. J. Lykken, E. Poppitz, S. P. TrivediBranes with GUTs and supersymmetry breakingNucl. Phys. B543 (1999) 105.

    MathSciNet  Google Scholar 

  15. J. McKayGraphs singularities and finite groups Proc. Symp. Pure Math. 37 (1980) 183; M. ReidMcKay correspondence alg-geom/9702016.

    Google Scholar 

  16. D. R. Morrison, M. R. PlesserNonspherical horizonsAdv. Theor. Math. Phys. 3 (1999) 1–8.

    MATH  Google Scholar 

  17. J. Park, R. Rabadün, A. M. UrangaOrientifolding the conifoldhep-th/9907086.

    Google Scholar 

  18. J. PolchinskiTASI lectures on D-braneshep-th/9611050.

    Google Scholar 

  19. A. Sagnotti in Cargese’87Non-perturbative quantum field theory, ed. G. Mack et al(Pergamon Press 1988), pag. 521 Some properties of open string theories.

    Google Scholar 

  20. A. V. Sardo InfirriResolutions of orbifold singularities and the transportation problem on the McKay quiveralg-geom/9610005.

    Google Scholar 

  21. R. von UngeBranes at generalized conifolds and toric geometryJ. High E. Phys. 9902 (1999) 023; K. Oh, R. TatarBranes at orbifolded conifold singularities and supersymmetric gauge field theories,J. High E. Phys. 9910 (1999) 031.

    Google Scholar 

  22. A. M. UrangaBrane configurations for branes at conifoldsJ. High Energy Phys. 9901(1999)022.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer Basel AG

About this paper

Cite this paper

Uranga, A.M. (2001). From Quiver Diagrams to Particle Physics. In: Casacuberta, C., Miró-Roig, R.M., Verdera, J., Xambó-Descamps, S. (eds) European Congress of Mathematics. Progress in Mathematics, vol 202. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8266-8_43

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8266-8_43

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9496-8

  • Online ISBN: 978-3-0348-8266-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics