Local symmetries in $f(T)$-like models: lessons from 2D

TL;DR

This paper explores the local symmetries and degrees of freedom in $f(T)$ gravity models using 2D torsional models as a simplified setting to better understand the complex structure and physical implications.

Contribution

It provides a detailed analysis of local symmetries in $f(T)$-like models within a 2D framework, offering insights into symmetry structure and degrees of freedom.

Findings

Characterization of local symmetries in 2D torsional gravity models

Clarification of the role of additional degrees of freedom in $f(T)$ gravity

Insights into symmetry breaking and physical implications in simplified models

Abstract

The comprehension of the intricate structure associated to the local symmetries encoded in the tetrad field, as well as its physical meaning, is perhaps the most important unsolved problem within $f(T)$ gravity. This is inextricably connected to the number, nature and potential impact that the additional degree/s of freedom might have within these --and other closely related--models of gravity in which the local Lorentz invariance is broken at some level. Here we review and further explain some recent results which make use of the more placid scenery provided by 2D-torsional models of gravity, where the local symmetries adapted to a given geometry can be fully characterized.