Aspects of plane wave (matrix) string dynamics

Article

Abstract

We analyse two issues that arise in the context of (matrix) string theories in plane wave backgrounds, namely (1) the use of Brinkmann- versus Rosen-variables in the quantum theory for general plane waves (which we settle conclusively in favour of Brinkmann variables), and (2) the regularisation of the quantum dynamics for a certain class of singular plane waves (discussing the benefits and limitations of regularisations of the plane-wave metric itself).

Keywords

Penrose limit and pp-wave background M(atrix) Theories Spacetime Singularities 

References

  1. [1]
    A.A. Tseytlin, Exact solutions of closed string theory, Class. Quant. Grav. 12 (1995) 2365 [hep-th/9505052] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  2. [2]
    G.T. Horowitz and A.R. Steif, Space-Time Singularities in String Theory, Phys. Rev. Lett. 64 (1990) 260 [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  3. [3]
    G.T. Horowitz and A.R. Steif, Strings in strong gravitational fields, Phys. Rev. D 42 (1990) 1950 [INSPIRE].ADSGoogle Scholar
  4. [4]
    H. de Vega and N. Sanchez, Strings falling into space-time singularities, Phys. Rev. D 42 (1992) 2783.Google Scholar
  5. [5]
    S. Hawking and G. Ellis, The Large Scale Structure of Space-Time, Cambridge University Press (1973).Google Scholar
  6. [6]
    M. Blau, M. Borunda, M. O’Loughlin and G. Papadopoulos, Penrose limits and space-time singularities, Class. Quant. Grav. 21 (2004) L43 [hep-th/0312029] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    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] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    G. Papadopoulos, Power-law singularities in string theory and M-theory, Class. Quant. Grav. 21 (2004) 5097 [hep-th/0404172] [INSPIRE].ADSMATHCrossRefGoogle Scholar
  9. [9]
    R. Penrose, Any space-time has a plane wave as a limit, in Differential geometry and relativity, Reidel, Dordrecht (1976), pg. 271.Google Scholar
  10. [10]
    R. Güven, Plane wave limits and T duality, Phys. Lett. B 482 (2000) 255 [hep-th/0005061] [INSPIRE].ADSGoogle Scholar
  11. [11]
    M. Blau, J.M. Figueroa-O’Farrill and G. Papadopoulos, Penrose limits, supergravity and brane dynamics, Class. Quant. Grav. 19 (2002) 4753 [hep-th/0202111] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  12. [12]
    P. Szekeres and V. Iyer, Spherically symmetric singularities and strong cosmic censorship, Phys. Rev. D 47 (1993) 4362 [INSPIRE].MathSciNetADSGoogle Scholar
  13. [13]
    M. Blau, D. Frank and S. Weiss, Fermi coordinates and Penrose limits, Class. Quant. Grav. 23 (2006) 3993 [hep-th/0603109] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  14. [14]
    M. Blau and S. Weiss, Penrose limits versus string expansions, Class. Quant. Grav. 25 (2008) 125014 [arXiv:0710.3480] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    M. Blau and M. O’Loughlin, DLCQ and Plane Wave Matrix Big Bang Models, JHEP 09 (2008) 097 [arXiv:0806.3255] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    N. Seiberg, Why is the matrix model correct?, Phys. Rev. Lett. 79 (1997) 3577 [hep-th/9710009] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  17. [17]
    A. Sen, D0-branes on T n and matrix theory, Adv. Theor. Math. Phys. 2 (1998) 51 [hep-th/9709220] [INSPIRE].MathSciNetMATHGoogle Scholar
  18. [18]
    A. Sen, An Introduction to nonperturbative string theory, hep-th/9802051 [INSPIRE].
  19. [19]
    B. Craps, S. Sethi and E.P. Verlinde, A Matrix big bang, JHEP 10 (2005) 005 [hep-th/0506180] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  20. [20]
    L. Motl, Proposals on nonperturbative superstring interactions, hep-th/9701025 [INSPIRE].
  21. [21]
    T. Banks and N. Seiberg, Strings from matrices, Nucl. Phys. B 497 (1997) 41 [hep-th/9702187] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  22. [22]
    R. Dijkgraaf, E.P. Verlinde and H.L. Verlinde, Matrix string theory, Nucl. Phys. B 500 (1997) 43 [hep-th/9703030] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    G. Papadopoulos, J. 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] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  24. [24]
    M. Blau and M. O’Loughlin, Homogeneous plane waves, Nucl. Phys. B 654 (2003) 135 [hep-th/0212135] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  25. [25]
    M. Blau, M. O’Loughlin, G. Papadopoulos and A.A. Tseytlin, Solvable models of strings in homogeneous plane wave backgrounds, Nucl. Phys. B 673 (2003) 57 [hep-th/0304198] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    M. Blau, M. Borunda and M. O’Loughlin, On the Hagedorn behaviour of singular scale-invariant plane waves, JHEP 10 (2005) 047 [hep-th/0412228] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  27. [27]
    G.T. Horowitz and B. Way, Lifshitz Singularities, Phys. Rev. D 85 (2012) 046008 [arXiv:1111.1243] [INSPIRE].ADSGoogle Scholar
