Holographic interpretation of renormalization group approach to singular perturbations in non-linear differential equations

TL;DR

This paper explains how the renormalization group approach to singular perturbations in nonlinear differential equations can be understood through the holographic principle, linking it to quantum field theory methods via AdS/CFT correspondence.

Contribution

It establishes a holographic interpretation of the renormalization group method for singular perturbations, connecting nonlinear differential equations to quantum field theory.

Findings

Demonstrates the equivalence between the RG approach in differential equations and quantum field theory RG methods.

Provides a holographic explanation using AdS/CFT correspondence.

Bridges concepts between nonlinear differential equations and quantum field theory.

Abstract

We give a holographic explanation how the renormalization group approach to singular perturbations in non-linear differential equations proposed by Chen, Goldenfeld and Oono is indeed equivalent to a renormalization group method in quantum field theories proposed by Gell-Mann and Low via AdS/CFT correspondence.