Resilience of DBI screened objects and their ladder symmetries

TL;DR

This paper investigates the linear response and symmetries of scalar fields with screening mechanisms around objects, revealing unique multipole behaviors and ladder symmetries that resemble black hole Love numbers.

Contribution

It introduces a novel ladder operator framework for analyzing scalar responses, uncovering symmetries and response patterns in Dirac-Born-Infeld theories with screening.

Findings

Certain multipoles have zero response for specific orders.

Logarithmic running of multipoles in even dimensions.

Ladder symmetries relate to conserved charges and response properties.

Abstract

Scalar field theories with a shift symmetry come equipped with the $K$-mouflage (or kinetic screening) mechanism that suppresses the scalar interaction between massive objects below a certain distance, the screening radius. In this work, we study the linear response of the scalar field distribution around a screened (point-like) object subject to a long range external scalar field perturbation for the Dirac-Born-Infeld theory. We find that, for regular boundary conditions at the position of the particle, some multipoles have vanishing response for a lacunar series of the multipole order $\ell$ for any dimension. Some multipoles also exhibit a logarithmic running when the number of spatial dimensions is even. We construct a ladder operator structure, with its associated ladder symmetries, formed by two sets of ladders that are related to the properties of the linear response and the existence of conserved charges. Our results exhibit a remarkable resemblance with the Love numbers properties of black holes in General Relativity, although some intriguing differences subsist.