Projective and amplified symmetries in metric-affine theories

TL;DR

This paper introduces a new amplified symmetry in metric-affine theories, extending projective symmetry, and demonstrates its invariance in the Standard Model and a modified gravitational Lagrangian, leading to a theory equivalent to Einstein-Cartan.

Contribution

It defines and proves the invariance of the amplified symmetry in metric-affine theories and extends it to the gravitational sector, unifying matter and gravity symmetries.

Findings

Standard Model Lagrangian is invariant under the amplified symmetry.

Modified gravitational Lagrangian can incorporate the amplified symmetry.

Resulting theory is dynamically equivalent to Einstein-Cartan theory.

Abstract

In this paper we extend the projective symmetry of the full metric-affine Einstein-Hilbert theory to a new symmetry transformation in the space of affine connections called the amplified symmetry. We prove that the Lagrangian of the Standard Model of particle physics is invariant under this new symmetry. We also show that the gravitational Lagrangian can be modified so that the amplified symmetry extends to the gravitational sector and hence to the whole action. The new theory so constructed is shown to be dynamically equivalent to Einstein-Cartan's though genuinely metric-affine.