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1 Introduction and Survey

The search for a physically viable theory of quantized gravitation is ongoing; in part because the physics it ought to describe is unknown, and in part because different approaches may not ‘approach’ the same physics. The most prominent contenders are string theory and loop quantum gravity, with ample literature available on either sides. For book-sized expositions see for example [97Jump To The Next Citation Point177Jump To The Next Citation Point112Jump To The Next Citation Point199Jump To The Next Citation Point]. The present report and [157Jump To The Next Citation Point] describe a circle of ideas which differ in several important ways from these approaches.

 1.1 Survey of the scenario
 1.2 Evidence for asymptotic safety
 1.3 Some working definitions
 1.4 Relation to other approaches
  1.4.1 Dynamical triangulations
  1.4.2 Loop quantum gravity
  1.4.3 String theory
 1.5 Discussion of possible objections

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