Classical Duals, Legendre Transforms and the Vainshtein Mechanism

TL;DR

This paper extends classical duals to a broad class of self-interacting theories, providing a perturbative approach to analyze modified gravity models with Vainshtein screening.

Contribution

It introduces a general method to find duals via Legendre transforms, applicable to complex theories with multiple fields and hierarchical scales.

Findings

Derived the classical dual of the quintic galileon theory.

Established a practical method for finding duals in various self-interacting theories.

Enabled perturbative analysis beyond classical breakdown scales.

Abstract

We show how to generalize the classical duals found by Gabadadze {\it et al} to a very large class of self-interacting theories. This enables one to adopt a perturbative description beyond the scale at which classical perturbation theory breaks down in the original theory. This is particularly relevant if we want to test modified gravity scenarios that exhibit Vainshtein screening on solar system scales. We recognise the duals as being related to the Legendre transform of the original Lagrangian, and present a practical method for finding the dual in general; our methods can also be applied to self-interacting theories with a hierarchy of strong coupling scales, and with multiple fields. We find the classical dual of the full quintic galileon theory as an example.