General relativity and its modifications as effective field theories of GL(4) breaking
Abstract
We discuss General Relativity and some of its modifications as effective field theories of the breaking of the affine general linear group using the coset approach and the Maurer-Cartan form. While the ultimate goal is to break the symmetry down to the Lorentz subgroup, we argue that there are three interesting breaking cascades in which the affine general linear group is first broken to a larger subgroup that contains the Lorentz group. In all cases, the breaking of translations always generates Goldstone modes that can be interpreted as metric degrees of freedom. We argue that the effective field theories that emerge as a result of the different breaking patterns are all dynamically equivalent at the lowest order of the derivative expansion, e.g., using Einstein-Hilbert-like actions, but can differ beyond the leading order.
Related
- General Relativity for Mathematicians - Part I
- Solutions for neutron stars in General Relativity from a complexity structure scalar boundary condition
- Towards General Relativity as a generalized Yang-Mills theory
- Linear Stability and a Turning Point Principle for Barotropic Liquid Stars with a Free Boundary in General Relativity
- General Relativity in Three Lines
BibTeX
@misc{viacava2026general,
title = {{General relativity and its modifications as effective field theories of $GL(4)$ breaking}},
author = {Tommaso Viacava and Omar Zanusso},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13323},
eprint = {2610.13323},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13323},
}
RIS
TY - UNPB
TI - General relativity and its modifications as effective field theories of GL(4) breaking
AU - Tommaso Viacava
AU - Omar Zanusso
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13323
UR - https://arxiv.org/abs/2610.13323
AB - We discuss General Relativity and some of its modifications as effective field theories of the breaking of the affine general linear group using the coset approach and the Maurer-Cartan form. While the ultimate goal is to break the symmetry down to the Lorentz subgroup, we argue that there are three interesting breaking cascades in which the affine general linear group is first broken to a larger subgroup that contains the Lorentz group. In all cases, the breaking of translations always generates Goldstone modes that can be interpreted as metric degrees of freedom. We argue that the effective field theories that emerge as a result of the different breaking patterns are all dynamically equivalent at the lowest order of the derivative expansion, e.g., using Einstein-Hilbert-like actions, but can differ beyond the leading order.
ER -