Scale transformations in metric-affine geometry

TL;DR

This paper classifies metric-affine theories based on their scale symmetries, constructing the most general quadratic actions for each case, and discusses potential generalizations to higher derivatives and other geometries.

Contribution

It provides a comprehensive classification of scale transformations in metric-affine theories and constructs the most general quadratic actions including parity-violating terms.

Findings

Classified three types of scale transformations in metric-affine geometry.

Constructed the most general second order quadratic actions for each transformation type.

Results can be extended to higher derivatives and other geometric frameworks.

Abstract

This article presents an exhaustive classification of metric-affine theories according to their scale symmetries. First it is clarified that there are three relevant definitions of a scale transformation. These correspond to a projective transformation of the connection, a rescaling of the orthonormal frame, and a combination of the two. The most general second order quadratic metric-affine action, including the parity-violating terms, is constructed in each of the three cases. The results can be straightforwardly generalised by including higher derivatives, and implemented in the general metric-affine, teleparallel, and symmetric teleparallel geometries.