Re-dressing Emperor: Four Dimensional Yang-Mills Theory, Gauge Invariant Mass And Fluctuating Three Branes

TL;DR

This paper explores a novel approach to four-dimensional Yang-Mills theory by coupling it with a fluctuating three brane in higher dimensions, resulting in a gauge-invariant massive vector field in four-dimensional space.

Contribution

It introduces a framework where Yang-Mills theory is interpreted as a higher-dimensional gravity theory, incorporating brane dynamics that preserve gauge invariance and generate mass.

Findings

Derivation of a gauge-invariant massive vector field in 4D

Interpretation of Yang-Mills as a higher-dimensional gravity theory

Brane fluctuations induce mass without breaking gauge symmetry

Abstract

We consider the coupling between four dimensional Yang-Mills field and a three brane that fluctuates into higher dimensions. For this we interpret the Yang-Mills theory as a higher dimensional bulk gravity theory with dynamics that is governed by the Einstein action, and with a metric tensor constructed from the gauge field in a manner that displays the original gauge symmetry as an isometry. The brane moves in this higher dimensional space-time under the influence of its bulk gravity, with dynamics determined by the Nambu action. This introduces the desired interaction between the brane and the gauge field in a way that preserves the original gauge invariance as an isometry of the induced metric. After a prudent change of variables the result can be interpreted as a gauge invariant and massive vector field that propagates in the original space-time $\mathbb R^4$: The presence of the brane becomes entirely invisible, except for the mass.