# Non-Abelian basis tensor gauge theory

## TL;DR

This paper introduces a non-Abelian basis tensor gauge theory, reformulating gauge theories with a vierbein-like approach, and verifies its consistency by computing key quantum corrections that match traditional results.

## Contribution

It develops a nonlinear non-Abelian basis tensor gauge theory formalism and demonstrates its validity through one-loop calculations matching standard gauge theory results.

## Key findings

- Beta function matches known non-Abelian gauge theory results
- Two-point function computed at one-loop level
- Formalism reproduces established quantum corrections

## Abstract

Basis tensor gauge theory is a vierbein analog reformulation of ordinary gauge theories in which the difference of local field degrees of freedom has the interpretation of an object similar to a Wilson line. Here we present a non-Abelian basis tensor gauge theory formalism. Unlike in the Abelian case, the map between the ordinary gauge field and the basis tensor gauge field is nonlinear. To test the formalism, we compute the beta function and the two-point function at the one-loop level in non-Abelian basis tensor gauge theory and show that it reproduces the well-known results from the usual formulation of non-Abelian gauge theory.