Asymptotic structure of Carrollian limits of Einstein-Yang-Mills theory in four spacetime dimensions

TL;DR

This paper explores the asymptotic structure and symmetries of Carrollian limits of Einstein-Yang-Mills theory in four dimensions, revealing new algebraic extensions, boundary conditions, and gauge enhancements.

Contribution

It introduces a new infinite-dimensional BMS-like extension via Carroll-Galileo duality, and uncovers an infinite-dimensional color enhancement in the electric Carrollian limit of Yang-Mills.

Findings

Discovery of a new BMS-like algebra extension.

Identification of larger boundary condition space with more symmetries.

Uncovering of angle-dependent Yang-Mills transformations at spatial infinity.

Abstract

In this paper, three things are done. First, we study from an algebraic point of view the infinite-dimensional BMS-like extensions of the Carroll algebra relevant to the asymptotic structure of the electric and magnetic Carrollian limits of Einstein gravity. In the course of this study we exhibit by "Carroll-Galileo duality" a new infinite-dimensional BMS-like extension of the Galilean algebra and of its centrally extended Bargmann algebra. Second, we consider the electric Carrollian limit of the pure Einstein theory and indicate that more flexible boundary conditions than the ones that follow from just taking the limit of the Einsteinian boundary conditions are actually consistent. These boundary conditions lead to a bigger asymptotic symmetry algebra that involves spatial supertranslations depending on three functions of the angles (instead of one). Third, we turn to the Carrollian limit of the coupled Einstein-Yang-Mills system. An infinite-dimensional color enhancement of the gauge algebra is found in the electric Carrollian limit of the Yang-Mills field, which allows angle-dependent Yang-Mills transformations at spatial infinity, not available in the Einstein-Yang-Mills case prior to taking the Carrollian electric limit. This enhancement does not occur in the magnetic limit.