Inequivalence of Coset Constructions for Spacetime Symmetries: Coupling with Gravity

TL;DR

This paper investigates how different parametrizations of spacetime symmetries, like Galileon duality, affect their coupling to gravity, revealing that such reparametrizations can alter the hierarchy of scales and influence superluminality properties.

Contribution

It demonstrates that changing coset parametrizations modifies the gravitational coupling and scale separation, impacting physical features like superluminality in Galileon theories.

Findings

Reparametrization affects the scale hierarchy in gravitational coupling.

Superluminality can appear or disappear depending on the coset parametrization.

Higher-dimension operators become relevant in dual theories.

Abstract

We study how the coupling with gravity of theories with non-linearly realized space-time symmetries is modified when one changes the parametrization of the coset. As an example, we focus on the so-called Galileon duality: a reparametrization which maps a Galilean invariant action into another one which enjoys the same symmetry. Starting with a standard coupling with gravity, with a parametric separation between the Planck scale and the typical scale of the coset, one ends up with a theory without such a separation. In particular an infinite set of higher-dimension operators are relevant when the superluminality of the Galileon is measurable in the effective theory. This addresses an apparent paradox since superluminality arises in the dual theory even when absent in the original one.