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In a theory that predicts gravitons, shouldn't the background be flat and gravitational interaction then be modeled as a scattering event?

Answer included below.

Credit to /u/broguetrain on Reddit for providing the answer when I asked on there some time ago. I wanted to post this Q&A here (with some edits for clarity) due to recent drama on Reddit so as to assure my ability to reference it in the future.

I do encourage additional answers on this that might provide further useful details. For example: elucidating on how specific metrics can be described as the coherent state of strings in the graviton state.

Logan J. Fisher
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There are two equivalent ways to describe a string in a gravitational field:

  1. To place it in a classical background field with curvature, i.e. a non-Minkowski $g_{\mu\nu}$

  2. To make a coherent state of strings, all of which are in the graviton state by exponentiating the graviton worldsheet operator.

If you have some scattering event that takes place in a classical background field, the overall amplitude will be equivalent (at least to first order) to the same scattering event in a coherent state graviton bath of other strings. Therefore, we conclude that creating a coherent state of string gravitons is equivalent to changing the background metric.

Relevant PSE question: Do strings propagate through space time or do they make space time?

Logan J. Fisher
  • 1,845