Reformulations of Yang-Mills Theories with Space-time Tensor Fields

TL;DR

This paper reformulates Yang-Mills theories using gauge invariant metric variables in 3D and 4D, analyzing gluon condensates and polarization with new gauge invariant descriptions, revealing non-zero condensates and dual properties.

Contribution

It introduces a novel gauge invariant reformulation of Yang-Mills theories in three and four dimensions, providing new insights into gluon condensates and duality properties.

Findings

Non-zero dimension two gluon condensate in 3D similar to photon mass squared

A dual property Lagrangian in 4D sharing features with dual superconductor models

Discussion on the validity of one-loop approximation in these reformulations

Abstract

We provide the reformulations of Yang-Mills theories in terms of gauge invariant metric-like variables in three and four dimensions. The reformulations are used to analyze the dimension two gluon condensate and give gauge invariant descriptions of gluon polarization. In three dimensions, we obtain a non-zero dimension two gluon condensate by one loop computation, whose value is similar to the square of photon mass in the Schwinger model. In four dimensions, we obtain a Lagrangian with the dual property, which shares the similar but different property with the dual superconductor scenario. We also make discussions on the effectiveness of one loop approximation.