  28. [28]
    M. O’Loughlin and L. Seri, The Non-Abelian gauge theory of matrix big bangs, JHEP 07 (2010) 036 [arXiv:1003.0620] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  29. [29]
    B. Craps, F. De Roo and O. Evnin, Quantum evolution across singularities: The Case of geometrical resolutions, JHEP 04 (2008) 036 [arXiv:0801.4536] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    O. Evnin and T. Nguyen, On discrete features of the wave equation in singular pp-wave backgrounds, JHEP 09 (2008) 105 [arXiv:0806.3057] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  31. [31]
    B. Craps, F. De Roo and O. Evnin, Can free strings propagate across plane wave singularities?, JHEP 03 (2009) 105 [arXiv:0812.2900] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    B. Craps and O. Evnin, Light-like Big Bang singularities in string and matrix theories, Class. Quant. Grav. 28 (2011) 204006 [arXiv:1103.5911] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  33. [33]
    K. Madhu and K. Narayan, String spectra near some null cosmological singularities, Phys. Rev. D 79 (2009) 126009 [arXiv:0904.4532] [INSPIRE].MathSciNetADSGoogle Scholar
  34. [34]
    K. Narayan, Null cosmological singularities and free strings, Phys. Rev. D 81 (2010) 066005 [arXiv:0909.4731] [INSPIRE].MathSciNetADSGoogle Scholar
  35. [35]
    K. Narayan, Null cosmological singularities and free strings: II, JHEP 01 (2011) 145 [arXiv:1012.0113] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  36. [36]
    A. Corichi, J. Cortez and G.A. Mena Marugan, Quantum Gowdy T 3 model: A Unitary description, Phys. Rev. D 73 (2006) 084020 [gr-qc/0603006] [INSPIRE].MathSciNetADSGoogle Scholar
  37. [37]
    J. Cortez, G.A. Mena Marugan, R. Serodio and J.M. Velhinho, Uniqueness of the Fock quantization of a free scalar field on S 1 with time dependent mass, Phys. Rev. D 79 (2009) 084040 [arXiv:0903.5508] [INSPIRE].ADSGoogle Scholar
  38. [38]
    J. Cortez, G.A. Mena Marugan and J.M. Velhinho, Fock quantization of a scalar field with time dependent mass on the three-sphere: Unitarity and uniqueness, Phys. Rev. D 81 (2010) 044037 [arXiv:1001.0946] [INSPIRE].ADSGoogle Scholar
  39. [39]
    J. Cortez, G.A. Mena Marugan, J. Olmedo and J.M. Velhinho, A Unique Fock quantization for fields in non-stationary spacetimes, JCAP 10 (2010) 030 [arXiv:1004.5320] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  40. [40]
    J. Cortez, G.A.M. Marugan, J. Olmedo and J.M. Velhinho, Uniqueness of the Fock quantization of fields with unitary dynamics in nonstationary spacetimes, Phys. Rev. D 83 (2011) 025002 [arXiv:1101.2397] [INSPIRE].ADSGoogle Scholar
  41. [41]
    G. Gibbons, Quantized Fields Propagating in Plane Wave Space-Times, Commun. Math. Phys. 45 (1975) 191 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  42. [42]
    M. Blau, J.M. Figueroa-O’Farrill, C. Hull and G. Papadopoulos, A New maximally supersymmetric background of IIB superstring theory, JHEP 01 (2002) 047 [hep-th/0110242] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  43. [43]
    R. Metsaev, Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background, Nucl. Phys. B 625 (2002) 70 [hep-th/0112044] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  44. [44]
    R. Metsaev and A.A. Tseytlin, Exactly solvable model of superstring in Ramond-Ramond plane wave background, Phys. Rev. D 65 (2002) 126004 [hep-th/0202109] [INSPIRE].ADSGoogle Scholar
  45. [45]
    M. Blau, J.M. Figueroa-O’Farrill, C. Hull and G. Papadopoulos, Penrose limits and maximal supersymmetry, Class. Quant. Grav. 19 (2002) L87 [hep-th/0201081] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  46. [46]
    D.E. Berenstein, J.M. Maldacena and H.S. Nastase, Strings in flat space and pp waves from \( \mathcal{N} = 4 \) super Yang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  47. [47]
    H. Kleinert and A. Chervyakov, Simple explicit formulas for Gaussian path integrals with time dependent frequencies, Phys. Lett. A 245 (1998) 345 [quant-ph/9803016] [INSPIRE].MathSciNetADSGoogle Scholar
  48. [48]
    M. Blau and M. O’Loughlin, Multiple M2-Branes and Plane Waves, JHEP 09 (2008) 112 [arXiv:0806.3253] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  49. [49]
    B. Craps and O. Evnin, Adiabaticity and emergence of classical space-time in time-dependent matrix theories, JHEP 01 (2011) 130 [arXiv:1011.0820] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  50. [50]
    G. Milanesi, M. O’Loughlin, L. Seri, in preparation.Google Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Matthias Blau
    • 1
  • Martin O’Loughlin
    • 2
  • Lorenzo Seri
    • 3
  1. 1.Albert Einstein Center for Fundamental Physics, Institute for Theoretical PhysicsBern UniversityBernSwitzerland
  2. 2.University of Nova GoricaNova GoricaSlovenia
  3. 3.SISSATriesteItaly

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