Positivity bounds on effective theories with gravity

4 problems

• How negative can forward-limit coefficients be once gravity is included

  Contested

  Without gravity, a certain coefficient in the scattering of two particles must be positive. With gravity it may be slightly negative, and the size of the allowed negative value is not known.

• Bounds on four-dimensional gravitational couplings free of infrared logarithms

  Partially resolved

  In four dimensions, the known bounds that account for gravity depend, through a logarithm, on an arbitrary largest distance, because gravity's pull falls off too slowly. A version free of this dependence is not known.

• Does electromagnetism plus gravity require new particles far below the Planck scale

  Contested

  Applying positivity rules to electrons and photons with gravity seems to demand new particles at an energy far below the Planck scale (the energy where quantum gravity becomes strong). It is unsettled whether this is a real prediction or an artifact of how the graviton contribution is handled.

• Prove high-energy growth bound for gravitational amplitudes from first principles

  Partially resolved

  All positivity arguments assume that scattering amplitudes do not grow too fast at high energy. For gravity this growth limit is assumed, not proven.