The renormalization of fluctuating branes, the Galileon and asymptotic safety

TL;DR

This paper investigates the renormalization properties of fluctuating branes and their connection to the Galileon theory, revealing an ultraviolet fixed point akin to asymptotic safety in gravity.

Contribution

It introduces a geometric invariant-based effective action for branes and analyzes its renormalization group flow, uncovering a fixed point similar to asymptotic safety.

Findings

Evidence for an ultraviolet fixed point in brane theories.

The structure of the Galileon theory is preserved at the quantum level.

Connections between brane renormalization and asymptotic safety are established.

Abstract

We consider the renormalization of d-dimensional hypersurfaces (branes) embedded in flat (d+1)-dimensional space. We parametrize the truncated effective action in terms of geometric invariants built from the extrinsic and intrinsic curvatures. We study the renormalization-group running of the couplings and explore the fixed-point structure. We find evidence for an ultraviolet fixed point similar to the one underlying the asymptotic-safety scenario of gravity. We also examine whether the structure of the Galileon theory, which can be reproduced in the nonrelativistic limit, is preserved at the quantum level.