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Planckian Scattering as a Holographic Field Theory
Sebastian de Haro
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Recently, 't Hooft's S-matrix for black hole evaporation, obtained from
the gravitational interactions between the in-falling particles and Hawking
radiation, has been generalised to include transverse effects. The action
describing the collision turned out to be a string theory action with an
antisymmetric tensor background. In this article we show that the model
reproduces both the correct longitudinal and transverse dynamics, even when
one goes beyond the eikonal approximation or particles collide at nonvanishing
incidence angles. It also gives the correct momentum tranfer that takes place in
the process.Including a curvature on the horizon provides the action with an
extra term, which can be interpreted as a dilaton contribution. The amplitude of
the scattering is seen to reproduce the Veneziano amplitude in a certain limit,
as in earlier work by 't Hooft. The theory resembles a "holographic" field
theory, in the sense that it only depends on the horizon degrees of freedom, and
the in- and out-Hilbert spaces are the same. The operators representing the
oordinates of in- and out-going particles are non-commuting, and Heisenberg's
uncertainty principle must be corrected by a term proportional to the ratio of
the ingoing momentum to the impact parameter, times Newton's constant. Reducing
to 2+1 dimensions, we find that the coordinates satisfy an SO(2,1) algebra.
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gr-qc/9806028
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