Confinement with Kalb - Ramond Fields

TL;DR

This paper studies models with multiple U(1) gauge and Kalb-Ramond fields, demonstrating confinement mechanisms and dualities that relate monopole condensation to the area law in Wilson loops.

Contribution

It introduces solvable large N models with U(1) and Kalb-Ramond fields exhibiting confinement and a novel low energy gauge symmetry.

Findings

Models exhibit confinement with an area law for Wilson loops.

Duality transformation links monopole condensation to confinement.

Large N solutions demonstrate different confinement mechanisms.

Abstract

We consider models with N U(1) gauge fields A_{\mu}^n, N Kalb-Ramond fields B_{\mu \nu}^n, an arbitrary bare action and a fixed UV cutoff \Lambda. Under mild assumptions these can be obtained as effective low energy theories of SU(N+1) Yang Mills theories in the maximal abelian gauge. For a large class of bare actions they can be solved in the large N limit and exhibit confinement. The confining phase is characterized by an approximate ``low energy'' vector gauge symmetry under which the Kalb-Ramond fields B_{\mu\nu}^n transform. The same symmetry allows for a duality transformation showing that magnetic monopoles have condensed. The models allow for various mechanisms of confinement, depending on which sources for A_{\mu}^n or B_{\mu \nu}^n are switched on, but the area law for the Wilson loop is obtained in any case.