Vacuum instability in the Abelian Higgs model with strings
  Using the effective potential approach for composite operators, we have analytically evaluated the truly nonperturbative vacuum energy density in the Abelian Higgs model of dual QCD ground state. This quantity is defined as integrating out of the truly nonperturbative part of the full gluon propagator over the deep infrared region (soft momentum region). Defined in this way it is manifestly gauge invariant.We have explicitly shown that the corresponding effective potential always has an imaginary part. This means that the vacuum of this model with string contributions is unstable against quantum corrections. 
V. Gogohia, M. Priszny\'ak