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The non-Abelian gauge theory of matrix big bangs

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Abstract

We study at the classical and quantum mechanical level the time-dependent Yang-Mills theory that one obtains via the generalisation of discrete light-cone quantization to singular homogeneous plane waves. The non-Abelian nature of this theory is known to be important for physics near the singularity, at least as far as the number of degrees of freedom is concerned. We will show that the quartic interaction is always subleading as one approaches the singularity and that close enough to t = 0 the evolution is driven by the diverging tachyonic mass term. The evolution towards asymptotically flat space-time also reveals some surprising features.

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References

  1. S.W. Hawking and R. Penrose, The Singularities of gravitational collapse and cosmology, Proc. Roy. Soc. Lond. A 314 (1970) 529 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  2. L.J. Dixon, J.A. Harvey, C. Vafa and E. Witten, Strings on orbifolds, Nucl. Phys. B 261 (1985) 678 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  3. L.J. Dixon, J.A. Harvey, C. Vafa and E. Witten, Strings on orbifolds. 2, Nucl. Phys. B 274 (1986) 285 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  4. L. Cornalba and M.S. Costa, A new cosmological scenario in string theory, Phys. Rev. D 66 (2002) 066001 [hep-th/0203031] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  5. H. Liu, G.W. Moore and N. Seiberg, Strings in a time-dependent orbifold, JHEP 06 (2002) 045 [hep-th/0204168] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  6. H. Liu, G.W. Moore and N. Seiberg, Strings in time-dependent orbifolds, JHEP 10 (2002) 031 [hep-th/0206182] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  7. G.T. Horowitz and J. Polchinski, Instability of spacelike and null orbifold singularities, Phys. Rev. D 66 (2002) 103512 [hep-th/0206228] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  8. B. Craps, S. Sethi and E.P. Verlinde, A matrix big bang, JHEP 10 (2005) 005 [hep-th/0506180] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  9. L. Susskind, Another conjecture about M(atrix) theory, hep-th/9704080 [SPIRES].

  10. B. Craps, Big bang models in string theory, Class. Quant. Grav. 23 (2006) S849 [hep-th/0605199] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  11. B. Craps, T. Hertog and N. Turok, Quantum resolution of cosmological singularities using AdS/CFT, arXiv:0712.4180 [SPIRES].

  12. M. Blau and M. O’Loughlin, DLCQ and plane wave matrix big bang models, JHEP 09 (2008) 097 [arXiv:0806.3255] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  13. M. Blau, M. Borunda, M. O’Loughlin and G. Papadopoulos, The universality of Penrose limits near space-time singularities, JHEP 07 (2004) 068 [hep-th/0403252] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  14. G. Papadopoulos, J.G. Russo and A.A. Tseytlin, Solvable model of strings in a time-dependent plane-wave background, Class. Quant. Grav. 20 (2003) 969 [hep-th/0211289] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  15. J.G. Russo and A.A. Tseytlin, A class of exact pp-wave string models with interacting light-cone gauge actions, JHEP 09 (2002) 035 [hep-th/0208114] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  16. J.-H. She, A matrix model for Misner universe, JHEP 01 (2006) 002 [hep-th/0509067] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  17. A. Awad, S.R. Das, S. Nampuri, K. Narayan and S.P. Trivedi, Gauge theories with time dependent couplings and their cosmological duals, Phys. Rev. D 79 (2009) 046004 [arXiv:0807.1517] [SPIRES].

    ADS  Google Scholar 

  18. B. Craps, F. De Roo and O. Evnin, Can free strings propagate across plane wave singularities?, JHEP 03 (2009) 105 [arXiv:0812.2900] [SPIRES].

    Article  ADS  Google Scholar 

  19. M. Blau and M. O’Loughlin, Homogeneous plane waves, Nucl. Phys. B 654 (2003) 135 [hep-th/0212135] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  20. N. Seiberg, Why is the matrix model correct?, Phys. Rev. Lett. 79 (1997) 3577 [hep-th/9710009] [SPIRES].

    Article  MATH  MathSciNet  ADS  Google Scholar 

  21. A. Sen, D0 branes on T(n) and matrix theory, Adv. Theor. Math. Phys. 2 (1998) 51 [hep-th/9709220] [SPIRES].

    MATH  MathSciNet  Google Scholar 

  22. A. Awad, S.R. Das, K. Narayan and S.P. Trivedi, Gauge theory duals of cosmological backgrounds and their energy momentum tensors, Phys. Rev. D 77 (2008) 046008 [arXiv:0711.2994] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  23. I.Y. Aref’eva, A.S. Koshelev and P.B. Medvedev, Chaos-order transition in matrix theory, Mod. Phys. Lett. A 13 (1998) 2481 [hep-th/9804021] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  24. E. Witten, Bound states of strings and p-branes, Nucl. Phys. B 460 (1996) 335 [hep-th/9510135] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  25. T.S. Biró, Chaos and gauge field theory, World Scientific lecture notes in physics. Volume 56, World Scientific, Singapore (1994).

    Google Scholar 

  26. M. Blau and M. O’Loughlin. Notes on the time-dependent harmonic oscillator, unpublished notes.

  27. H.R. Lewis, Class of exact invariants for classical and quantum time-dependent harmonic oscillators, J. Math. Phys. 9 (1968) 1976 [SPIRES].

    Article  MATH  ADS  Google Scholar 

  28. H.R. Lewis and W.B. Riesenfeld, An Exact quantum theory of the time dependent harmonic oscillator and of a charged particle time dependent electro magnetic field, J. Math. Phys. 10 (1969) 1458 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  29. M. Blau, M. O’Loughlin and L. Seri, Non-abelian QFT and space-time singularities, to appear.

  30. T. Furusawa, Quantum chaos of mixmaster universe. 2, Prog. Theor. Phys. 76 (1986) 67 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  31. T. Furusawa. Quantum chaos of mixmaster universe, Prog. Theor. Phys. 75 (1986) 59.

    Article  MathSciNet  ADS  Google Scholar 

  32. B.K. Berger, Quantum chaos in the mixmaster universe, Phys. Rev. D 39 (1989) 2426 [SPIRES].

    ADS  Google Scholar 

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Authors and Affiliations

  1. University of Nova Gorica, Vipavska 13, 5000, Nova Gorica, Slovenia

    Martin O’Loughlin

  2. SISSA, Via Beirut 3, 34151, Trieste, Italy

    Lorenzo Seri

  3. INFN, Sezione di Trieste, Via Valerio 2, 34127, Trieste, Italy

    Lorenzo Seri

Authors
  1. Martin O’Loughlin
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  2. Lorenzo Seri
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Correspondence to Martin O’Loughlin.

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ArXiv ePrint: 1003.0620

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O’Loughlin, M., Seri, L. The non-Abelian gauge theory of matrix big bangs. J. High Energ. Phys. 2010, 36 (2010). https://doi.org/10.1007/JHEP07(2010)036

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