Skip to main content
SpringerLink
Log in

Matrix theory origins of non-geometric fluxes

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

We explore the origins of non-geometric fluxes within the context of M theory described as a matrix model. Building upon compactifications of Matrix theory on non-commutative tori and twisted tori, we formulate the conditions which describe compactifications with non-geometric fluxes. These turn out to be related to certain deformations of tori with non-commutative and non-associative structures on their phase space. Quantization of flux appears as a natural consequence of the framework and leads to the resolution of non-associativity at the level of the unitary operators. The quantum-mechanical nature of the model bestows an important role on the phase space. In particular, the geometric and non-geometric fluxes exchange their properties when going from position space to momentum space thus providing a duality among the two. Moreover, the operations which connect solutions with different fluxes are described and their relation to T-duality is discussed. Finally, we provide some insights on the effective gauge theories obtained from these matrix compactifications.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. T. Banks, W. Fischler, S. Shenker and L. Susskind, M theory as a matrix model: A Conjecture, Phys. Rev. D 55 (1997) 5112 [hep-th/9610043] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  2. M. Graña, Flux compactifications in string theory: A Comprehensive review, Phys. Rept. 423 (2006) 91 [hep-th/0509003] [INSPIRE].

    Article  ADS  Google Scholar 

  3. M.R. Douglas and S. Kachru, Flux compactification, Rev. Mod. Phys. 79 (2007) 733 [hep-th/0610102] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. T. Eguchi and H. Kawai, Reduction of Dynamical Degrees of Freedom in the Large-N Gauge Theory, Phys. Rev. Lett. 48 (1982) 1063 [INSPIRE].

    Article  ADS  Google Scholar 

  5. N. Ishibashi, H. Kawai, Y. Kitazawa and A. Tsuchiya, A Large-N reduced model as superstring, Nucl. Phys. B 498 (1997) 467 [hep-th/9612115] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  6. H. Aoki, N. Ishibashi, S. Iso, H. Kawai, Y. Kitazawa and T. Tada, Noncommutative Yang-Mills in IIB matrix model, Nucl. Phys. B 565 (2000) 176 [hep-th/9908141] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  7. H. Aoki, S. Iso, H. Kawai, Y. Kitazawa and T. Tada, Space-time structures from IIB matrix model, Prog. Theor. Phys. 99 (1998) 713 [hep-th/9802085] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. J. Nishimura and F. Sugino, Dynamical generation of four-dimensional space-time in the IIB matrix model, JHEP 05 (2002) 001 [hep-th/0111102] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. H. Kawai, S. Kawamoto, T. Kuroki, T. Matsuo and S. Shinohara, Mean field approximation of IIB matrix model and emergence of four-dimensional space-time, Nucl. Phys. B 647 (2002) 153 [hep-th/0204240] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. H. Steinacker, Emergent Geometry and Gravity from Matrix Models: an Introduction, Class. Quant. Grav. 27 (2010) 133001 [arXiv:1003.4134] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  11. H. Aoki, Chiral fermions and the standard model from the matrix model compactified on a torus, Prog. Theor. Phys. 125 (2011) 521 [arXiv:1011.1015] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  12. A. Chatzistavrakidis, H. Steinacker and G. Zoupanos, Intersecting branes and a standard model realization in matrix models, JHEP 09 (2011) 115 [arXiv:1107.0265] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  13. S.-W. Kim, J. Nishimura and A. Tsuchiya, Expanding (3 + 1)-dimensional universe from a Lorentzian matrix model for superstring theory in (9 + 1)-dimensions, Phys. Rev. Lett. 108 (2012) 011601 [arXiv:1108.1540] [INSPIRE].

    Article  ADS  Google Scholar 

  14. S.-W. Kim, J. Nishimura and A. Tsuchiya, Expanding universe as a classical solution in the Lorentzian matrix model for nonperturbative superstring theory, Phys. Rev. D 86 (2012) 027901 [arXiv:1110.4803] [INSPIRE].

    ADS  Google Scholar 

  15. J. Nishimura, The Origin of space-time as seen from matrix model simulations, PTEP 2012 (2012) 01A101 [arXiv:1205.6870] [INSPIRE].

  16. A. Connes, M.R. Douglas and A.S. Schwarz, Noncommutative geometry and matrix theory: Compactification on tori, JHEP 02 (1998) 003 [hep-th/9711162] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. D.A. Lowe, H. Nastase and S. Ramgoolam, Massive IIA string theory and matrix theory compactification, Nucl. Phys. B 667 (2003) 55 [hep-th/0303173] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  18. A. Chatzistavrakidis and L. Jonke, Matrix theory compactifications on twisted tori, Phys. Rev. D 85 (2012) 106013 [arXiv:1202.4310] [INSPIRE].

    ADS  Google Scholar 

  19. M. Anazawa, D0-branes in a H field background and noncommutative geometry, Nucl. Phys. B 569 (2000) 680 [hep-th/9905055] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  20. S. Hellerman, J. McGreevy and B. Williams, Geometric constructions of nongeometric string theories, JHEP 01 (2004) 024 [hep-th/0208174] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  21. A. Dabholkar and C. Hull, Duality twists, orbifolds and fluxes, JHEP 09 (2003) 054 [hep-th/0210209] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  22. A. Flournoy, B. Wecht and B. Williams, Constructing nongeometric vacua in string theory, Nucl. Phys. B 706 (2005) 127 [hep-th/0404217] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. O.J. Ganor, S. Ramgoolam and W. Taylor, Branes, fluxes and duality in M(atrix) theory, Nucl. Phys. B 492 (1997) 191 [hep-th/9611202] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  24. D. Brace, B. Morariu and B. Zumino, Dualities of the matrix model from T duality of the Type II string, Nucl. Phys. B 545 (1999) 192 [hep-th/9810099] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  25. D. Brace, B. Morariu and B. Zumino, T duality and Ramond-Ramond backgrounds in the matrix model, Nucl. Phys. B 549 (1999) 181 [hep-th/9811213] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. J. Shelton, W. Taylor and B. Wecht, Nongeometric flux compactifications, JHEP 10 (2005) 085 [hep-th/0508133] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  27. J. Shelton, W. Taylor and B. Wecht, Generalized Flux Vacua, JHEP 02 (2007) 095 [hep-th/0607015] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. S. Kachru, M.B. Schulz, P.K. Tripathy and S.P. Trivedi, New supersymmetric string compactifications, JHEP 03 (2003) 061 [hep-th/0211182] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  29. J. Scherk and J.H. Schwarz, How to Get Masses from Extra Dimensions, Nucl. Phys. B 153 (1979) 61 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  30. N. Kaloper and R.C. Myers, The Odd story of massive supergravity, JHEP 05 (1999) 010 [hep-th/9901045] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. C. Hull and R. Reid-Edwards, Flux compactifications of string theory on twisted tori, Fortsch. Phys. 57 (2009) 862 [hep-th/0503114] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. G. Dall’Agata and N. Prezas, Scherk-Schwarz reduction of M-theory on G2-manifolds with fluxes, JHEP 10 (2005) 103 [hep-th/0509052] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. C. Hull and R. Reid-Edwards, Flux compactifications of M-theory on twisted Tori, JHEP 10 (2006) 086 [hep-th/0603094] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  34. M. Graña, R. Minasian, M. Petrini and A. Tomasiello, A Scan for new N = 1 vacua on twisted tori, JHEP 05 (2007) 031 [hep-th/0609124] [INSPIRE].

    Article  ADS  Google Scholar 

  35. C. Hull, A Geometry for non-geometric string backgrounds, JHEP 10 (2005) 065 [hep-th/0406102] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  36. C. Hull and R. Reid-Edwards, Non-geometric backgrounds, doubled geometry and generalised T-duality, JHEP 09 (2009) 014 [arXiv:0902.4032] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  37. G. Dall’Agata, N. Prezas, H. Samtleben and M. Trigiante, Gauged Supergravities from Twisted Doubled Tori and Non-Geometric String Backgrounds, Nucl. Phys. B 799 (2008) 80 [arXiv:0712.1026] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. D. Andriot, M. Larfors, D. Lüst and P. Patalong, A ten-dimensional action for non-geometric fluxes, JHEP 09 (2011) 134 [arXiv:1106.4015] [INSPIRE].

    Article  ADS  Google Scholar 

  39. D. Andriot, O. Hohm, M. Larfors, D. Lüst and P. Patalong, A geometric action for non-geometric fluxes, Phys. Rev. Lett. 108 (2012) 261602 [arXiv:1202.3060] [INSPIRE].

    Article  ADS  Google Scholar 

  40. G. Aldazabal, W. Baron, D. Marques and C. Núñez, The effective action of Double Field Theory, JHEP 11 (2011) 052 [Erratum ibid. 1111 (2011) 109] [arXiv:1109.0290] [INSPIRE].

    Article  ADS  Google Scholar 

  41. D. Geissbuhler, Double Field Theory and N = 4 Gauged Supergravity, JHEP 11 (2011) 116 [arXiv:1109.4280] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. M. Graña and D. Marques, Gauged Double Field Theory, JHEP 04 (2012) 020 [arXiv:1201.2924] [INSPIRE].

    Article  ADS  Google Scholar 

  43. G. Dibitetto, J. Fernandez-Melgarejo, D. Marques and D. Roest, Duality orbits of non-geometric fluxes, Fortsch. Phys. 60 (2012) 1123 [arXiv:1203.6562] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  44. R. Blumenhagen, A. Deser, D. Lüst, E. Plauschinn and F. Rennecke, Non-geometric Fluxes, Asymmetric Strings and Nonassociative Geometry, J. Phys. A 44 (2011) 385401 [arXiv:1106.0316] [INSPIRE].

    ADS  Google Scholar 

  45. R. Blumenhagen, A. Deser, E. Plauschinn and F. Rennecke, Bianchi Identities for Non-Geometric Fluxes - From Quasi-Poisson Structures to Courant Algebroids, arXiv:1205.1522 [INSPIRE].

  46. D.S. Berman, E.T. Musaev, D.C. Thompson and D.C. Thompson, Duality Invariant M-theory: Gauged supergravities and Scherk-Schwarz reductions, JHEP 10 (2012) 174 [arXiv:1208.0020] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  47. V. Mathai and J.M. Rosenberg, T duality for torus bundles with H fluxes via noncommutative topology, Commun. Math. Phys. 253 (2004) 705 [hep-th/0401168] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  48. P. Bouwknegt, K. Hannabuss and V. Mathai, Nonassociative tori and applications to T-duality, Commun. Math. Phys. 264 (2006) 41 [hep-th/0412092] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  49. I. Ellwood and A. Hashimoto, Effective descriptions of branes on non-geometric tori, JHEP 12 (2006) 025 [hep-th/0607135] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  50. P. Grange and S. Schäfer-Nameki, T-duality with H-flux: Non-commutativity, T-folds and G×G structure,Nucl. Phys. B 770 (2007) 123 [hep-th/0609084] [INSPIRE].

    Article  ADS  Google Scholar 

  51. D. Lüst, T-duality and closed string non-commutative (doubled) geometry, JHEP 12 (2010) 084 [arXiv:1010.1361] [INSPIRE].

    Article  Google Scholar 

  52. D. Lüst, Twisted Poisson Structures and Non-commutative/non-associative Closed String Geometry, PoS(CORFU2011) 086 [arXiv:1205.0100] [INSPIRE].

  53. R. Jackiw, 3 - Cocycle in mathematics and physics, Phys. Rev. Lett. 54 (1985) 159 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  54. R. Jackiw, Anomalies And Topology, in proceedings of Theoretical Advanced Study Institute in Elementary Particle Physics, MIT-CTP-1298, M.J. Boswick and F. Gursey eds., World Scientific, Singapore (1985).

  55. R.J. Szabo, Quantum field theory on noncommutative spaces, Phys. Rept. 378 (2003) 207 [hep-th/0109162] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  56. D. Mylonas, P. Schupp and R.J. Szabo, Membrane σ-models and Quantization of Non-Geometric Flux Backgrounds, JHEP 09 (2012) 012 [arXiv:1207.0926] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  57. R. Blumenhagen and E. Plauschinn, Nonassociative Gravity in String Theory?, J. Phys. A 44 (2011) 015401 [arXiv:1010.1263] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  58. C. Condeescu, I. Florakis and D. Lüst, Asymmetric Orbifolds, Non-Geometric Fluxes and Non-Commutativity in Closed String Theory, JHEP 04 (2012) 121 [arXiv:1202.6366] [INSPIRE].

    Article  ADS  Google Scholar 

  59. P.-M. Ho, Twisted bundle on quantum torus and BPS states in matrix theory, Phys. Lett. B 434 (1998) 41 [hep-th/9803166] [INSPIRE].

    Article  ADS  Google Scholar 

  60. W. Taylor, D-brane field theory on compact spaces, Phys. Lett. B 394 (1997) 283 [hep-th/9611042] [INSPIRE].

    Article  ADS  Google Scholar 

  61. A. Chatzistavrakidis, On Lie-algebraic solutions of the type IIB matrix model, Phys. Rev. D 84 (2011) 106010 [arXiv:1108.1107] [INSPIRE].

    ADS  Google Scholar 

  62. C. Hull and B. Zwiebach, Double Field Theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  63. N. Hitchin, Generalized Calabi-Yau manifolds, Quart. J. Math. Oxford Ser. 54 (2003) 281 [math/0209099] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  64. M. Gualtieri, Generalized complex geometry, math/0401221 [INSPIRE].

  65. O. Hohm and B. Zwiebach, Large Gauge Transformations in Double Field Theory, arXiv:1207.4198 [INSPIRE].

  66. M.R. Douglas and C.M. Hull, D-branes and the noncommutative torus, JHEP 02 (1998) 008 [hep-th/9711165] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  67. T. Kawano and K. Okuyama, Matrix theory on noncommutative torus, Phys. Lett. B 433 (1998) 29 [hep-th/9803044] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  68. C.-S. Chu and P.-M. Ho, Noncommutative open string and D-brane, Nucl. Phys. B 550 (1999) 151 [hep-th/9812219] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  69. R.C. Myers, Dielectric branes, JHEP 12 (1999) 022 [hep-th/9910053] [INSPIRE].

    Article  ADS  Google Scholar 

  70. L. Cornalba and R. Schiappa, Nonassociative star product deformations for D-brane world volumes in curved backgrounds, Commun. Math. Phys. 225 (2002) 33 [hep-th/0101219] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  71. P. Bordalo, L. Cornalba and R. Schiappa, Towards quantum dielectric branes: Curvature corrections in Abelian β-function and nonAbelian Born-Infeld action, Nucl. Phys. B 710 (2005) 189 [hep-th/0409017] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  72. D.N. Blaschke and H. Steinacker, On the 1-loop effective action for the IKKT model and non-commutative branes, JHEP 10 (2011) 120 [arXiv:1109.3097] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  73. Y. Asano, H. Kawai and A. Tsuchiya, Factorization of the Effective Action in the IIB Matrix Model, Int. J. Mod. Phys. A 27 (2012) 1250089 [arXiv:1205.1468] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bethe Center for Theoretical Physics and Physikalisches Institut, University of Bonn, Nussallee 12, D-53115, Bonn, Germany

    Athanasios Chatzistavrakidis & Larisa Jonke

  2. Theoretical Physics Division, Rudjer Bošković Institute, Bijenička 54, 10000, Zagreb, Croatia

    Larisa Jonke

Authors
  1. Athanasios Chatzistavrakidis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Larisa Jonke
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Larisa Jonke.

Additional information

ArXiv ePrint: 1207.6412

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chatzistavrakidis, A., Jonke, L. Matrix theory origins of non-geometric fluxes. J. High Energ. Phys. 2013, 40 (2013). https://doi.org/10.1007/JHEP02(2013)040

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP02(2013)040

Keywords

Search

Navigation