Non-perturbative aspects of galileon duality

TL;DR

This paper investigates the quantum properties of galileon duality, revealing that the duality transformation's singularities can affect the vacuum structure and spectral properties, challenging previous notions of non-local UV behavior.

Contribution

It demonstrates how regulating the galileon duality transformation preserves vacuum structure and uncovers semi-classical effects impacting high-energy spectral properties.

Findings

Duality transformation singularities influence vacuum structure.

Semi-classical contributions affect high-energy spectral properties.

Challenges previous evidence for non-local UV structure.

Abstract

We study quantum aspects of the galileon duality, especially in the case of a particular interacting galileon theory that is said to be dual to a free theory through the action of a simultaneous field and coordinate transformation. This would appear to map a theory with multiple vacua to one with a unique vacuum state. However, by regulating the duality transformation using external sources, we are able to preserve the full vacuum structure in the dual frame. By explicitly calculating the one-particle irreducible effective action on a maximally symmetric background, we identify a semi-classical contribution to the Wightman functions that has not been taken into account in previous analyses due to the singular point in the duality map. This may affect its spectral properties at high energy scales. These observations cast doubt on the main evidence in support of a non-local UV structure for galileons.