Gluodynamics in External Field: a Test of the Dual Superconductor Picture ∗,†

We study gluodynamics in an external Abelian electromagnetic field within the dual superconductor approach. We show that the SU (2) gluodynamics should possess a deconfining phase transition at zero temperature at certain value of the external field. A dual superconductor model for the SU (3) gauge theory in external field predicts a rich phase structure containing confinement, asymmetric confinement and deconfinement phases. These results can be used to check the validity of the dual superconductor description of gluodynamics in external fields. We also discuss the gauge–independence of the obtained results. 1. We discuss the properties of the SU (2) and SU (3) gluodynamics in the external electromagnetic field using the dual superconductor approach 1 based on the Abelian monopole condensation. The condensate – observed 2 in various numerical simulations at low temperatures– forces a chromoelec-tric flux coming from (anti-)quarks to squeeze into a confining string. This picture of confinement has been confirmed in various lattice simulations 3. A common feature of known superconductors is that at strong enough magnetic fields the superconductivity is destroyed and the superconductor goes in the normal (metal) state. In the dual superconductor model a similar effect 4 leads to the deconfinement phase transition. Below we study the phase diagram of gluodynamics within the dual superconductor approach. We work in the Bogomol'ny limit 5 supported by lattice simulations 6. 2. Let us first consider the SU (2) gauge theory in the 4D Euclidean space. The infrared properties of the vacuum of this model can be described by the Abelian Higgs (or, Ginzburg–Landau) Lagrangian: