Four-dimensional Yang–Mills theory, gauge invariant mass and fluctuating three-branes

Abstract

We are interested in a gauge invariant coupling between four-dimensional Yang–Mills field and a three-brane that can fluctuate 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 spacetime 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 spacetime . The presence of the brane becomes entirely invisible, expect for the mass.