Reformulation of QCD in the language of general relativity

TL;DR

This paper demonstrates that QCD can be reformulated using variables similar to those in general relativity, linking gauge fields with gravitational concepts through tetrads and metrics.

Contribution

It introduces a novel reformulation of QCD where the Lagrangian resembles the Einstein-Hilbert form, connecting gauge theory with gravity via tetrad and metric constructions.

Findings

QCD Lagrangian can be expressed as a sum of Einstein's Palatini Lagrangian and matter fields.

Tetrad fields and metrics are constructed from initial SU(3) Yang-Mills fields.

The reformulation bridges gauge theories and gravitational frameworks.

Abstract

It is shown that there exists such collection of variables that the standard QCD Lagrangian can be represented as the sum of usual Palatini Lagrangian for Einstein general relativity and the Lagrangian of matter and some other fields where the tetrad fields and the metric are constructed from initial $SU(3)$ Yang - Mills fields.