London's Equation from Abelian Projection

TL;DR

This paper derives an effective London equation within non-Abelian gauge theories using Abelian projection, providing a theoretical link to the Meissner effect in QCD vacuum analogous to superconductivity.

Contribution

It introduces a method to obtain London's equation from non-Abelian gauge theories via Abelian projection, connecting QCD confinement to superconductivity phenomena.

Findings

Effective London equation derived from non-Abelian gauge theory.

Abelian projected gauge field acts as the electromagnetic field.

Non-Abelian components form a gluon condensate modeled by an effective scalar field.

Abstract

Confinement in non-Abelian gauge theories, such as QCD, is often explained using an analogy to type II superconductivity. In this analogy the existence of the ``Meissner'' effect for quarks with respect to the QCD vacuum is an important element. Here we show that using the ideas of Abelian projection it is possible to arrive at an effective London equation from a non-Abelian gauge theory. (London's equation gave a phenomenological description of the Meissner effect prior to the Ginzburg-Landau or BCS theory of superconductors). The Abelian projected gauge field acts as the E&M field in normal superconductivity, while the remaining non-Abelian components form a gluon condensate which is described via an effective scalar field. This effective scalar field plays a role similar to the scalar field in Ginzburg-Landau theory.