Skip to main content
SpringerLink
Log in

Solving the simplest theory of quantum gravity

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

Abstract

We solve what is quite likely the simplest model of quantum gravity, the worldsheet theory of an infinitely long, free bosonic string in Minkowski space. Contrary to naive expectations, this theory is non-trivial. We illustrate this by constructing its exact factorizable S-matrix. Despite its simplicity, the theory exhibits many of the salient features expected from more mature quantum gravity models, including the absence of local off-shell observables, a minimal length, as well as (integrable relatives of) black holes. All these properties follow from the exact S-matrix. We show that the complete finite volume spectrum can be reconstructed analytically from this S-matrix with the help of the thermodynamic Bethe Ansatz. We argue that considered as a UV complete relativistic 2-dimensional quantum field theory the model exhibits a new type of renormalization group flow behavior, “asymptotic fragility”. Asymptotically fragile flows do not originate from a UV fixed point.

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. J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].

    MathSciNet  ADS  MATH  Google Scholar 

  2. S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  3. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].

    MathSciNet  ADS  MATH  Google Scholar 

  4. E. Witten, String theory dynamics in various dimensions, Nucl. Phys. B 443 (1995) 85 [hep-th/9503124] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  5. 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 

  6. M. Luscher, Volume dependence of the energy spectrum in massive quantum field theories. 2. Scattering states, Commun. Math. Phys. 105 (1986) 153.

    Article  MathSciNet  ADS  Google Scholar 

  7. M. Lüscher and U. Wolff, How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation, Nucl. Phys. B 339 (1990) 222 [INSPIRE].

    Article  ADS  Google Scholar 

  8. N. Arkani-Hamed, S. Dubovsky, A. Nicolis, E. Trincherini and G. Villadoro, A measure of de Sitter entropy and eternal inflation, JHEP 05 (2007) 055 [arXiv:0704.1814] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  9. S. Weinberg and E. Witten, Limits on massless particles, Phys. Lett. B 96 (1980) 59 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  10. J.L. Cardy, Conformal invariance and universality in finite-size scaling, J. Phys. A 17 (1984) L385 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  11. A. Zamolodchikov, Thermodynamic Bethe ansatz in relativistic models. Scaling three state potts and Lee-Yang models, Nucl. Phys. B 342 (1990) 695 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  12. C.G. Callan Jr., S.B. Giddings, J.A. Harvey and A. Strominger, Evanescent black holes, Phys. Rev. D 45 (1992) 1005 [hep-th/9111056] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  13. J.G. Russo, L. Susskind and L. Thorlacius, Black hole evaporation in (1+1)-dimensions, Phys. Lett. B 292 (1992) 13 [hep-th/9201074] [INSPIRE].

    Article  ADS  Google Scholar 

  14. T.M. Fiola, J. Preskill, A. Strominger and S.P. Trivedi, Black hole thermodynamics and information loss in two-dimensions, Phys. Rev. D 50 (1994) 3987 [hep-th/9403137] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  15. A. Ashtekar, F. Pretorius and F.M. Ramazanoglu, Surprises in the evaporation of 2-dimensional black holes, Phys. Rev. Lett. 106 (2011) 161303 [arXiv:1011.6442] [INSPIRE].

    Article  ADS  Google Scholar 

  16. S. Hawking, Breakdown of predictability in gravitational collapse, Phys. Rev. D 14 (1976) 2460 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  17. P.H. Ginsparg and G.W. Moore, Lectures on 2D gravity and 2D string theory, hep-th/9304011 [INSPIRE].

  18. S. Dubovsky, R. Flauger and V. Gorbenko, Effective string theory revisited, arXiv:1203.1054 [INSPIRE].

  19. J. Polchinski and A. Strominger, Effective string theory, Phys. Rev. Lett. 67 (1991) 1681 [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. J. Polchinski, String theory. Volume 1: an introduction to the bosonic string, Cambridge University Press, Cambridge U.K. (1998).

    Book  Google Scholar 

  21. P. Fendley and H. Saleur, Massless integrable quantum field theories and massless scattering in (1 + 1)-dimensions, hep-th/9310058 [INSPIRE].

