Self-Completeness of Einstein Gravity

TL;DR

The paper argues that the Planck length $L_P$ is the absolute minimal length scale in Einstein gravity, with any attempt to probe shorter distances forcing the formation of macroscopic black holes and thereby translating deep-UV physics into deep-IR gravity. It introduces the black-hole barrier and a non-Wilsonian notion of self-completeness, where trans-Planckian degrees of freedom do not exist as propagating quantum states but are encoded in IR classical BHs. It analyzes the roles of string theory and the species framework, showing how KK towers and light non-gravitational species demand a UV completion via gravitational degrees of freedom and/or string-theoretic structures, while preserving holographic information bounds. The work further explores generalizations beyond Einstein gravity, the interplay with entropy, and speculative non-Wilsonian UV completions for the Standard Model, including potential Higgs-less scenarios mediated by gravity-borne BH physics.

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.