Is String Theory a Theory of Quantum Gravity?

Abstract

Some problems in finding a complete quantum theory incorporating gravity are discussed. One is that of giving a consistent unitary description of high-energy scattering. Another is that of giving a consistent quantum description of cosmology, with appropriate observables. While string theory addresses some problems of quantum gravity, its ability to resolve these remains unclear. Answers may require new mechanisms and constructs, whether within string theory, or in another framework.

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Notes

  1. 1.

    For further discussion, see [5].

  2. 2.

    We adopt the convention \(M_{D}^{D-2} = (2\pi)^{D-4}/(8\pi G_{D})\).

  3. 3.

    Even theories without Lorentz invariance, e.g. with modified dispersion relations, appear to need to address such a regime, or confront even greater complications. One example would be in black hole formation from non-relativistic particles.

  4. 4.

    More precisely, we might think about the perturbative expansion around the classical geometry corresponding to the saddlepoint in the eikonal amplitude. This will be described below.

  5. 5.

    Note that one can consider either tree diagrams with all but one free “field-point” leg connected to the high-energy sources, which gives an analog to the calculation of the classical metric of [24, 25], or with all legs connected to the external sources, corresponding to contributions to the two-two amplitude like in Fig. 2. These are clearly related, and argued to have corresponding divergences at (2.11).

  6. 6.

    One also might try semicompact sources like those described in [54]. The expression (3.11) would not give compact F, but needs to be modified to take into account the extent of the source. This remains an open question, though one also expects to encounter difficulties either like those outlined in the previous or next subsections.

  7. 7.

    I thank T. Okuda and J. Polchinski for discussions on this point.

  8. 8.

    For a gaussian wavepacket, the longitudinal width of the packet must satisfy , which places a bound on the amplitude for tails of wavepackets colliding at zero impact parameter to be “outside” the horizon: . Similar arguments can be given for transverse widths.

  9. 9.

    I thank J. Polchinski and M. Gary for discussions on this point.

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Acknowledgements

This work was supported in part by the Department of Energy under Contract DE-FG02-91ER40618. I thank G. Horowitz and D. Marolf for comments on a draft of part of this paper, and M. Gary and J. Polchinski for useful discussions.

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Giddings, S.B. Is String Theory a Theory of Quantum Gravity?. Found Phys 43, 115–139 (2013). https://doi.org/10.1007/s10701-011-9612-x

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Keywords

  • String theory
  • Quantum gravity
  • Ultraplanckian scattering
  • Unitarity
  • S-matrix
  • Black holes
  • Information paradox
  • Cosmology
  • Local observables
  • Locality
  • Locality bound