  22. A. Zamolodchikov, From tricritical Ising to critical Ising by thermodynamic Bethe ansatz, Nucl. Phys. B 358 (1991) 524 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  23. T.R. Klassen and E. Melzer, Purely elastic scattering theories and their ultraviolet limits, Nucl. Phys. B 338 (1990) 485 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  24. N. Arkani-Hamed, F. Cachazo and J. Kaplan, What is the simplest quantum field theory?, JHEP 09 (2010) 016 [arXiv:0808.1446] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  25. D. Kastor, E. Martinec and S. Shenker, RG flow in N = 1 discrete series, Nucl. Phys. B 316 (1989)590 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. P. Dorey and R. Tateo, Excited states by analytic continuation of TBA equations, Nucl. Phys. B 482 (1996) 639 [hep-th/9607167] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  27. J. Teschner, On the spectrum of the sinh-Gordon model in finite volume, Nucl. Phys. B 799 (2008)403 [hep-th/0702214] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. F. Smirnov, Form-factors in completely integrable models of quantum field theory, Adv. Ser. Math. Phys. 14 (1992) 1.

    Article  Google Scholar 

  29. G. Delfino, G. Mussardo and P. Simonetti, Correlation functions along a massless flow, Phys. Rev. D 51 (1995) 6620 [hep-th/9410117] [INSPIRE].

    ADS  Google Scholar 

  30. N. Seiberg, L. Susskind and N. Toumbas, Space-time noncommutativity and causality, JHEP 06 (2000) 044 [hep-th/0005015] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  31. P. Goddard, J. Goldstone, C. Rebbi and C.B. Thorn, Quantum dynamics of a massless relativistic string, Nucl. Phys. B 56 (1973) 109 [INSPIRE].

    Article  ADS  Google Scholar 

  32. G. ’t Hooft, The black hole interpretation of string theory, Nucl. Phys. B 335 (1990) 138 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  33. D. Eardley and V. Moncrief, The global existence of Yang-Mills Higgs fields in four-dimensional Minkowski space. 2. Completion of proof, Commun. Math. Phys. 83 (1982) 193.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  34. D. Eardley and V. Moncrief, The global existence of Yang-Mills Higgs fields in four-dimensional minkowski space. 1. Local existence and smoothness properties, Commun. Math. Phys. 83 (1982) 171.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  35. M.R. Douglas, D.N. Kabat, P. Pouliot and S.H. Shenker, D-branes and short distances in string theory, Nucl. Phys. B 485 (1997) 85 [hep-th/9608024] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  36. T. Banks, Prolegomena to a theory of bifurcating universes: a nonlocal solution to the cosmological constant problem or little Λ goes back to the future, Nucl. Phys. B 309 (1988) 493 [INSPIRE].

    Article  ADS  Google Scholar 

  37. S. Hawking, The effective action for wormholes, Nucl. Phys. B 363 (1991) 117 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  38. V. Rubakov, Modeling macroscopic and baby universes by fundamental strings, Nucl. Phys. B 453 (1995) 395 [hep-th/9505159] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  39. N. Arkani-Hamed, J. Orgera and J. Polchinski, Euclidean wormholes in string theory, JHEP 12 (2007)018 [arXiv:0705.2768] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  40. S. Weinberg, Critical phenomena for field theorists, lectures presented at the International School of Subnuclear Physics “Ettore Majorana”, July 23-August 8, Erice, Italy (1976).

Download references

Author information

Authors and Affiliations

  1. Center for Cosmology and Particle Physics, Department of Physics, New York University, New York, NY, 10003, U.S.A.

    Sergei Dubovsky, Raphael Flauger & Victor Gorbenko

  2. School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, 08540, U.S.A.

    Raphael Flauger

Authors
  1. Sergei Dubovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Raphael Flauger
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Victor Gorbenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Raphael Flauger.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dubovsky, S., Flauger, R. & Gorbenko, V. Solving the simplest theory of quantum gravity. J. High Energ. Phys. 2012, 133 (2012). https://doi.org/10.1007/JHEP09(2012)133

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP09(2012)133

Keywords

Search

Navigation