Self-Completeness of Einstein Gravity

TL;DR

This paper argues that Einstein gravity is self-complete at the Planck scale, with trans-Planckian physics effectively replaced by classical black holes, and explores implications for string theory and other models.

Contribution

It introduces the concept that Einstein gravity is self-complete in the deep-UV without Wilsonian completion and links this to black hole physics and string theory limits.

Findings

Trans-Planckian degrees of freedom are equivalent to classical black holes.

Einstein gravity is self-complete in the deep-UV but not in the Wilsonian sense.

Strong-coupling string theory limit is inherent in Einstein gravity.

Abstract

We argue, that in Einsteinian gravity the Planck length is the shortest length of nature, and any attempt of resolving trans-Planckian physics bounces back to macroscopic distances due to black hole formation. In Einstein gravity trans-Planckian propagating quantum degrees of freedom cannot exist, instead they are equivalent to the classical black holes that are fully described by lighter infra-red degrees of freedom and give exponentially-soft contribution into the virtual processes. Based on this property we argue that pure-Einstein (super)gravity and its high-dimensional generalizations are self-complete in deep-UV, but not in standard Wilsonian sense. We suggest that certain strong-coupling limit of string theory is built-in in pure Einstein gravity, whereas the role of weakly-coupled string theory limit is to consistently couple gravity to other particle species, with their number being set by the inverse string coupling. We also discuss some speculative ideas generalizing the notion of non-Wilsonian self-completeness to other theories, such as the standard model without the Higgs.